➗ 数学工具Math
百分比计算器Percentage Calculator
在线百分比计算：求某数的百分之几、占比多少、涨跌幅百分比。Calculate X% of Y, what percent X is of Y, and percentage change.
进制转换Number Base Converter
在线进制转换：二进制、八进制、十进制、十六进制及任意 2–36 进制互转，支持大数。Convert numbers between binary, octal, decimal, hex and any base 2–36 (big numbers supported).
分数计算器Fraction Calculator
分数加减乘除计算，自动约分，显示带分数和小数结果。Add, subtract, multiply and divide fractions with simplification, mixed numbers and decimals.
一元二次方程求解Quadratic Equation Solver
求解 ax²+bx+c=0，给出实数或复数根、判别式、顶点和对称轴。Solve ax²+bx+c=0 with real or complex roots, discriminant and vertex.
最大公约数/最小公倍数GCD & LCM Calculator
计算多个整数的最大公约数（GCD）和最小公倍数（LCM），支持大数。Find the greatest common divisor and least common multiple of several integers (big numbers OK).
质数判断与分解质因数Prime Checker & Factorization
判断一个数是否为质数，并分解质因数，显示所有因数。Check if a number is prime, factorize it and list all divisors.
质数表生成器Prime Number List Generator
列出指定范围内的所有质数（埃拉托斯特尼筛法），统计个数。List all prime numbers in a range using the Sieve of Eratosthenes.
阶乘计算器Factorial Calculator
计算 n!（支持到 5000!，大数精确结果），显示位数和末尾零个数。Calculate n! exactly (up to 5000!) with digit count and trailing zeros.
排列组合计算器Permutation & Combination Calculator
计算排列数 nPr、组合数 nCr，以及可重复排列和可重复组合。Compute permutations nPr, combinations nCr, and with-repetition variants.
统计计算器（平均数/中位数/标准差）Statistics Calculator (Mean, Median, SD)
输入一组数据，计算平均数、中位数、众数、方差、标准差、四分位数等。Compute mean, median, mode, variance, standard deviation, quartiles and more.
科学计数法转换Scientific Notation Converter
数字与科学计数法、E 记数法、工程计数法互相转换。Convert numbers to scientific, E and engineering notation and back.
罗马数字转换Roman Numeral Converter
阿拉伯数字与罗马数字互相转换（1–3999），自动识别输入。Convert between Arabic numbers and Roman numerals (1–3999), auto-detected.
数字转英文单词Number to Words Converter
把数字转换为英文单词（如 1234 → one thousand two hundred thirty-four），含序数词和支票金额写法。Convert numbers to English words, ordinals and check-writing format.
数字千分位格式化Number Formatter (Thousands Separator)
给数字添加千分位分隔符，按不同国家格式显示，以及万/亿和 K/M/B 缩写。Format numbers with thousands separators, locale styles, and compact forms (K/M/B, 万/亿).
比例计算器Ratio Calculator
解比例方程 A:B = C:X，化简比例，按比例缩放尺寸（如 16:9）。Solve A:B = C:X, simplify ratios and scale dimensions (e.g. 16:9).
勾股定理计算器Pythagorean Theorem Calculator
已知直角三角形任意两边，求第三边（a² + b² = c²），以及面积和角度。Find the missing side of a right triangle (a² + b² = c²), plus area and angles.
三角形计算器Triangle Calculator
已知三条边求三角形面积（海伦公式）、周长、三个角和类型。Find triangle area (Heron's formula), perimeter, angles and type from three sides.
圆计算器Circle Calculator
输入半径、直径、周长或面积中的任意一个，计算圆的其余参数。Enter radius, diameter, circumference or area to get the rest.
体积计算器Volume Calculator
计算立方体、长方体、球体、圆柱、圆锥、棱锥的体积和表面积。Calculate volume and surface area of cube, box, sphere, cylinder, cone and pyramid.
面积计算器Area Calculator
计算矩形、三角形、圆、梯形、椭圆、平行四边形等常见图形面积。Calculate the area of rectangles, triangles, circles, trapezoids, ellipses and parallelograms.
对数计算器Logarithm Calculator
计算任意底数的对数 logₐ(x)，以及自然对数 ln、常用对数 lg 和 log₂。Calculate logarithms in any base, plus ln, log₁₀ and log₂.
幂与开方计算器Exponent & Root Calculator
计算 x 的 y 次方和 x 的 n 次方根，大整数幂精确计算。Compute x to the power y and the nth root of x (exact big-integer powers).
四舍五入计算器Rounding Calculator
按小数位或有效数字四舍五入，支持银行家舍入（四舍六入五成双）、向上、向下取整。Round numbers by decimals or significant figures: half-up, half-even (banker's), ceil, floor, truncate.
加权平均数计算器Weighted Average Calculator
输入数值和权重，计算加权平均数，可用于计算学分绩点和综合评分。Calculate a weighted average from values and weights (grades, scores, portfolios).
矩阵计算器Matrix Calculator
计算方阵的行列式、逆矩阵、转置和秩（最大 6×6）。Compute determinant, inverse, transpose and rank of a square matrix (up to 6×6).
斐波那契数列计算器Fibonacci Calculator
计算第 n 个斐波那契数（大数精确），并列出前 n 项数列。Get the nth Fibonacci number (exact big integers) and list the sequence.
小数转分数Decimal to Fraction Converter
把小数精确转换为最简分数（有限小数按 10ⁿ 约分），也可用近似模式把循环小数/无理数近似为分数，支持百分数。Convert decimals to exact simplest fractions (finite decimals via 10ⁿ), or approximate repeating decimals with a max denominator.
线性方程组求解System of Linear Equations Solver
求解一元到六元一次方程组（高斯消元），每行输入一个方程的系数。Solve 1×1 up to 6×6 systems of linear equations (Gaussian elimination).
二进制/十六进制计算器Binary & Hex Calculator
在二进制、八进制、十六进制下做加减乘除和位运算（AND、OR、XOR、移位）。Arithmetic and bitwise operations (AND, OR, XOR, shifts) in binary, octal or hex.
Z 分数计算器Z-Score Calculator
根据数值、平均值和标准差计算 Z 分数，以及对应的百分位和左右尾概率。Z-score from value, mean and standard deviation, with percentile and tail probabilities.
二项分布概率计算器Binomial Probability Calculator
计算 n 次独立试验中恰好、至多、至少成功 k 次的概率，以及期望和方差。Probability of exactly, at most and at least k successes in n trials, plus mean and variance.
正态分布计算器Normal Distribution Calculator
计算正态分布在区间 [a, b] 内的概率、累积概率，以及给定概率对应的分位数。Probability between a and b for a normal distribution, cumulative probabilities and inverse (quantile).
置信区间计算器Confidence Interval Calculator
根据样本均值、标准差和样本量计算均值的置信区间（使用 t 分布）。Confidence interval for a mean from sample mean, standard deviation and size (Student's t-distribution).
样本量计算器Sample Size Calculator
计算调查所需样本量：置信水平、误差范围、预期比例和总体规模（有限总体修正）。Survey sample size from confidence level, margin of error, expected proportion and population size.
线性回归计算器Linear Regression Calculator
输入 x、y 数据对，计算最小二乘回归直线 y = a + bx、相关系数 r 和决定系数 R²，可做预测。Least-squares regression line y = a + bx, correlation r and R² from x/y pairs, with prediction.
有效数字计算器Significant Figures Calculator
统计一个数的有效数字位数，并按指定有效数字位数进行四舍五入（含科学计数法）。Count significant figures in a number and round it to a chosen number of sig figs.
竖式除法计算器（带步骤）Long Division Calculator (with steps)
整数长除法，显示商、余数和每一步竖式计算过程，适合小学生学习。Integer long division showing quotient, remainder and every step — great for learning.
取模/取余计算器Modulo Calculator
计算 a mod n 的三种定义：向下取整（floor，结果与 n 同号，Python 的 %）、截断（truncated，结果与 a 同号，JS/C/Java 的 %）和欧几里得（结果总是非负），并给出对应的商，支持大整数。a mod n under three definitions — floored (sign of n, Python %), truncated (sign of a, JS/C/Java %) and Euclidean (always non-negative) — each with its matching quotient; BigInt supported.
大数计算器Big Number Calculator
任意精度整数计算：加、减、乘、除、取余、乘方、阶乘，结果不丢失精度（BigInt）。Arbitrary-precision integer arithmetic: + − × ÷ mod, power and factorial without losing digits (BigInt).
两点距离/中点/斜率计算器Distance, Midpoint & Slope Calculator
输入平面上两点坐标，计算距离、中点、斜率、倾斜角和直线方程。Distance, midpoint, slope, angle and line equation between two points.
百分比误差计算器Percent Error Calculator
计算测量值与真实值之间的绝对误差、相对误差和百分比误差。Absolute, relative and percent error between a measured and a true value.
数字性质查询Number Properties Checker
查看一个整数的各种性质：奇偶、质数、完全数、平方数、因数个数、数字和、二进制等。See an integer's properties: parity, prime, perfect, square, divisors, digit sum, binary and more.
乘法表生成器（九九乘法表）Multiplication Table Generator
生成九九乘法表或任意范围的乘法表，可打印，适合小学生练习。Generate a 9×9 or any-size multiplication table, printable for kids.
等差/等比数列求和Arithmetic & Geometric Series Calculator
计算等差数列和等比数列的第 n 项与前 n 项和，以及无穷等比级数的和。nth term and sum of the first n terms of arithmetic and geometric series, plus infinite geometric sums.
复数计算器Complex Number Calculator
复数加减乘除、模、辐角、共轭和极坐标形式，输入格式如 3+4i。Add, subtract, multiply and divide complex numbers; modulus, argument, conjugate and polar form.
向量计算器Vector Calculator
二维/三维向量的加减、点积、叉积、模长和夹角计算，输入如 1,2,3。2D/3D vectors: sum, difference, dot product, cross product, magnitude and angle. Input like 1,2,3.
百分位数计算器Percentile Calculator
计算数据集的任意百分位数、四分位数（Q1/Q2/Q3）和四分位距，或求某个值的百分位排名。Any percentile, quartiles (Q1/Q2/Q3) and IQR of a data set, or the percentile rank of a value.
黄金比例计算器Golden Ratio Calculator
按黄金比例 φ ≈ 1.618 计算长边、短边和总长，常用于设计排版和摄影构图。Split or extend a length by the golden ratio φ ≈ 1.618 — handy for design and layout.
三角函数计算器Trigonometry Calculator
计算角度（度/弧度）的 sin、cos、tan、cot、sec、csc，或由函数值反求角度（arcsin、arccos、arctan、arccot）。sin, cos, tan, cot, sec and csc of an angle in degrees or radians, or inverse functions (arcsin, arccos, arctan, arccot) from a value.
直角三角形计算器Right Triangle Calculator
输入直角三角形任意两个量（两边或一边一角），求其余边、角、面积、周长和斜边上的高。Enter any two values of a right triangle (two sides, or a side and an angle) to get the other sides, angles, area, perimeter and altitude.
等差数列计算器Arithmetic Sequence Calculator
输入首项、公差和项数，求第 n 项、前 n 项和，并列出数列各项。Find the nth term and the sum of the first n terms of an arithmetic sequence and list its terms.
等比数列生成器Geometric Sequence Generator
输入首项、公比和项数，生成等比数列，并计算第 n 项、前 n 项和与无穷级数和（|r|<1 时）。Generate a geometric sequence from the first term, ratio and count, with the nth term, partial sum and infinite sum (when |r| < 1).
圆柱体积计算器Cylinder Volume Calculator
由半径（或直径）和高计算圆柱体积、侧面积、表面积，并换算为升和加仑。Cylinder volume, lateral and total surface area from radius (or diameter) and height, with liters and gallons.
扇形面积计算器Sector Area Calculator
由半径和圆心角（度或弧度）计算扇形面积、弧长、弦长、扇形周长和弓形面积。Sector area, arc length, chord, perimeter and segment area from radius and central angle (degrees or radians).
绝对值计算器Absolute Value Calculator
求一组数的绝对值（任意长度小数按原文精确处理），或计算两数之差的绝对值（数轴距离）。Absolute value of a list of numbers (exact for any length), or the distance |a − b| between two numbers.
小数计算器Decimal Calculator
精确的小数加减乘除，不会出现 0.1+0.2=0.30000000000000004 这样的浮点误差；除法可指定保留位数。Exact decimal add, subtract, multiply and divide with no floating-point errors like 0.1 + 0.2 = 0.30000000000000004; set the precision for division.
球体计算器Sphere Calculator
输入半径、直径、表面积或体积中的任意一个，求球的其余参数（含体积换算为升）。Enter a sphere's radius, diameter, surface area or volume to get all the others (with volume in liters).
圆锥体积计算器Cone Volume Calculator
由底面半径和高计算圆锥体积、母线长、侧面积和表面积，也可计算圆台（截头圆锥）。Cone volume, slant height, lateral and total surface area from radius and height; also handles a frustum.
因数计算器Factor Calculator
列出一个整数的全部因数、因数对、因数个数与和，并给出质因数分解。List all factors and factor pairs of a whole number, count and sum them, and show its prime factorization.
数字各位和计算Digit Sum Calculator
计算任意长度整数各位数字之和、数字根（反复求和至一位）、交错和，并判断能否被 3、9、11 整除。Digit sum of any length number, its digital root (repeated sum), alternating sum, and divisibility by 3, 9 and 11.
等值分数计算器Equivalent Fractions Calculator
把分数化为最简分数并列出一组等值分数，或判断两个分数是否相等（交叉相乘）。Simplify a fraction, list its equivalent fractions, or check whether two fractions are equal by cross-multiplying.
带分数计算器Mixed Number Calculator
带分数、分数和小数的加减乘除（如 1 1/2 + 2 3/4），结果给出带分数、假分数和小数，精确无误差。Add, subtract, multiply and divide mixed numbers, fractions and decimals (e.g. 1 1/2 + 2 3/4); exact results as a mixed number, improper fraction and decimal.
储罐容积计算器Tank Volume Calculator
计算立式/卧式圆柱罐、长方体罐的总容积和按液位高度的已装容积（升、立方米、美制加仑）。Total and filled volume of vertical or horizontal cylindrical tanks and rectangular tanks from the liquid level, in liters, m³ and US gallons.
向量点积计算器Dot Product Calculator
计算任意维度两个向量的点积（数量积）、模长、夹角以及 a 在 b 上的投影。Dot product of two vectors of any dimension, with magnitudes, the angle between them and the projection of a onto b.
平方和计算器Sum of Squares Calculator
计算一组数的平方和 Σx²、离均差平方和 Σ(x−x̄)²（统计学 SS），以及 1² + 2² + … + n² 公式和。Sum of squares Σx², the deviation sum of squares Σ(x − x̄)² used in statistics, and 1² + 2² + … + n².
分数比较大小Comparing Fractions Calculator
比较两个或多个分数（含带分数、小数）的大小，给出通分过程并从小到大排序。Compare two or more fractions, mixed numbers or decimals, show them over a common denominator and sort them.
综合除法计算器Synthetic Division Calculator
用综合除法把多项式除以 (x − r)，给出商式、余数和完整的综合除法表（余数定理）。Divide a polynomial by (x − r) with synthetic division: quotient, remainder and the full working table (remainder theorem).
椭圆计算器Ellipse Calculator
由长半轴和短半轴计算椭圆面积、周长（AGM 精确算法）、离心率、焦距和半通径。Area, perimeter (exact AGM method), eccentricity, focal distance and semi-latus rectum of an ellipse from its semi-axes.
指数增长计算器Exponential Growth Calculator
按增长率计算指数增长（或衰减）后的数值，支持离散复合和连续增长，并给出翻倍（或减半）时间。Value after exponential growth or decay at a given rate, discrete or continuous, with doubling (or halving) time.
矩形计算器Rectangle Calculator
由长和宽计算矩形面积、周长、对角线和对角线夹角；也可由面积/周长加一条边反求。Area, perimeter, diagonal and diagonal angle of a rectangle from length and width, or solve from area/perimeter and one side.
周长计算器Perimeter Calculator
计算正方形、矩形、三角形、圆、椭圆、梯形、平行四边形和正多边形的周长。Perimeter of squares, rectangles, triangles, circles, ellipses, trapezoids, parallelograms and regular polygons.
概率计算器Probability Calculator
输入两个独立事件 A、B 的概率，计算交集、并集、互斥或、都不发生和补集概率；也可计算 n 次重复中至少发生一次的概率。For two independent events A and B: P(A∩B), P(A∪B), exactly one, neither and complements; plus the chance of at least one success in n repeated trials.
P值计算器P-Value Calculator
由 z 值、t 值（自由度）、卡方值或 F 值计算单尾/双尾 P 值，并与显著性水平 α 比较。P-value from a z-score, t-score (with df), chi-square or F statistic, one- or two-tailed, compared with a significance level α.
标准误计算器Standard Error Calculator
由样本数据或标准差与样本量计算均值标准误 SE = s/√n，并给出 95% 置信区间。Standard error of the mean SE = s/√n from raw data or from SD and sample size, with a 95% confidence interval.
导数计算器Derivative Calculator
求函数的导数：支持多项式、三角、指数、对数和复合函数，可求 1–5 阶导数并代入某点求导数值，结果自动化简并给出 LaTeX。Differentiate functions — polynomials, trig, exponential, logarithmic and composite — up to the 5th derivative, evaluate at a point, with simplified results and LaTeX.
积分计算器Integral Calculator
计算不定积分（原函数）和定积分：支持多项式、三角、指数、对数、有理函数等，定积分给出数值结果，找不到初等原函数时会明确提示。Compute indefinite integrals (antiderivatives) and definite integrals for polynomials, trig, exponential, logarithmic and rational functions; definite integrals give a numeric value, and it tells you clearly when no elementary antiderivative is found.
代数计算器Algebra Calculator
代数式化简、展开、因式分解，解方程（一元多项式方程，含复数根），以及代入数值求值，结果给出精确形式和 LaTeX。Simplify, expand and factor algebraic expressions, solve equations (single-variable polynomial equations, complex roots included) and evaluate with a value substituted — exact results with LaTeX.
公因数计算器Common Factor Calculator
输入两个或多个整数，列出它们的全部公因数，并给出最大公因数（GCF）和各数的因数个数。List every common factor of two or more whole numbers, with the greatest common factor (GCF) and how many factors each number has.
分数转小数计算器（含循环小数）Fraction to Decimal Calculator (with Repeating Decimals)
把分数或带分数（如 3/8、1 2/7、−5/6）转换为小数，自动识别循环节并用括号标出，例如 1/7 = 0.(142857)，同时给出四舍五入的近似值。Convert a fraction or mixed number such as 3/8, 1 2/7 or −5/6 to a decimal, detecting the repeating block and showing it in brackets — 1/7 = 0.(142857) — plus a rounded value.
分数转百分数计算器Fraction to Percentage Calculator
把分数、带分数或小数转换为百分数，给出精确值（必要时显示循环节）和按指定小数位四舍五入的结果，例如 3/8 = 37.5%，1/3 = 33.(3)%。Turn a fraction, mixed number or decimal into a percentage — exact (with the repeating block if any) and rounded to your chosen decimal places, e.g. 3/8 = 37.5%, 1/3 = 33.(3)%.
百分比差异计算器Percentage Difference Calculator
计算两个数之间的百分比差异：|A − B| ÷ ((A + B) ÷ 2) × 100%，并分别给出从 A 到 B、从 B 到 A 的百分比变化，避免混淆两者。Find the percentage difference between two values, |A − B| ÷ ((A + B) ÷ 2) × 100%, alongside the percentage change from A to B and from B to A so the two are not confused.
赔率换算计算器Odds Calculator
在小数赔率、分数赔率、美式赔率和隐含概率之间互相换算，并按下注金额计算可赢金额和总回报。Convert between decimal, fractional and American (moneyline) odds and implied probability, and work out the profit and total return for a stake.
中程数计算器Midrange Calculator
输入一组数据，计算中程数（最大值与最小值的平均数）、极差，并与平均数、中位数对比。Find the midrange — the average of the largest and smallest values — of a data set, with the range, mean and median for comparison.
期望值计算器Expected Value Calculator
输入离散随机变量的取值和对应概率，计算期望值 E(X)、方差和标准差；概率可填小数、百分数或分数，并检查概率之和是否为 1。Compute the expected value E(X), variance and standard deviation of a discrete random variable from its outcomes and probabilities — given as decimals, percentages or fractions — and check that they add up to 1.
单位比率计算器Unit Rate Calculator
把“多少 A 对应多少 B”化为单位比率（每 1 个 B 对应多少 A），例如 300 公里 / 4 小时 = 75 公里/小时；也可同时比较两个比率的高低（单价越低越划算，每元能买到的数量越高越划算）。Turn a rate like "A per B" into a unit rate — the amount for one unit of B — e.g. 300 km in 4 hours = 75 km per hour, and optionally compare a second rate to see which is the better deal.
点斜式方程计算器Point-Slope Form Calculator
由两点或一点加斜率求直线的点斜式方程 y − y₁ = m(x − x₁)，并同时给出斜截式和一般式（标准式），斜率尽量以分数显示。Get the point-slope equation y − y₁ = m(x − x₁) of a line from two points or a point and the slope, with the slope-intercept and standard forms too; slopes are shown as fractions where possible.
斜截式方程计算器Slope-Intercept Form Calculator
由两点或一点加斜率求直线的斜截式 y = mx + b，给出斜率、y 截距、x 截距和一般式，分数系数会尽量保持精确。Find the slope-intercept equation y = mx + b from two points or a point and the slope, with the slope, y-intercept, x-intercept and standard form, keeping fractions exact where possible.
相对风险（RR）计算器Relative Risk Calculator
根据 2×2 列联表（暴露组/对照组 × 发生/未发生）计算相对风险 RR 及 95% 置信区间、绝对风险差、需治疗人数 NNT 和比值比 OR。Calculate relative risk (risk ratio) with a 95% confidence interval from a 2×2 table — exposed/control × event/no event — plus the absolute risk difference, number needed to treat (NNT) and odds ratio.
卡方检验计算器（列联表独立性）Chi-Square Test Calculator (Contingency Table)
输入任意 r×c 列联表的观察频数，计算 Pearson 卡方统计量、自由度、P 值和期望频数，判断两个分类变量是否独立；2×2 表可选 Yates 连续性校正。Run a Pearson chi-square test of independence on any r × c table of observed counts: get χ², degrees of freedom, the p-value and the expected counts, with an optional Yates correction for 2 × 2 tables.
单因素方差分析（ANOVA）计算器One-Way ANOVA Calculator
每行输入一组数据，计算单因素方差分析表：组间/组内平方和、自由度、均方、F 值、P 值和 η²，并给出各组均值与标准差。Run a one-way ANOVA with one group per line: get the full table — between/within sums of squares, degrees of freedom, mean squares, F, the p-value and η² — plus each group's mean and standard deviation.
异常值计算器（IQR 法）Outlier Calculator (IQR Method)
用四分位距（IQR）法找出数据中的异常值：计算 Q1、Q3、IQR 和 Tukey 内篱笆（1.5×IQR）与外篱笆（3×IQR），标出温和异常值和极端异常值。Find outliers with the interquartile-range method: get Q1, Q3, the IQR and Tukey's inner (1.5 × IQR) and outer (3 × IQR) fences, and flag mild and extreme outliers.
平均变化率计算器Average Rate of Change Calculator
求函数 f(x) 在区间 [a, b] 上的平均变化率 (f(b) − f(a)) ÷ (b − a)，即割线斜率；可输入函数表达式，也可直接输入两点的函数值。Find the average rate of change of f(x) over [a, b] — (f(b) − f(a)) ÷ (b − a), the slope of the secant line — from a function expression or directly from two function values.
配方法计算器Completing the Square Calculator
把二次式 ax² + bx + c 配方为顶点式 a(x − h)² + k，列出配方步骤，并给出顶点、对称轴和方程 ax² + bx + c = 0 的解（含复数根）。Rewrite ax² + bx + c in vertex form a(x − h)² + k by completing the square, with the steps, the vertex, the axis of symmetry and the solutions of ax² + bx + c = 0, including complex roots.
离散卷积计算器Convolution Calculator
计算两个有限序列的离散线性卷积 (x * h)[n] = Σ x[k]·h[n − k]，也可选择循环卷积；给出结果序列、长度和逐项计算明细，等同于多项式乘法的系数。Compute the discrete linear convolution (x * h)[n] = Σ x[k]·h[n − k] of two finite sequences, or circular convolution, with the result, its length and a term-by-term breakdown — the same as multiplying polynomial coefficients.
翻倍时间计算器Doubling Time Calculator
按每期增长率计算数量翻倍所需时间 ln 2 ÷ ln(1 + r)，并与“72 法则”和“70 法则”估算比较；也可由起始值、结束值和经过时间反推增长率和翻倍时间。Find how long it takes something to double at a growth rate per period — ln 2 ÷ ln(1 + r) — compared with the Rule of 72 and Rule of 70, or work back from a start value, end value and elapsed time.
等边三角形计算器Equilateral Triangle Calculator
已知等边三角形的边长、高、面积、周长、内切圆或外接圆半径中的任意一个，求出其余所有量。Give any one of an equilateral triangle's side, height, area, perimeter, inradius or circumradius and get all the others.
余弦定理计算器Law of Cosines Calculator
用余弦定理 c² = a² + b² − 2ab·cos C 解三角形：已知两边及夹角（SAS）求第三边和其余角，或已知三边（SSS）求三个角，同时给出面积和周长。Solve a triangle with the law of cosines, c² = a² + b² − 2ab·cos C: from two sides and the included angle (SAS) find the third side and the other angles, or from three sides (SSS) find all three angles, plus area and perimeter.
正弦定理计算器Law of Sines Calculator
用正弦定理 a/sin A = b/sin B = c/sin C 解三角形：支持两角一边（ASA/AAS）和两边一对角（SSA），SSA 的模糊情形会列出两个解或说明无解。Solve a triangle with the law of sines, a/sin A = b/sin B = c/sin C, for two angles and a side (ASA/AAS) or two sides and a non-included angle (SSA) — including the ambiguous case with two solutions or none.
正方体计算器Cube Calculator
已知正方体的棱长、体积、表面积、面对角线或体对角线中的任意一个，求出其余所有量。Give any one of a cube's edge, volume, surface area, face diagonal or space diagonal and get the rest.
正多边形计算器Regular Polygon Calculator
输入正多边形的边数和边长、外接圆半径、内切圆半径（边心距）或面积中的任意一个，求出面积、周长、内角、外角、对角线数量等。Enter the number of sides and any one of the side length, circumradius, inradius (apothem) or area of a regular polygon to get its area, perimeter, interior and exterior angles, diagonals and more.
梯形计算器Trapezoid Calculator
输入梯形的上底、下底和高求面积和中位线；再填两条腰长可求周长和四个内角，也可以选择由面积反求高。Find a trapezoid's area and midsegment from its two bases and height; add the two legs to get the perimeter and all four angles, or work back from the area to the height.
竖式乘法计算器（列竖式）Long Multiplication Calculator
用竖式（列竖式）计算两个整数或小数相乘，逐行显示每一位的部分积和最终结果，支持任意长度的大数，适合学生检查作业步骤。Multiply two whole numbers or decimals by long multiplication, showing each partial product row and the final answer, with no limit on length — handy for checking homework steps.
矩阵乘法计算器Matrix Multiplication Calculator
输入两个矩阵（每行一行，元素用空格或逗号分隔），计算矩阵乘积 A × B，检查维数是否匹配，并可显示每个元素的计算过程。Multiply two matrices — one row per line, entries separated by spaces or commas — to get A × B, with a dimension check and the working for each entry.
求和（Σ）计算器Summation Calculator (Sigma Notation)
计算 Σ 求和：输入通项表达式（变量 n）和上下限，算出总和，并列出前几项；可识别等差、等比数列求和，适合检查级数作业。Evaluate a sigma-notation sum: enter the general term in n and the lower and upper limits to get the total and the first terms — handy for checking series homework.
三重积分计算器（数值）Triple Integral Calculator (Numerical)
数值计算三重积分 ∭ f(x, y, z) dz dy dx：x 的上下限为常数，y 的上下限可以是 x 的函数，z 的上下限可以是 x、y 的函数，使用高斯-勒让德求积，适合计算体积、质量和重心。Evaluate a triple integral ∭ f(x, y, z) dz dy dx numerically: constant x limits, y limits that may depend on x, and z limits that may depend on x and y, using Gauss–Legendre quadrature — useful for volumes, masses and centroids.
真值表生成器Truth Table Calculator
输入逻辑表达式（如 (A ∧ B) → ¬C、A xor B、p -> q），自动生成完整真值表，判断是否为重言式、矛盾式或可满足式，并给出最小项和主析取范式。Enter a logical expression such as (A ∧ B) → ¬C, A xor B or p -> q to get its full truth table, whether it is a tautology, contradiction or contingency, and its minterms and canonical DNF.
不等式求解器（一次、二次、绝对值，区间表示）Inequality Solver (Linear, Quadratic, Absolute Value, Interval Notation)
求解三类不等式并用区间表示解集：一次不等式 ax + b ? c（系数为负时自动变号）、二次不等式 ax² + bx + c ? 0（按根和开口方向判断），以及绝对值不等式 |ax + b| ? c。同时给出解题步骤。本地处理。Solve three kinds of inequality and write the answer in interval notation: linear ax + b ? c (flipping the sign for a negative coefficient), quadratic ax² + bx + c ? 0 (using the roots and the direction of the parabola) and absolute value |ax + b| ? c, with the steps shown. Processed locally.
四分位距计算器（三种方法、五数概括、离群值）Interquartile Range Calculator (Three Methods, Five-Number Summary, Outliers)
输入一组数据，求 Q1、Q3 和四分位距 IQR，可选三种常用算法（线性插值包含端点，同 Excel QUARTILE.INC；不含端点，同 QUARTILE.EXC；Tukey 中位数分半法）。同时给出五数概括、1.5 × IQR 离群值界限和找到的离群值。本地处理。Enter a data set to get Q1, Q3 and the interquartile range with one of three common methods (inclusive interpolation as in Excel QUARTILE.INC, exclusive as in QUARTILE.EXC, or Tukey median of halves), plus the five-number summary, the 1.5 × IQR outlier fences and any outliers found. Processed locally.
向量线性无关判定器（任意个数和维数，含秩与相关关系）Linear Independence Calculator (Any Number and Size of Vectors, with Rank and Dependency)
每行输入一个向量（分量用逗号或空格分隔，最多 8 个向量、8 维），用高斯消元求矩阵的秩，判断这些向量是否线性无关；如果线性相关，给出一组使线性组合为零向量的系数。二维情形同时显示行列式。本地处理。Enter one vector per line (components separated by commas or spaces, up to 8 vectors of up to 8 components) to get the rank by Gaussian elimination and decide whether the vectors are linearly independent; if they are dependent, a set of coefficients that combines them to the zero vector is given. For two 2D vectors the determinant is shown too. Processed locally.
带分数与假分数互化（含约分和步骤）Mixed Numbers to Improper Fractions (and Back, with Steps)
把带分数（如 2 3/4，可为负数）化成假分数并约分，显示“整数 × 分母 + 分子”的计算步骤和小数值；也可以把假分数（如 11/4）化回带分数。可以直接输入“2 3/4”，也可以分别填写整数、分子和分母。本地处理。Turn a mixed number (such as 2 3/4, negatives allowed) into a simplified improper fraction with the whole × denominator + numerator steps and the decimal value, or turn an improper fraction (such as 11/4) back into a mixed number. Type 2 3/4 directly or fill in the whole number, numerator and denominator. Processed locally.
多项式乘法计算器（任意多项式展开合并）Multiplying Polynomials Calculator (Expand and Combine Any Polynomials)
输入两个多项式（如 2x + 3、x^2 − 4x + 1，可用任意一个字母作变量），按分配律逐项相乘并合并同类项，给出展开结果、次数、系数列表、逐项相乘的过程，以及代入 x 值后的结果。本地处理。Enter two polynomials (such as 2x + 3 and x^2 − 4x + 1, using any single letter as the variable) to multiply every term by every term and combine like terms, with the expanded result, its degree, the coefficient list, the term-by-term products and the value at a chosen x. Processed locally.
三角形垂心计算器（含外心、重心、内心和欧拉线）Orthocenter Calculator (with Circumcentre, Centroid, Incentre and Euler Line)
输入三角形三个顶点的坐标，求垂心（三条高的交点），并同时给出重心、外心、内心、三边长、三个角、面积和三角形类型（锐角、直角、钝角）。还会检验垂心、重心、外心是否在同一条欧拉线上。本地处理。Enter the coordinates of a triangle three vertices to get the orthocentre (where the altitudes meet), along with the centroid, circumcentre, incentre, side lengths, angles, area and type (acute, right or obtuse). It also checks that the orthocentre, centroid and circumcentre lie on the Euler line. Processed locally.
完全平方三项式计算器（展开、判断、因式分解、配方）Perfect Square Trinomial Calculator (Expand, Test, Factor, Complete the Square)
三种用法：把 (ax ± b)² 展开成 a²x² ± 2abx + b²；判断 Ax² + Bx + C 是否为完全平方三项式（B² = 4AC）并分解成 (√A·x ± √C)²；或对任意二次式配方，写成 A(x + h)² + k 的形式。本地处理。Three uses: expand (ax ± b)² into a²x² ± 2abx + b²; test whether Ax² + Bx + C is a perfect square trinomial (B² = 4AC) and factor it as (√A·x ± √C)²; or complete the square on any quadratic to write it as A(x + h)² + k. Processed locally.
正多边形计算器（已知任意一个量求全部）Regular Polygon Calculator (Any One Measurement Gives the Rest)
输入边数和任意一个已知量（边长、外接圆半径、内切圆半径/边心距、周长或面积），求正多边形的其余所有量：边长、周长、面积、外接圆半径、边心距、内角、外角、中心角和对角线条数。本地处理。Enter the number of sides and any one known measurement (side, circumradius, inradius or apothem, perimeter or area) to get every other property of the regular polygon: side, perimeter, area, circumradius, apothem, interior, exterior and central angles, and the number of diagonals. Processed locally.
幂集计算器（大小、列出所有子集、按元素个数统计）Power Set Calculator (Size, List Every Subset, Count by Size)
输入集合元素（如 a, b, c）或只输入元素个数 n，求幂集的大小 2ⁿ（大整数精确值），按子集大小列出组合数 C(n, k)，元素不超过 10 个时列出全部子集。重复元素会自动去重。本地处理。Enter the elements of a set (such as a, b, c) or just the number of elements n to get the size of the power set 2ⁿ exactly with big integers, the number of subsets of each size C(n, k), and, for up to 10 elements, every subset listed. Duplicate elements are removed. Processed locally.
和与积计算器（数列求和求积 / 已知和与积求两数）Product and Sum Calculator (Sum and Product of a List, or Two Numbers from Sum and Product)
两种用法：对一列数字求和、求积（整数用大整数精确计算），并给出个数、平均值、平方和、最大值和最小值；或者已知两个数的和 S 与积 P，解方程 x² − Sx + P = 0 求出这两个数（因式分解常用的“和积法”）。本地处理。Two uses: the sum and product of a list of numbers (exact with big integers for whole numbers) with the count, mean, sum of squares, largest and smallest; or, from the sum S and product P of two numbers, solve x² − Sx + P = 0 to find them (the sum-product method used in factoring). Processed locally.
有理式计算器（求值、化简、渐近线、定义域）Rational Expression Calculator (Evaluate, Simplify, Asymptotes, Domain)
两种输入：线性分式 (ax + b)/(cx + d)，或者用系数列表输入任意多项式分子和分母。求在 x 处的值，用多项式最大公因式约分化简，列出使分母为 0 的排除值、零点、竖直渐近线、水平或斜渐近线以及“洞”（可去间断点）。本地处理。Two inputs: a linear fraction (ax + b)/(cx + d), or any polynomial numerator and denominator entered as coefficient lists. Evaluates at x, simplifies by cancelling the polynomial GCD, and lists excluded values, zeros, vertical asymptotes, the horizontal or slant asymptote, and holes (removable discontinuities). Processed locally.
有理根计算器（候选根 + 逐一检验 + 分解）Rational Zeros Calculator (Candidates, Testing and Factoring)
按有理根定理列出所有可能的有理根 ±p/q（p 是常数项的因数，q 是首项系数的因数）。如果输入完整的整数系数多项式，还会逐一代入检验，用综合除法找出真正的有理根（含重根），并给出剩余因式。本地处理。Lists every possible rational zero ±p/q from the Rational Root Theorem (p divides the constant term, q divides the leading coefficient). Enter the full integer-coefficient polynomial to test each candidate, find the actual rational zeros with synthetic division (including repeated ones), and see the remaining factor. Processed locally.
原始分计算器（由 z 分数、百分位或 T 分数反推）Raw Score Calculator (From a z-Score, Percentile or T-Score)
由 z 分数、百分位数或 T 分数加上均值和标准差，反推原始分 x = μ + z·σ；也可以反过来由原始分求 z 分数、T 分数和百分位（正态分布）。本地处理。Finds the raw score x = μ + z·σ from a z-score, a percentile or a T-score together with the mean and standard deviation, or goes the other way from a raw score to its z-score, T-score and percentile under a normal distribution. Processed locally.
倒数计算器（小数、分数、带分数）Reciprocal Calculator (Decimals, Fractions, Mixed Numbers)
求任意数的倒数 1/x。可以输入小数，也可以输入分数（3/4）或带分数（2 1/3），结果给出最简分数和小数形式，并验证 x × 1/x = 1。本地处理。Finds the reciprocal 1/x of any number. Enter a decimal, a fraction (3/4) or a mixed number (2 1/3) and get the result as a simplified fraction and a decimal, with the check x × 1/x = 1. Processed locally.
参考角计算器（度、弧度、象限、同终边角）Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles)
把任意角（可为负数或大于 360°）化到 0–90° 的参考角，支持度、弧度和 π 弧度输入。同时给出 0–360° 内的同终边角、所在象限或坐标轴，以及 sin、cos、tan 在该象限的符号。本地处理。Reduces any angle (negative or above 360°) to its reference angle between 0 and 90°, with degrees, radians or multiples of π as input. Also gives the coterminal angle in 0–360°, the quadrant or axis, and the signs of sin, cos and tan there. Processed locally.
黎曼和计算器（左/右/中点/梯形，任意函数）Riemann Sum Calculator (Left, Right, Midpoint, Trapezoid for Any Function)
输入函数 f(x)（如 x^2、sin(x)、exp(-x)），区间 [a, b] 和分割数 n，计算左端点、右端点、中点黎曼和以及梯形法则的近似值，并与辛普森法的高精度积分对比误差，列出每个子区间的取样点。也保留常数函数模式。本地处理。Enter a function f(x) (such as x^2, sin(x) or exp(-x)), an interval [a, b] and the number of subintervals n to get the left, right and midpoint Riemann sums and the trapezoid rule, compared against a high-accuracy Simpson integral, with the sample points listed for each subinterval. The constant-function mode is kept. Processed locally.
SAS 三角形计算器（两边夹角求全部）SAS Triangle Calculator (Two Sides and the Included Angle)
已知两边 a、b 及其夹角 C，用余弦定理求第三边 c，用正弦/余弦定理求另外两个角 A、B，并给出面积、周长、三条高、外接圆和内切圆半径，以及三角形类型（锐角/直角/钝角）。本地处理。Given two sides a and b and the included angle C, finds the third side c by the law of cosines and the other angles A and B, plus the area, perimeter, all three heights, circumradius, inradius and the triangle type (acute, right or obtuse). Processed locally.
学期成绩计算器（加权平均、百分比权重、期末需考多少分）Semester Grade Calculator (Weighted Average, Percentage Weights, Final Exam Needed)
两种用法：输入各项成绩和权重（可以是学分、次数或百分比）求加权平均分并换算等级；或者输入目前的学期成绩、期末考试所占比例和目标总评，算出期末考试至少需要考多少分。本地处理。Two uses: enter each grade with its weight (credits, counts or percentages) for the weighted average and letter grade; or enter your current grade, the weight of the final exam and the grade you want, to see the minimum score you need on the final. Processed locally.
相似三角形计算器（比例因子、求未知边、面积比）Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio)
已知一对对应边 a 和 a′，求比例因子 k = a′/a，再求另一条边的对应边；或输入两个三角形的三条边，检验是否相似（SSS），并给出比例因子、周长比和面积比（k²）。本地处理。From one pair of corresponding sides a and a′ get the scale factor k = a′/a and the matching side for another side; or enter all three sides of both triangles to test similarity (SSS) and get the scale factor, perimeter ratio and area ratio (k²). Processed locally.
根式化简计算器（平方根、立方根、n 次根、系数）Simplify Radicals Calculator (Square, Cube and nth Roots, With a Coefficient)
把 k·ⁿ√x 化成最简根式 a·ⁿ√b（b 不含 n 次方因数），支持平方根、立方根和任意 n 次根，可带系数，负数的奇次根会保留负号。同时给出质因数分解、提出的因数和小数值。本地处理。Simplifies k·ⁿ√x to simplest radical form a·ⁿ√b (b has no nth-power factor) for square, cube or any nth roots, with an optional coefficient; odd roots of negative numbers keep the minus sign. Also shows the prime factorisation, the factor taken out and the decimal value. Processed locally.
坡度计算器（百分比、角度、比例 1:n 互换）Slope Calculator (Percent, Degrees and 1:n Ratio)
由升高和水平距离求坡度百分比、角度和 1:n 比例，或者从已知百分比、角度、比例中任意一个换算出其余，并给出斜面长度。常用于道路、坡道（无障碍坡道 1:12 ≈ 8.33 %）、屋顶和排水坡度。本地处理。From rise and run get slope as a percentage, an angle and a 1:n ratio, or convert from any one of percent, degrees or ratio to the others, with the slope length. Useful for roads, ramps (accessible ramps 1:12 ≈ 8.33 %), roofs and drainage. Processed locally.
子集计算器（C(n,k) 计数、列出子集、真子集、至多/至少 k 个）Subset Calculator (Count C(n,k), List Subsets, Proper Subsets, At Most or At Least k)
计算从 n 个元素中取 k 个的子集数 C(n, k)（大整数精确值），以及全部子集数 2ⁿ、真子集数 2ⁿ − 1、至多 k 个和至少 k 个元素的子集数；输入具体元素时列出所有 k 元子集，或检验一个集合是否是另一个集合的子集。本地处理。Counts the subsets with k of n elements, C(n, k), exactly with big integers, plus all subsets 2ⁿ, proper subsets 2ⁿ − 1, and subsets with at most or at least k elements; with actual elements it lists every k-element subset, or tests whether one set is a subset of another. Processed locally.
代入法解方程组计算器（二元/三元一次，含步骤）Substitution Method Calculator (2×2 and 3×3 Linear Systems, With Steps)
用代入法解二元一次方程组 a₁x + b₁y = c₁、a₂x + b₂y = c₂，并写出每一步：从一个方程解出一个变量、代入另一个方程、求值、回代。判断无解（平行）或无穷多解（重合），并可切换到三元一次方程组。本地处理。Solves a₁x + b₁y = c₁ and a₂x + b₂y = c₂ by substitution, showing each step: isolate a variable in one equation, substitute it into the other, solve, and back-substitute. Detects no solution (parallel lines) or infinitely many (the same line), and also handles 3×3 systems. Processed locally.
正切计算器（tan、cot、反正切，度/弧度）Tangent Calculator (tan, cot, Arctangent, Degrees or Radians)
计算角的正切 tan θ 和余切 cot θ，支持度和弧度；常见角会给出精确值（如 tan 30° = √3/3）。也可以反过来由正切值求角度 arctan，或由直角三角形的对边和邻边求 tan 和角度。本地处理。Calculates tan θ and cot θ in degrees or radians, with exact values for common angles (tan 30° = √3/3). Also works backwards with arctan from a tangent value, or from the opposite and adjacent sides of a right triangle. Processed locally.
顶点式计算器（一般式 ↔ 顶点式，顶点、对称轴、根）Vertex Form Calculator (Standard ↔ Vertex Form, Vertex, Axis, Roots)
把 y = ax² + bx + c 化成顶点式 y = a(x − h)² + k（整数系数时给出精确分数），或由顶点式展开成一般式；同时给出顶点、对称轴、开口方向、最值、与 x 轴的交点和 y 截距。本地处理。Turn y = ax² + bx + c into vertex form y = a(x − h)² + k (exact fractions for integer coefficients), or expand vertex form back to standard form. Also shows the vertex, axis of symmetry, direction of opening, minimum or maximum, x-intercepts and y-intercept. Processed locally.
三棱锥体积计算器（底面积、三边、正四面体）Triangular Pyramid Volume Calculator (Base Area, Three Sides, Regular Tetrahedron)
三棱锥（四面体）体积 V = 底面积 × 高 ÷ 3。底面可直接填面积、填三角形底和高、填三边（海伦公式），也可按正四面体只填棱长（V = a³ ÷ (6√2)）。本地处理。Triangular pyramid (tetrahedron) volume V = base area × height ÷ 3. Give the base as an area, as a triangle base and height, or as three sides (Heron's formula), or choose a regular tetrahedron and enter only the edge (V = a³ ÷ (6√2)). Processed locally.
分数化简计算器（最简分数、带分数、循环小数）Simplify Fractions Calculator (Lowest Terms, Mixed Number, Repeating Decimal)
把分数化成最简分数：给出最大公约数、约分步骤、带分数、小数（循环小数用括号标出循环节）和百分数，分子分母可为负数。本地处理。Reduce a fraction to lowest terms with the greatest common divisor, the reduction step, the mixed number, the decimal (repeating digits shown in brackets) and the percentage. Negative numerators and denominators are allowed. Processed locally.
分数加减计算器（带分数、通分步骤、最简结果）Adding and Subtracting Fractions Calculator (Mixed Numbers, Common Denominator Steps)
计算两个分数或带分数的和与差：先化成假分数，用最小公倍数通分，给出每一步、最简结果、带分数和小数。整数部分可留空，分子可为负数。本地处理。Add or subtract two fractions or mixed numbers: convert to improper fractions, use the least common denominator, and see every step, the result in lowest terms, as a mixed number and as a decimal. Whole parts may be blank; numerators may be negative. Processed locally.
圆锥计算器（体积、侧面积、表面积、母线、由体积反求高）Cone Calculator (Volume, Lateral and Total Surface Area, Slant Height, Height from Volume)
圆锥的体积 V = πr²h/3、母线 l = √(r² + h²)、侧面积 πrl、表面积 πr(r + l) 和顶角。已知量可以是半径和高、半径和母线，或半径和体积（反求高）。本地处理。Cone volume V = πr²h/3, slant height l = √(r² + h²), lateral area πrl, total surface area πr(r + l) and apex angle. Start from radius and height, radius and slant height, or radius and volume (solves for the height). Processed locally.
圆台计算器（体积、母线、侧面积、表面积、容积升数）Conical Frustum Calculator (Volume, Slant Height, Lateral and Surface Area, Capacity in Litres)
圆台（截头圆锥）体积 V = πh(R² + Rr + r²)/3，母线 s = √((R − r)² + h²)，侧面积 π(R + r)s，表面积再加两个底面；以厘米为单位时还给出容积（升），适合水桶、花盆等。本地处理。Conical frustum (truncated cone) volume V = πh(R² + Rr + r²)/3, slant height s = √((R − r)² + h²), lateral area π(R + r)s and total surface area including both bases; in centimetres it also gives the capacity in litres, handy for buckets and planters. Processed locally.
平面两点距离计算器（精确根式、中点、斜率、方位角）2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing)
计算平面上两点 (x₁, y₁)、(x₂, y₂) 的距离 d = √((x₂ − x₁)² + (y₂ − y₁)²)，整数坐标时给出化简根式（如 2√5），同时给出 Δx、Δy、中点、斜率和方向角。本地处理。Distance between two points (x₁, y₁) and (x₂, y₂) in the plane, d = √((x₂ − x₁)² + (y₂ − y₁)²), as a simplified radical for integer coordinates (e.g. 2√5), plus Δx, Δy, midpoint, slope and direction angle. Processed locally.
五次方根计算器（实根、是否为完全五次方、全部 5 个复数根）Fifth Root Calculator (Real Root, Perfect Fifth Power Check, All 5 Complex Roots)
求 x 的五次方根：负数也有实数五次方根（如 ⁵√−32 = −2）；判断是否为完全五次方，并列出 5 个复数根 r^(1/5)·(cos θ + i sin θ)。本地处理。Find the fifth root of x: negative numbers have a real fifth root too (⁵√−32 = −2). Checks for a perfect fifth power and lists all 5 complex roots r^(1/5)·(cos θ + i sin θ). Processed locally.
最小公倍数计算器（多个数、质因数分解、最大公约数）LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD)
求 2–20 个正整数的最小公倍数（LCM）和最大公约数（GCD），列出每个数的质因数分解，并说明 LCM 取每个质因数的最高次幂。用空格、换行或逗号分隔（如 12 18 30）。大数用精确整数计算。本地处理。Least common multiple (LCM) and greatest common divisor (GCD) of 2–20 positive integers, with the prime factorisation of each and how the LCM takes the highest power of every prime. Separate numbers with spaces, line breaks or commas (e.g. 12 18 30). Exact integer arithmetic for large results. Processed locally.
竖式减法计算器（任意位数、小数、逐位借位步骤）Long Subtraction Calculator (Any Number of Digits, Decimals, Borrowing Step by Step)
用竖式计算两个数相减：支持任意位数的整数和小数（精确计算，不经过浮点），显示竖式排列、每一位的借位，以及结果为负时的处理。本地处理。Long (column) subtraction of two numbers: integers and decimals of any length, computed exactly without floating point. Shows the column layout, each borrow and how a negative result is handled. Processed locally.
数位计算器（每一位的数位名称、位值、展开式，含小数）Place Value Calculator (Place Names, Digit Values, Expanded Form, Decimals)
列出一个数每一位数字所在的数位（个、十、百、千、万…以及十分位、百分位…），每位的位值和展开式；支持最多 30 位整数和 15 位小数，可带负号。本地处理。Shows the place of every digit (ones, tens, hundreds, thousands… and tenths, hundredths…), the value of each digit and the expanded form, for up to 30 integer digits and 15 decimal places, with an optional minus sign. Processed locally.
长方体计算器（体积、表面积、体对角线、面对角线）Rectangular Prism Calculator (Volume, Surface Area, Space and Face Diagonals)
由长、宽、高求长方体（立方体为特例）的体积 V = lwh、表面积 2(lw + lh + wh)、体对角线 √(l2 + w2 + h2) 和三个面的对角线；以厘米为单位时还给出容积升数。本地处理。From length, width and height get the volume V = lwh, surface area 2(lw + lh + wh), space diagonal √(l2 + w2 + h2) and the three face diagonals of a rectangular prism (a cube is a special case); in centimetres it also gives the capacity in litres. Processed locally.
菱形Rhombus Calculator
由对角线：面积 = d1d2/2，边 = √((d1/2)2+(d2/2)2)。本地处理。可设置「对角线 1」、「对角线 2」。From diagonals: area = d1d2/2; side = √((d1/2)2+(d2/2)2). Processed locally. Settings: Diagonal 1, Diagonal 2.
求和Sum Calculator
对一列数字求和（空格/逗号/换行分隔）。本地处理。Sum a list of numbers (space/comma/newline separated). Processed locally.
三棱柱Triangular Prism Calculator
V = 底面积 * 长；底为三角形 (½ab sin C 或 ½bh)。本地处理。可设置「底边」、「底高」、「棱柱长」。V = base area * length; triangular base ½bh. Processed locally. Settings: Base, Base height, Length.
三角函数Trigonometric Functions Calculator
sin / cos / tan（度或弧度）。本地处理。可设置「角度 / 弧度值」、「单位」。sin / cos / tan in degrees or radians. Processed locally. Settings: Angle value, Unit.
圆柱Cylinder Calculator
V = πr2h，侧面积 2πrh，全面积再加两底。本地处理。可设置「半径」、「高」。V = πr2h; lateral 2πrh; total adds both bases. Processed locally. Settings: Radius, Height.
长方体表面积计算器（含体积）Surface Area of a Cuboid Calculator (with Volume)
由长、宽、高求长方体表面积 2(lw + lh + wh) 和体积 lwh。边长须大于 0。本地处理。From length, width and height get the cuboid surface area 2(lw + lh + wh) and the volume lwh. Edges must be greater than 0. Processed locally.
筝形（菱形风筝）面积计算器Area of a Kite Calculator
筝形（两边对称的四边形）面积 = d₁d₂/2，其中 d₁、d₂ 是两条对角线。对角线须大于 0。本地处理。Kite area = d₁d₂/2 from the two diagonals (which are perpendicular). Diagonals must be greater than 0. Processed locally.
正多边形面积计算器（边长，含周长）Area of a Regular Polygon Calculator (Side Length, with Perimeter)
正 n 边形面积 A = (n s²) / (4 tan(π/n))，并给出周长 n s。边数 3-1000 的整数，边长大于 0。本地处理。Regular n-gon area A = (n s²) / (4 tan(π/n)), plus perimeter n s. Sides: whole number 3-1000; side length greater than 0. Processed locally.
半球体积计算器（含表面积）Volume of a Hemisphere Calculator (with Surface Area)
实心半球体积 V = (2/3) π r³，含底表面积 3 π r²（曲面 2 π r² + 底面 π r²）。半径须大于 0。本地处理。Solid hemisphere volume V = (2/3) π r³, and surface area including the base 3 π r² (curved 2 π r² + base π r²). Radius must be greater than 0. Processed locally.
可重复组合计算器（多重组合 C(n+r−1, r)）Combinations with Repetition Calculator (Multichoose C(n+r−1, r))
计算可重复组合数 C(n+r−1, r) = (n+r−1)! / (r!(n−1)!)，即从 n 种里取 r 个且允许重复、不计顺序。用精确大整数。本地处理。Combinations with repetition C(n+r−1, r) = (n+r−1)! / (r!(n−1)!): choose r from n types with repetition, order ignored. Exact big integers. Processed locally.
正比例计算器（y = kx）Direct Variation Calculator (y = kx)
由一组已知 (x, y) 求常数 k = y/x，再预测另一 x 对应的 y。已知 x 不能为 0。本地处理。可设置「已知 x」、「已知 y」、「求 y 的 x」。From one known (x, y) get k = y/x, then predict y at another x. Known x cannot be 0. Processed locally. Settings: Known x, Known y, x for y.
三角形外心计算器（外接圆圆心与半径）Circumcenter of a Triangle Calculator (Circumradius)
由平面三点坐标求外心（三边垂直平分线交点）和外接圆半径。共线时无外心。本地处理。From three planar points get the circumcenter (intersection of perpendicular bisectors) and circumradius. Collinear points have none. Processed locally.
三角形中位线计算器Midsegment of a Triangle Calculator
连接三角形两边中点的中位线平行于第三边且长度为其一半。输入第三边长即可。本地处理。The midsegment joining midpoints of two sides is parallel to the third side and half as long. Enter that third side length. Processed locally.
自然对数计算器（ln x 与 log₁₀ x）Natural Log Calculator (ln x and log₁₀ x)
计算 ln(x) = log_e(x)，并同时给出常用对数 log₁₀(x)。x 须大于 0。本地处理。可设置「x (>0)」。Computes ln(x) = log_e(x) and also common log log₁₀(x). x must be greater than 0. Processed locally. Settings: x (>0).
圆的切线长计算器Tangent Length to a Circle Calculator
圆外一点到切点的切线长 L = √(d² − r²)，d 为该点到圆心的距离，r 为半径（须 d > r）。本地处理。Tangent length from an external point L = √(d² − r²), with d = distance to centre and r = radius (need d > r). Processed locally.
正十二边形面积计算器Regular Dodecagon Area Calculator
正十二边形面积 A = 3 s² (2+√3)，并给出周长 12s。边长须大于 0。本地处理。Regular dodecagon area A = 3 s² (2+√3), plus perimeter 12s. Side length must be greater than 0. Processed locally.
正十边形面积计算器Regular Decagon Area Calculator
正十边形面积 A = (5/2) s² √(5+2√5)，并给出周长 10s。边长须大于 0。本地处理。Regular decagon area A = (5/2) s² √(5+2√5), plus perimeter 10s. Side length must be greater than 0. Processed locally.
圆柱侧面积计算器（含全面积）Lateral Surface Area of a Cylinder Calculator (with Total)
圆柱侧面积 2πrh，全面积 2πr(r+h)（含两个底面）。半径与高须大于 0。本地处理。Cylinder lateral area 2πrh and total surface 2πr(r+h) including both bases. Radius and height must be greater than 0. Processed locally.
钝角三角形判定器（锐角/直角/钝角）Obtuse Triangle Checker (Acute / Right / Obtuse)
由三边用余弦定理判定锐角、直角或钝角：比较最大边平方与另两边平方和。须满足三角不等式。本地处理。Classify acute, right or obtuse from three sides via the cosine rule: compare the largest side squared with the sum of the other squares. Must satisfy the triangle inequality. Processed locally.
矩形对角线计算器（含面积与周长）Rectangle Diagonal Calculator (with Area and Perimeter)
矩形对角线 d = √(l² + w²)，并给出面积 lw 与周长 2(l+w)。边长须大于 0。本地处理。Rectangle diagonal d = √(l² + w²), plus area lw and perimeter 2(l+w). Sides must be greater than 0. Processed locally.
不等边三角形计算器（海伦面积）Scalene Triangle Calculator (Heron Area)
由三边判定是否不等边（三边两两不等），并用海伦公式求面积与周长。须满足三角不等式。本地处理。Checks whether all three sides differ (scalene) and finds area by Heron plus the perimeter. Must satisfy the triangle inequality. Processed locally.
梯形棱柱体积计算器Trapezoidal Prism Volume Calculator
梯形棱柱体积 V = 梯形底面积 × 棱柱长，梯形面积 = (a+b)/2 × h。各边与高须大于 0。本地处理。Trapezoidal prism volume V = trapezoid area × length, with area = (a+b)/2 × h. Bases, height and length must be greater than 0. Processed locally.
二进制加法计算器Binary Addition Calculator
两个非负二进制整数相加，给出二进制和与十进制。可带 0b 前缀或下划线分隔。本地处理。Add two non-negative binary integers; show binary sum and decimal. Optional 0b prefix or underscore separators. Processed locally.
二进制除法计算器（整除与余数）Binary Division Calculator (Quotient and Remainder)
非负二进制整数整除：给出商、余数（二进制）及十进制验算。除数不能为 0。本地处理。Integer division of non-negative binaries: quotient, remainder (binary) and decimal check. Divisor cannot be 0. Processed locally.
二进制乘法计算器Binary Multiplication Calculator
两个非负二进制整数相乘，给出二进制积与十进制。可带 0b 前缀。本地处理。可设置「因数 A」、「因数 B」。Multiply two non-negative binary integers; show binary product and decimal. Optional 0b prefix. Processed locally. Settings: Factor A, Factor B.
二进制减法计算器Binary Subtraction Calculator
两个非负二进制整数相减，要求被减数 ≥ 减数，结果非负。给出二进制差与十进制。本地处理。Subtract non-negative binaries with minuend ≥ subtrahend (non-negative result). Shows binary difference and decimal. Processed locally.
欧氏距离（2D/3D）Euclidean Distance
2D 或 3D 两点距离。本地处理。可设置「维数」、「x₁」、「y₁」、「z₁」、「x₂」。2D or 3D distance between two points. Processed locally. Settings: Dimensions, x₁, y₁, z₁, x₂.
锐角三角形判定Acute Triangle Check
三边构成三角形且 a²+b²>c²（对最大边）则为锐角。本地处理。可设置「边 a」、「边 b」、「边 c」。Sides form a triangle and a²+b²>c² for the largest side → acute. Processed locally. Settings: Side a, Side b, Side c.
线段长度Length of a Line Segment
平面两点距离 √((x₂-x₁)²+(y₂-y₁)²)。本地处理。可设置「x₁」、「y₁」、「x₂」、「y₂」。Plane distance √((x₂-x₁)²+(y₂-y₁)²). Processed locally. Settings: x₁, y₁, x₂, y₂.
百分数转小数Percent to Decimal
小数 = 百分数 ÷ 100。本地处理。可设置「百分数 %」。Decimal = percent ÷ 100. Processed locally. Settings: Percent %.
三棱柱体积Triangular Prism Volume
V = (底边 × 高 / 2) × 棱长。本地处理。可设置「底边」、「三角形高」、「棱长」。V = (base × height / 2) × length. Processed locally. Settings: Base, Triangle height, Length.
智商百分位示意IQ Percentile (demo)
假设 IQ ~ N(100,15²)，用误差函数估百分位。本地处理。可设置「智商」。Assume IQ ~ N(100,15²); percentile via erf. Processed locally. Settings: IQ.
抛硬币概率Coin Flip Probability
n 次中恰好 k 次正面：C(n,k) / 2^n（公平硬币）。本地处理。可设置「次数」、「正面次数」。Exactly k heads in n fair flips: C(n,k)/2^n. Processed locally. Settings: Flips, Heads.
简单移动平均Simple Moving Average
对数列做窗口为 w 的 SMA。本地处理。可设置「数据（空格/逗号分隔）」、「窗口」。SMA of a series with window w. Processed locally. Settings: Data (space/comma separated), Window.
勾股定理Pythagorean Theorem
求直角三角形未知边。本地处理。可设置「求」、「边 a」、「边 b」、「斜边 c」。Solve the unknown side of a right triangle. Processed locally. Settings: Solve for, Leg a, Leg b, Hypotenuse c.
正四棱锥Square Pyramid
体积 V = a² h / 3；侧面斜高与侧面积示意。本地处理。可设置「底边」、「高」。Volume V = a² h / 3; slant height and lateral area demo. Processed locally. Settings: Base edge, Height.
胜率Winning Percentage
胜率 = (胜 + 0.5×平) / (胜+负+平)。本地处理。可设置「胜」、「负」、「平」。Win% = (wins + 0.5×draws) / (wins+losses+draws). Processed locally. Settings: Wins, Losses, Draws.
斜三角形（SAS）Oblique Triangle (SAS)
两边夹一角：第三边 c²=a²+b²-2ab cos C。本地处理。可设置「边 a」、「边 b」、「夹角 C °」。Two sides and included angle: c²=a²+b²-2ab cos C. Processed locally. Settings: Side a, Side b, Angle C °.
长方体Cuboid Calculator
体积 = lwh；表面积 = 2(lw+lh+wh)。本地处理。可设置「长」、「宽」、「高」。Volume = lwh; surface = 2(lw+lh+wh). Processed locally. Settings: Length, Width, Height.
贝叶斯定理Bayes Theorem
P(A|B) = P(B|A)P(A) / P(B)。本地处理。可设置「P(A)」、「P(B given A)」、「P(B)」。P(A|B) = P(B|A)P(A) / P(B). Processed locally. Settings: P(A), P(B given A), P(B).
Beta 分布（均值/方差）Beta Distribution (mean/var)
均值 = α/(α+β)；方差 = αβ/((α+β)²(α+β+1))。本地处理。可设置「α」、「β」。Mean = α/(α+β); variance = αβ/((α+β)²(α+β+1)). Processed locally. Settings: α, β.
指数分布Exponential Distribution
均值 = 1/λ；P(X≤x) = 1-e^(-λx)。本地处理。可设置「λ」、「x」。Mean = 1/λ; P(X≤x) = 1-e^(-λx). Processed locally. Settings: λ, x.
几何分布Geometric Distribution
首次成功均值 = 1/p（试验次数）。本地处理。可设置「成功概率 p」、「试验次数 k」。Mean trials until first success = 1/p. Processed locally. Settings: Success probability p, Trials k.
超几何分布Hypergeometric Distribution
P(X=k) = C(K,k)C(N-K,n-k)/C(N,n)。本地处理。可设置「总体 N」、「成功标签 K」、「抽取 n」、「抽中 k」。P(X=k) = C(K,k)C(N-K,n-k)/C(N,n). Processed locally. Settings: Population N, Success states K, Draws n, Observed k.
中位数绝对偏差 MADMedian Absolute Deviation
MAD = median(|x_i - median(x)|)。本地处理。可设置「数据」。MAD = median(|x_i - median(x)|). Processed locally. Settings: Data.
众数Mode Calculator
出现次数最多的数（可多个）。本地处理。可设置「数据」。Most frequent value(s). Processed locally. Settings: Data.
极差Range Calculator
极差 = max - min。本地处理。可设置「数据」。Range = max - min. Processed locally. Settings: Data.
均方根 RMSRoot Mean Square
RMS = √(Σx² / n)。本地处理。可设置「数据」。RMS = √(Σx² / n). Processed locally. Settings: Data.
威布尔分布（均值示意）Weibull Distribution (mean demo)
均值 ≈ λ Γ(1+1/k)（Γ 用数值近似）。本地处理。可设置「形状 k」、「尺度 λ」。Mean ≈ λ Γ(1+1/k) (Γ numerically approximated). Processed locally. Settings: Shape k, Scale λ.
等边三角形面积Equilateral Triangle Area
面积 = √3 / 4 × a²。本地处理。可设置「边长」。Area = √3 / 4 × a². Processed locally. Settings: Side.
Cholesky 分解（2×2）Cholesky Decomposition (2×2)
对 SPD 矩阵 [[a,b],[b,c]] 求 L。本地处理。可设置「a」、「b」、「c」。Factor SPD [[a,b],[b,c]] as L Lᵀ. Processed locally. Settings: a, b, c.
矩阵列空间（基与秩）Column Space Calculator
用行化简（RREF）找主元列，原矩阵的主元列构成列空间的一组基；同时给出秩。本地处理。Row-reduce (RREF) to find pivot columns; those columns of the original matrix form a basis of the column space. Rank is shown too. Processed locally.
数根（数字根）Digital Root Calculator
反复把各位数字相加直到只剩一位；也等于 1 + (n - 1) mod 9。支持很长的整数。本地处理。Repeatedly add the digits until one digit remains; equals 1 + (n - 1) mod 9. Works with very long integers. Processed locally.
整除判断（2-13）Divisibility Test Calculator
判断整数能否被 2-13 及自定义除数整除，并说明常用规则。本地处理。可设置「整数」、「自定义除数（可选）」。Check whether an integer is divisible by 2-13 and a custom divisor, with the usual rules. Processed locally. Settings: Integer, Custom divisor (optional).
2×2 矩阵特征值与特征向量Eigenvalue & Eigenvector Calculator (2×2)
解 det(A - λI) = 0 得特征值（含复数），并给出对应的特征向量。本地处理。可设置「a₁₁」、「a₁₂」、「a₂₁」、「a₂₂」。Solve det(A - λI) = 0 for the eigenvalues (complex included) and give eigenvectors. Processed locally. Settings: a₁₁, a₁₂, a₂₁, a₂₂.
误差函数 erf / erfcError Function Calculator
erf(x) = 2/√π ∫₀ˣ e^(-t²) dt，用高精度级数/连分式计算，并给出 erfc = 1 - erf。本地处理。erf(x) = 2/√π ∫₀ˣ e^(-t²) dt via high-precision series / continued fraction, plus erfc = 1 - erf. Processed locally.
伽马函数 Γ(x)Gamma Function Calculator
用 Lanczos 近似和反射公式计算 Γ(x)（x 可为负的非整数），同时给出 ln|Γ(x)|。正整数时 Γ(n) = (n - 1)!。本地处理。Γ(x) via the Lanczos approximation and reflection formula (negative non-integers allowed), plus ln|Γ(x)|. For positive integers Γ(n) = (n - 1)!. Processed locally.
黄金矩形Golden Rectangle Calculator
黄金比 φ = (1 + √5)/2 ≈ 1.618。已知长边或短边，求另一边、面积和周长。本地处理。Golden ratio φ = (1 + √5)/2 ≈ 1.618. From the long or short side, get the other side, area and perimeter. Processed locally.
双曲函数 sinh / cosh / tanhHyperbolic Functions Calculator
计算 sinh、cosh、tanh、coth、sech、csch 以及反双曲函数 asinh、acosh、atanh。本地处理。可设置「x」。sinh, cosh, tanh, coth, sech, csch and the inverses asinh, acosh, atanh. Processed locally. Settings: x.
不规则多边形面积（坐标法）Irregular Polygon Area Calculator
按顺序输入各顶点坐标（每行一个"x y"），用鞋带公式计算面积和周长。本地处理。Enter the vertices in order (one "x y" per line); the shoelace formula gives the area and perimeter. Processed locally.
幻方生成器Magic Square Generator
生成 n 阶幻方（n = 3-20）：奇数阶用暹罗法，4 的倍数用对角线互补法，其余偶数用 LUX 法；每行、每列、两条对角线之和都相等。本地处理。Generate an n×n magic square (n = 3-20): Siamese method for odd n, diagonal complement for multiples of 4 and the LUX method for other even n. Every row, column and both diagonals have the same sum. Processed locally.
矩阵幂 AⁿMatrix Power Calculator
用快速幂计算方阵的 n 次幂（n = 0-1000），每行一行、空格分隔输入矩阵。本地处理。Raise a square matrix to the power n (0-1000) by repeated squaring; enter one row per line, space separated. Processed locally.
矩阵的秩（含行最简形）Matrix Rank Calculator
用高斯-若尔当消元求矩阵的秩，并显示行最简形（RREF）和零度（列数 - 秩）。每行一行、空格分隔。本地处理。Find the rank by Gauss-Jordan elimination, with the reduced row echelon form (RREF) and nullity (columns - rank). One row per line, space separated. Processed locally.
矩阵的迹Matrix Trace Calculator
方阵的迹 = 主对角线元素之和，等于全部特征值之和；同时给出主对角线元素。本地处理。The trace of a square matrix is the sum of its main-diagonal entries, which equals the sum of its eigenvalues. Processed locally.
负二项分布Negative Binomial Distribution Calculator
每次成功概率为 p，第 r 次成功恰好出现在第 k 次试验的概率 P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ，以及累计概率、均值和方差。本地处理。With success probability p, the chance that the r-th success happens exactly on trial k is P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ; plus cumulative probabilities, mean and variance. Processed locally.
可重复排列Permutations with Repetition Calculator
从 n 种元素中可重复地取 r 个排成一列：nʳ 种；也可计算多重集排列 n! / (n₁! n₂! …)（例如 MISSISSIPPI 的字母排列）。结果用大整数精确计算。本地处理。Arrange r items chosen from n kinds with repetition: nʳ ways; or permutations of a multiset n! / (n₁! n₂! …), e.g. letters of MISSISSIPPI. Exact big-integer results. Processed locally.
相对标准偏差 RSD（变异系数）Relative Standard Deviation Calculator
RSD = 标准差 ÷ |平均值| × 100%，也叫变异系数（CV）。可选样本标准差（n - 1）或总体标准差（n）。本地处理。RSD = standard deviation ÷ |mean| × 100%, also called the coefficient of variation (CV). Choose sample (n - 1) or population (n) standard deviation. Processed locally.
球面方程Sphere Equation Calculator
由球心 (a, b, c) 和半径 r 写出标准方程 (x - a)² + (y - b)² + (z - c)² = r² 与一般方程，并给出体积和表面积。本地处理。From centre (a, b, c) and radius r, write the standard equation (x - a)² + (y - b)² + (z - c)² = r² and the general form, plus volume and surface area. Processed locally.
长方体表面积Surface Area of a Rectangular Prism
表面积 = 2(lw + lh + wh)，同时给出侧面积 2h(l + w)、体积和体对角线长度。本地处理。Surface area = 2(lw + lh + wh), plus lateral area 2h(l + w), volume and space diagonal. Processed locally.
矩阵张量积（克罗内克积）Tensor Product Calculator (Kronecker Product)
A ⊗ B：把 A 的每个元素 aᵢⱼ 换成 aᵢⱼB，得到 (m·p) × (n·q) 的矩阵。也适用于向量（单行或单列）。本地处理。A ⊗ B replaces each entry aᵢⱼ of A with aᵢⱼB, giving an (m·p) × (n·q) matrix. Works for vectors too (a single row or column). Processed locally.
三角形重心Triangle Centroid Calculator
重心 G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)，是三条中线的交点；同时给出面积。本地处理。Centroid G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3), where the three medians meet; the area is shown too. Processed locally.
长方体体积Volume of a Rectangular Prism
体积 V = 长 × 宽 × 高，并换算成升和立方英尺（按米输入时）；同时给出表面积。本地处理。Volume V = length × width × height, also in litres and cubic feet (for metre inputs), plus the surface area. Processed locally.
同底数幂相乘Multiplying Exponents Calculator
同底数幂相乘指数相加：aᵐ × aⁿ = aᵐ⁺ⁿ；幂的乘方指数相乘：(aᵐ)ⁿ = aᵐⁿ；同指数不同底：aⁿ × bⁿ = (ab)ⁿ。给出化简式和数值。本地处理。Same base: add exponents, aᵐ × aⁿ = aᵐ⁺ⁿ; power of a power: (aᵐ)ⁿ = aᵐⁿ; same exponent: aⁿ × bⁿ = (ab)ⁿ. Shows the simplified form and the value. Processed locally.
分数乘法（自动约分）Multiplying Fractions Calculator
输入两个或多个分数（如 2/3 × 3/4，也支持整数和带分数"1 1/2"），分子乘分子、分母乘分母并约分，给出最简分数、带分数和小数。本地处理。Enter two or more fractions (e.g. 2/3 × 3/4; whole numbers and mixed numbers like "1 1/2" work too). Numerators and denominators are multiplied and reduced to the simplest fraction, mixed number and decimal. Processed locally.
减法计算器（精确小数）Subtraction Calculator
计算 a - b - c …，用十进制精确运算，避免 0.3 - 0.1 = 0.19999… 这类浮点误差；支持很长的数字。本地处理。Compute a - b - c … with exact decimal arithmetic, avoiding floating-point artefacts such as 0.3 - 0.1 = 0.19999…; very long numbers work. Processed locally.
商和余数Quotient and Remainder Calculator
整数除法：商 = trunc(被除数 ÷ 除数)，余数 = 被除数 - 商 × 除数。可设置「被除数」、「除数」。Integer division: quotient = trunc(dividend ÷ divisor), remainder = dividend - quotient × divisor. Settings: Dividend, Divisor.
五数概括5-Number Summary Calculator
Min / Q1 / 中位数 / Q3 / Max。Min / Q1 / median / Q3 / Max.
45-45-90 三角形45-45-90 Triangle Calculator
斜边 = 腿 × √2。可设置「已知」、「长度」。hyp = leg × √2. Settings: Given, Length.
周长转直径Circumference to Diameter Calculator
圆：d = C / π，也可由直径求周长。可设置「已知」、「数值」。Circle: d = C / π; also C from diameter. Settings: Given, Value.
30-60-90 三角形30-60-90 Triangle Calculator
边比 1 : √3 : 2（短直角边 : 长直角边 : 斜边）。可设置「已知」、「长度」。Side ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). Settings: Given, Length.
以 2 为底的对数Log Base 2 Calculator
log₂(x) = ln(x)/ln(2)。可设置「x」。log₂(x) = ln(x)/ln(2). Settings: x.
10 的幂Power of 10 Calculator
计算 10ⁿ，也可由 y 求 n = log₁₀(y)。可设置「模式」、「数值」。Compute 10ⁿ, or n = log₁₀(y). Settings: Mode, Value.
单位面积速查Unit Area Reference
查看 1 个面积单位等于多少其他单位。可设置「单位」。See what 1 of an area unit equals in others. Settings: Unit.
变异系数计算器Coefficient of Variation Calculator
输入一组数据，计算变异系数 CV = 标准差 ÷ 平均值，同时给出平均值和标准差；可选样本或总体标准差，用来比较量纲或平均水平不同的数据的离散程度。Enter a data set to get the coefficient of variation, CV = standard deviation ÷ mean, along with the mean and standard deviation. Choose sample or population SD; CV lets you compare spread between data with different units or levels.
经验法则（68-95-99.7）计算器Empirical Rule Calculator (68-95-99.7)
输入正态分布的平均值和标准差，给出平均值 ±1、±2、±3 个标准差的区间，以及各区间内数据所占的比例（约 68%、95%、99.7%），还可以查某个数值的 z 分数。Enter the mean and standard deviation of a normal distribution to get the ranges within ±1, ±2 and ±3 standard deviations and the share of data in each (about 68%, 95% and 99.7%), plus the z-score of any value.
几何平均数计算器Geometric Mean Calculator
计算一组正数的几何平均数（n 个数乘积的 n 次方根），也可以输入每期增长率（%）求平均增长率；同时给出算术平均数作对比。Calculate the geometric mean of positive numbers (the n-th root of their product), or enter growth rates in percent to get the average growth rate, with the arithmetic mean for comparison.
调和平均数计算器Harmonic Mean Calculator
计算一组正数的调和平均数 n ÷ Σ(1/x)，适合求平均速度、平均单价等「比率」的平均；可选填权重求加权调和平均，并给出算术、几何平均作对比。Calculate the harmonic mean n ÷ Σ(1/x) of positive numbers — the right average for rates such as speeds or unit prices — with optional weights, and the arithmetic and geometric means for comparison.
泊松分布计算器Poisson Distribution Calculator
输入平均发生次数 λ 和次数 k，计算泊松分布的 P(X = k)、P(X ≤ k)、P(X < k)、P(X ≥ k) 和 P(X > k)，并给出均值、方差和标准差。Enter the average rate λ and a count k to get the Poisson probabilities P(X = k), P(X ≤ k), P(X < k), P(X ≥ k) and P(X > k), with the mean, variance and standard deviation.
二次回归计算器Quadratic Regression Calculator
输入若干对 (x, y) 数据，用最小二乘法拟合二次函数 y = ax² + bx + c，给出系数、决定系数 R²、残差平方和，并可代入 x 求预测值。Fit a quadratic y = ax² + bx + c to (x, y) data by least squares, with the coefficients, R², residual sum of squares and a prediction for any x.
二项式系数（组合数）计算器Binomial Coefficient Calculator
计算组合数 C(n, k) = n! ÷ (k!(n − k)!)，即从 n 个不同元素中取 k 个的方法数，用大整数精确计算并给出位数和科学记数法；n 最大 100,000。Calculate the binomial coefficient C(n, k) = n! ÷ (k!(n − k)!), the number of ways to choose k items from n, exactly with big integers, with the digit count and scientific notation; n up to 100,000.
效应量计算器（Cohen's d）Effect Size Calculator (Cohen's d)
输入两组的平均值、标准差和样本量，计算 Cohen's d（合并标准差）、小样本校正的 Hedges' g 和 Glass's Δ，并按 Cohen（1988）的常用基准给出大小参考。Enter the mean, standard deviation and sample size of two groups to get Cohen's d (pooled SD), the small-sample-corrected Hedges' g and Glass's Δ, with Cohen's (1988) conventional benchmarks.
误差范围计算器（调查抽样）Margin of Error Calculator (Surveys)
输入样本量、置信水平和样本比例，计算调查结果的误差范围 ± z·√(p(1 − p)/n)，可填总体规模做有限总体校正，并给出置信区间。Calculate a survey's margin of error, ± z·√(p(1 − p)/n), from the sample size, confidence level and sample proportion, with an optional finite-population correction and the confidence interval.
点估计计算器（比例）Point Estimate Calculator (Proportion)
输入成功次数和试验次数，计算比例的四种点估计：最大似然（x/n）、拉普拉斯、Jeffreys 和 Wilson，并按常用规则给出推荐值。Enter the number of successes and trials to get four point estimates of a proportion — maximum likelihood (x/n), Laplace, Jeffreys and Wilson — with the one a common rule recommends.
相关系数计算器Correlation Coefficient Calculator
输入成对的 (x, y) 数据，计算皮尔逊相关系数 r、决定系数 r²、斯皮尔曼等级相关系数 ρ 和协方差，并给出相关强度的常用描述。Enter paired (x, y) data to get the Pearson correlation coefficient r, r², Spearman's rank correlation ρ and the covariance, with a common description of the strength.
残差计算器（线性回归）Residual Calculator (Linear Regression)
输入成对的 (x, y) 数据，拟合最小二乘直线 ŷ = a + bx，列出每个点的预测值和残差 y − ŷ，并给出残差平方和、残差标准误和最大残差。Enter paired (x, y) data to fit the least-squares line ŷ = a + bx and list each point's predicted value and residual y − ŷ, with the residual sum of squares, residual standard error and the largest residual.
单位向量计算器Unit Vector Calculator
输入 2–10 维向量，求它的模长和同方向的单位向量 û = v ÷ |v|；整数分量时给出带根号的精确形式，二维和三维还给出方向角。Enter a vector with 2 to 10 components to get its magnitude and the unit vector in the same direction, û = v ÷ |v| — exact with square roots for whole-number components, plus direction angles in 2D and 3D.
向量投影计算器Vector Projection Calculator
求向量 a 在向量 b 上的投影向量 proj_b a = (a·b ÷ |b|²) b、标量投影（a·b ÷ |b|）、与 b 垂直的分量（a − 投影）以及两向量夹角，支持 2–10 维。Project vector a onto vector b: the vector projection proj_b a = (a·b ÷ |b|²) b, the scalar projection a·b ÷ |b|, the component of a perpendicular to b (a − projection) and the angle between them, in 2 to 10 dimensions.
半圆面积计算器Area of a Semicircle Calculator
已知半径、直径、面积或周长中的任意一个，求半圆的面积 πr²/2、弧长 πr、周长（弧长 + 直径）以及形心到直径的距离 4r/(3π)。Given a semicircle's radius, diameter, area or perimeter, find its area πr²/2, arc length πr, perimeter (arc + diameter) and the distance from the diameter to its centroid, 4r/(3π).
终边相同的角计算器Coterminal Angle Calculator
求与给定角终边相同的角（θ ± 360°·k），给出 0°–360° 与 −180°–180° 内的标准角、所在象限和参考角，支持角度、弧度和 π 的倍数，也可判断两个角是否终边相同。Find angles coterminal with a given angle (θ ± 360°·k): its standard position in 0°–360° and −180°–180°, quadrant and reference angle, in degrees, radians or multiples of π — and check whether two angles are coterminal.
抛物线计算器Parabola Calculator
由一般式 y = ax² + bx + c 或顶点式 y = a(x − h)² + k 求抛物线的顶点、焦点、准线、对称轴、开口方向、焦距、通径长度以及与坐标轴的交点。From y = ax² + bx + c or the vertex form y = a(x − h)² + k, find a parabola's vertex, focus, directrix, axis of symmetry, direction, focal length, latus rectum and axis intercepts.
线性插值计算器Linear Interpolation Calculator
已知两点 (x₁, y₁)、(x₂, y₂)，用直线插值求任意 x 对应的 y（可一次输入多个 x），或由 y 反求 x；超出两点范围时会提示属于外推。Given two points (x₁, y₁) and (x₂, y₂), find y for any x on the straight line between them (several x values at once), or solve x from y — with a note when a value is outside the two points (extrapolation).
区间表示法转换器Interval Notation Calculator
在不等式和区间表示法之间互相转换：输入如 -2 < x <= 5、x < 1 or x > 4 或 [3, inf)、(1, 3] U [2, 6)，得到区间表示、不等式和集合描述，并自动合并重叠区间。Convert between inequalities and interval notation: enter things like -2 < x <= 5, x < 1 or x > 4, [3, inf) or (1, 3] U [2, 6) to get the interval notation, inequality and set-builder form, with overlapping intervals merged.
笛卡尔符号法则计算器Descartes' Rule of Signs Calculator
输入多项式（如 x^3 - 3x^2 + 4）或系数列表，用笛卡尔符号法则统计 P(x) 和 P(−x) 的变号次数，列出正实根、负实根和虚根个数的所有可能组合。Enter a polynomial (e.g. x^3 - 3x^2 + 4) or its coefficients to count sign changes in P(x) and P(−x) with Descartes' rule of signs and list every possible mix of positive, negative and complex roots.
分母有理化计算器Rationalize the Denominator Calculator
把 a ÷ (b√c) 或 a ÷ (b + d√c) 形式的分数化为分母不含根号的最简形式：单项式分母乘以 √c，二项式分母乘以共轭式，并显示每一步。Rationalize fractions of the form a ÷ (b√c) or a ÷ (b + d√c): multiply by √c for a single-term denominator or by the conjugate for a two-term one, simplified, with every step shown.
最小公分母（LCD）计算器Least Common Denominator (LCD) Calculator
输入几个分数（可含整数、小数和带分数），求它们的最小公分母，并把每个分数改写成以 LCD 为分母的等值分数，同时给出它们的和。Enter several fractions (whole numbers, decimals and mixed numbers allowed) to find their least common denominator, rewrite each one over the LCD, and see their sum.
小数转百分数计算器Decimal to Percent Calculator
把小数精确地转换为百分数（乘以 100，移动小数点两位，不产生浮点误差），也可反向把百分数转回小数；可一次转换多个数，并给出最简分数形式。Convert decimals to percentages exactly — multiply by 100 by moving the decimal point two places, with no floating-point error — or percentages back to decimals, several at once, with the simplest fraction too.
乘法逆元计算器（倒数与模逆）Multiplicative Inverse Calculator
求一个数的乘法逆元：普通数的倒数（支持分数、带分数和小数，结果给出最简分数），或整数在模 m 下的模逆元 a⁻¹ mod m（扩展欧几里得算法，显示步骤，支持大整数）。Find a multiplicative inverse: the reciprocal of a number (fractions, mixed numbers and decimals, as a simplified fraction), or the modular inverse a⁻¹ mod m by the extended Euclidean algorithm, with steps and big integers.
竖式加法计算器（列竖式）Long Addition Calculator
用竖式（列竖式）把两个或多个非负整数或小数相加，按小数点对齐，逐列显示进位和每一步，支持任意长度的大数，适合检查作业。Add two or more non-negative whole numbers or decimals by long addition, lined up on the decimal point, with the carry and working shown for each column and no limit on length — handy for checking homework.
零空间（核）计算器Null Space Calculator
用分数精确计算矩阵的零空间（核）：化为行最简形（RREF），找出主元列和自由变量，给出零空间的一组基向量（可化为整数），以及秩和零度。Find the null space (kernel) of a matrix exactly with fractions: reduce it to row echelon form (RREF), identify pivot columns and free variables, and get a basis for the null space (optionally scaled to integers) with the rank and nullity.
特征多项式计算器Characteristic Polynomial Calculator
用分数精确计算方阵的特征多项式 p(λ) = det(λI − A)（Faddeev–LeVerrier 算法），同时给出迹、行列式，以及所有有理数特征值。Compute the characteristic polynomial p(λ) = det(λI − A) of a square matrix exactly with fractions (Faddeev–LeVerrier algorithm), with the trace, determinant and any rational eigenvalues.
格拉姆-施密特正交化计算器Gram–Schmidt Calculator
输入一组向量，用格拉姆-施密特过程精确求出正交基（分数）和标准正交基（小数，并给出每个向量的长度），线性相关的向量会被识别并跳过。Enter a set of vectors to get an orthogonal basis by the Gram–Schmidt process (exact fractions) and an orthonormal basis (decimals, with each vector's length); linearly dependent vectors are detected and skipped.
四则运算顺序（逐步计算）Order of Operations Calculator
输入算式，按运算顺序（括号 → 乘方 → 乘除从左到右 → 加减从左到右，即 PEMDAS/BODMAS）一步一步算出结果，每步只做一次运算；用分数精确计算，同时给出小数。Enter an expression to evaluate it step by step in the order of operations — parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right (PEMDAS/BODMAS) — one operation per step, exactly with fractions and with a decimal too.
圆周率 π 位数计算器（最多 10000 位）Pi Digits Calculator (up to 10,000 digits)
在浏览器里用梅钦公式（π = 16·arctan(1/5) − 4·arctan(1/239)）和大整数精确算出 π 小数点后 1–10000 位，可分组显示、复制，统计各数字出现次数，并查找生日等数字串第一次出现的位置。Compute π to 1–10,000 decimal places right in your browser with Machin's formula (π = 16·arctan(1/5) − 4·arctan(1/239)) and exact big-integer arithmetic. Group and copy the digits, count how often each digit appears, and find where a digit string such as a birthday first shows up.
黄金比例 φ 位数生成器（最多 10000 位）Golden Ratio Digits Generator (up to 10,000 digits)
用 φ = (1 + √5) / 2 和大整数平方根精确生成黄金比例小数点后 1–10000 位，也可以输出 1/φ（= φ − 1）或 φ²（= φ + 1），支持分组、复制和查找数字串。Generate the golden ratio φ = (1 + √5) / 2 to 1–10,000 decimal places with an exact big-integer square root — or its reciprocal 1/φ (= φ − 1) or square φ² (= φ + 1) — with grouping, copying and digit search.
完全数生成器 / 判断器Perfect Number Generator & Checker
由已知的梅森素数 2ᵖ − 1 按欧几里得–欧拉公式 2ᵖ⁻¹(2ᵖ − 1) 精确生成前 1–25 个偶完全数（最大 13066 位），或判断一个数是完全数、盈数还是亏数并列出它的真因数。Generate the first 1–25 even perfect numbers exactly from the known Mersenne primes 2ᵖ − 1 with the Euclid–Euler formula 2ᵖ⁻¹(2ᵖ − 1) — the largest has 13,066 digits — or check whether a number is perfect, abundant or deficient and list its proper divisors.
杨辉三角（帕斯卡三角形）生成器Pascal's Triangle Generator
用大整数精确生成杨辉三角前 1–100 行（居中三角、左对齐或 CSV），或单独算出第 0–1000 行的全部二项式系数；还能显示奇偶图案，看到其中的谢尔宾斯基三角形。Generate the first 1–100 rows of Pascal's triangle exactly with big integers — centred, left-aligned or as CSV — or get every binomial coefficient in a single row from 0 to 1000. An odd/even view reveals the Sierpiński triangle inside it.
中心极限定理计算器（样本均值的概率）Central Limit Theorem Calculator
输入总体均值 μ、标准差 σ 和样本量 n，按中心极限定理求样本均值 X̄ 的分布（均值 μ、标准误 σ/√n），并计算 X̄ 小于、大于或落在某个区间的概率。Enter the population mean μ, standard deviation σ and sample size n to get the sampling distribution of the mean X̄ by the central limit theorem (mean μ, standard error σ/√n), and the probability that X̄ is below, above or between given values.
箱线图生成器（五数概括 + 离群值）Box Plot Maker (Five-Number Summary)
输入一组或多组数据，算出五数概括（最小值、Q1、中位数、Q3、最大值）、四分位距 IQR、1.5×IQR 围栏和离群值，并画出可下载的 SVG 箱线图；多组数据并排对比，四分位数可选 4 种常见算法。Enter one or more data sets to get the five-number summary (minimum, Q1, median, Q3, maximum), the IQR, the 1.5 × IQR fences and any outliers, drawn as a downloadable SVG box plot. Several groups are compared side by side, and the quartiles can use any of four common methods.
坐标旋转计算器（绕原点或任意点）Rotation Calculator (Rotate Points)
把一个或多个点 (x, y) 绕原点或任意中心点旋转指定角度（逆时针或顺时针，角度或弧度），给出旋转后的坐标和旋转矩阵，适合几何作业、图形和 CAD 计算。Rotate one or more points (x, y) about the origin or any centre by a given angle — counter-clockwise or clockwise, in degrees or radians — and get the new coordinates and the rotation matrix. Handy for geometry homework, graphics and CAD.
数轴生成器（点、区间、不等式）Number Line Generator
按起点、终点和刻度间隔画出数轴，可以标出实心点、空心点、区间（如 [−2, 3)）和不等式（如 x ≥ 1、−1 < x ≤ 4），同时给出区间记号，并下载为 SVG 图片。Draw a number line from a start, an end and a tick step, and mark closed or open points, intervals such as [−2, 3) and inequalities such as x ≥ 1 or −1 < x ≤ 4. Each mark is also given in interval notation, and the line downloads as an SVG image.
极限计算器Limit Calculator
求函数的极限 lim f(x)：支持趋近于某个数、分数、pi 或 ±∞，可选双侧、左极限、右极限；符号计算给出精确值并用数值核对，能识别左右极限不相等、趋于无穷、振荡和无定义等“极限不存在”的情况。Find the limit of a function, lim f(x), as x approaches a number, a fraction, pi or ±∞ — two-sided, from the left or from the right. Exact values come from symbolic computation and are checked numerically, and it recognises limits that do not exist: unequal one-sided limits, oscillation or no real value nearby. Infinite limits are reported as ∞ or −∞.
部分分式分解计算器Partial Fraction Decomposition Calculator
把有理函数（多项式之比）分解成部分分式之和：支持一次因式、重复因式和不可约二次因式，分子次数不低于分母时先分离出多项式部分；结果给出普通写法和 LaTeX，并在多个点代入核对。Split a rational function (a ratio of polynomials) into a sum of partial fractions — linear, repeated and irreducible quadratic factors are all handled, and when the numerator's degree is not lower than the denominator's the polynomial part is separated out first. Results come in plain notation and LaTeX, checked numerically at several points.
三维空间两点距离计算器3D Distance Calculator
输入三维空间中两点的坐标 (x₁, y₁, z₁) 和 (x₂, y₂, z₂)，按 d = √(Δx² + Δy² + Δz²) 算出两点间的距离，同时给出各轴差值、距离平方和中点坐标。Enter two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in 3D space to get the distance d = √(Δx² + Δy² + Δz²), along with the difference on each axis, the squared distance and the midpoint.
菱形面积计算器Area of a Rhombus Calculator
按两条对角线、边长和高、或边长和内角三种方式计算菱形面积，同时给出边长、周长、两条对角线和内角。Find the area of a rhombus from its two diagonals, from side and height, or from side and an interior angle — with the side, perimeter, both diagonals and the interior angles.
圆环体（环面）体积计算器Torus Volume Calculator
输入圆环的主半径 R（中心到管中心）和管半径 r，按 V = 2π²Rr² 计算体积、按 S = 4π²Rr 计算表面积；也可以改用内半径和外半径输入。Enter the major radius R (centre to tube centre) and tube radius r of a torus to get its volume V = 2π²Rr² and surface area S = 4π²Rr — or enter the inner and outer radii instead.
椭球体积计算器Volume of an Ellipsoid Calculator
输入椭球的三个半轴 a、b、c，按 V = 4/3·πabc 计算体积，并用 Knud Thomsen 公式估算表面积（误差不超过约 1.06%）；三个半轴相等时就是球。Enter the three semi-axes a, b and c of an ellipsoid to get its volume V = 4/3·πabc and an estimate of its surface area from Knud Thomsen's formula (within about 1.06%). Equal semi-axes give a sphere.
棱锥体积计算器Volume of a Pyramid Calculator
计算矩形底（含正方形）或正多边形底直棱锥的体积 V = 底面积 × 高 ÷ 3，并给出底面积、斜高、侧面积和总表面积。Work out the volume V = base area × height ÷ 3 of a right pyramid with a rectangular (or square) base or a regular-polygon base, plus the base area, slant height, lateral area and total surface area.
反对数计算器Antilog Calculator
求以 10、e、2 或任意正数为底的反对数 y = bˣ（即已知对数 x 求原数），给出十进制结果和科学计数法；超过双精度范围的结果也能用科学计数法显示。Find the antilogarithm y = bˣ for base 10, e, 2 or any positive base — the number whose logarithm is x — as a decimal and in scientific notation, even when the result is beyond double-precision range.
展开式（数位分解）计算器Expanded Form Calculator
把整数或小数按数位展开成加法式、乘法式（数字 × 位值）和 10 的幂形式，小数部分同时给出分数形式；支持负数和最多 40 位数字，按字符串精确处理不丢位。Write a whole number or decimal in expanded form — as a sum of place values, as digit × place value, and with powers of ten, plus fraction form for the decimal places. Negative numbers and up to 40 digits are handled exactly as text.
埃及分数计算器Egyptian Fraction Calculator
用斐波那契–西尔维斯特贪心算法把分数 a/b 拆成互不相同的单位分数之和（如 4/13 = 1/4 + 1/18 + 1/468），大于 1 的分数先取出整数部分；用大整数精确计算并验算。Split a fraction a/b into a sum of distinct unit fractions with the Fibonacci–Sylvester greedy algorithm (e.g. 4/13 = 1/4 + 1/18 + 1/468), taking out the whole part first for fractions above 1. Big-integer arithmetic keeps it exact, and the sum is checked.
考拉兹猜想（3n+1）计算器Collatz Conjecture Calculator
输入正整数 n，按「偶数除以 2、奇数乘 3 加 1」反复迭代，给出到达 1 的步数、过程中的最大值、奇偶步数和完整序列；用大整数计算，支持最多 100 位的起始数。Enter a positive whole number n and apply 'halve if even, 3n + 1 if odd' until it reaches 1 — with the number of steps, the highest value reached, the odd and even step counts and the full sequence. Big integers allow starting numbers up to 100 digits.
伴随矩阵计算器Adjoint (Adjugate) Matrix Calculator
输入 2×2 到 6×6 的方阵，精确计算伴随矩阵 adj(A)（余子式矩阵的转置）、余子式矩阵和行列式，并在可逆时给出分数形式的逆矩阵 A⁻¹ = adj(A) / det(A)。整数和最多 6 位小数都按精确有理数计算。Enter a square matrix from 2×2 to 6×6 to get its adjugate adj(A) — the transpose of the cofactor matrix — exactly, together with the cofactor matrix, the determinant and, when it exists, the inverse A⁻¹ = adj(A) / det(A) as fractions. Whole numbers and decimals with up to 6 places are handled as exact rationals.
QR 分解计算器QR Decomposition Calculator
用 Householder 反射把 m×n 矩阵（m ≥ n，最大 8×8）分解为 A = QR：Q 的列为标准正交向量，R 为上三角矩阵（对角线取非负）。给出精简形式或完整形式，并验算 QR 与 A 的最大误差和 QᵀQ 的正交性。Factor an m×n matrix (m ≥ n, up to 8×8) as A = QR with Householder reflections: Q has orthonormal columns and R is upper triangular with a non-negative diagonal. Choose the reduced or full form, and see the largest error of QR against A and how close QᵀQ is to I.
茎叶图生成器Stem and Leaf Plot Calculator
把一组数据整理成茎叶图：自动或手动选择叶单位，可拆分茎（每个茎分两行），支持负数和小数，并给出个数、最小值、最大值、中位数和众数。Turn a list of numbers into a stem-and-leaf plot, with an automatic or chosen leaf unit, optional split stems (two lines per stem), support for negatives and decimals, and the count, minimum, maximum, median and mode.
直方图生成器Histogram Maker
粘贴一组数据，按 Sturges、平方根或 Freedman–Diaconis 规则自动分组（组距取整到 1、2、2.5、5 × 10ⁿ），或自定义组数、组距和起点，生成直方图和频数、频率、累计频率表，可下载 SVG 或复制 CSV。Paste your data to build a histogram, with bins from Sturges', the square-root or the Freedman–Diaconis rule (widths rounded to 1, 2, 2.5 or 5 × 10ⁿ) or your own bin count, width and start — plus a table of counts, relative and cumulative frequencies, an SVG download and CSV to copy.
韦恩图计算器Venn Diagram Calculator
按集合大小和交集数量（两个或三个集合），用容斥原理算出韦恩图每个区域的数量、并集和「都不属于」的个数；也可以直接列出各集合的元素，自动求交集、并集和差集。Work out every region of a two- or three-set Venn diagram from the set sizes and overlaps with inclusion–exclusion, including the union and the number in none of the sets — or list each set's items and get the intersections, union and differences automatically.
二进制加法计算器（多个二进制数求和）Add Binary Numbers
把两个或多个二进制数相加：每行一个，或用空格、逗号、加号分隔，支持很长的数（任意位数）、负数和 0b 前缀；可显示带进位的竖式，并同时给出十进制和十六进制结果，还能设置最少位数补 0、每 4 位分组。适合学习二进制加法、检查作业和数字电路练习，数据在本地处理。Add two or more binary numbers. Put one per line or separate them with spaces, commas or plus signs. Numbers of any length, negative numbers and the 0b prefix all work. Show the column addition with carries, see the result in decimal and hex too, pad to a minimum width and group every 4 bits. Handy for learning binary addition, checking homework and digital-logic exercises. Processed locally.
二进制乘法计算器（多个二进制数相乘）Multiply Binary Numbers
把两个或多个二进制数相乘：每行一个，或用空格、逗号、* 或 × 分隔，支持任意位数、负数和 0b 前缀；两个数相乘时可显示移位相加的竖式（部分积），同时给出十进制和十六进制结果，还能设置最少位数补 0、每 4 位分组。适合学习二进制乘法、计算机组成原理和数字电路练习，数据在本地处理。Multiply two or more binary numbers. Put one per line or separate them with spaces, commas, * or ×. Any length, negative numbers and the 0b prefix work. For two numbers you can show the shift-and-add working with each partial product, and see the result in decimal and hex too, padded to a minimum width or grouped every 4 bits. Handy for learning binary multiplication, computer architecture and digital-logic exercises. Processed locally.
二进制转负二进制（base −2）Convert Binary to Negabinary
把普通二进制数（可以带负号）转换成负二进制（以 −2 为底的进位制）：每行一个或用空格分隔，支持任意位数；可同时显示十进制值，或显示“输入 → 结果”对照。负二进制不需要负号就能表示负数，常见于编程题和数制练习，数据在本地处理。Convert ordinary binary numbers (a minus sign is allowed) into negabinary, the base −2 number system. One value per line or separated by spaces, any length. Optionally show the decimal value or an input → result table. Negabinary writes negative numbers without a sign and turns up in programming puzzles and number-system exercises. Processed locally.
十进制转负二进制（负二进制编码）Encode Negative Binary
把十进制整数（正数、负数或 0）编码成负二进制（以 −2 为底的进位制），每行一个或用空格分隔，支持任意大的整数；可显示“输入 → 结果”对照、各位权重展开式（如 7 = 16 − 8 − 2 + 1），也能设置最少位数补 0。适合学习数制、做编程题和验证算法，数据在本地处理。Encode decimal integers (positive, negative or zero) as negabinary, the base −2 number system. One value per line or separated by spaces, integers of any size. Show an input → result table or the place-value expansion (e.g. 7 = 16 − 8 − 2 + 1), and pad to a minimum width. Handy for learning number systems, programming puzzles and checking algorithms. Processed locally.
负二进制解码（base −2 转十进制）Decode Negative Binary
把负二进制数（以 −2 为底的进位制）解码成十进制整数，也可以同时给出普通二进制（带负号）：每行一个或用空格分隔，支持任意位数；可显示“输入 → 结果”对照和各位权重展开式（如 11011 = 16 − 8 − 2 + 1 = 7）。适合学习数制、做编程题和检查编码结果，数据在本地处理。Decode negabinary numbers (base −2) into decimal integers, optionally with the ordinary signed binary too. One value per line or separated by spaces, any length. Show an input → result table or the place-value expansion (e.g. 11011 = 16 − 8 − 2 + 1 = 7). Handy for learning number systems, programming puzzles and checking encoded results. Processed locally.
二进制减法计算器（带借位竖式）Subtract Binary Numbers
用第一个二进制数依次减去后面的数：每行一个，或用空格、逗号、加号或减号分隔，支持任意位数、负数和 0b 前缀。两个非负数相减时可显示带借位的竖式；结果为负数时默认用负号表示，也可以按指定位数显示成补码。同时给出十进制和十六进制结果，可设置最少位数补 0、每 4 位分组。适合学习二进制减法、补码和数字电路练习，数据在本地处理。Subtract binary numbers: the first value minus each of the others. Put one per line or separate them with spaces, commas, plus signs or minus signs. Any length, negative numbers and the 0b prefix work. For two non-negative values you can show the column subtraction with borrows. A negative result is written with a minus sign, or as two's complement in a width you choose. See the result in decimal and hex too, pad to a minimum width or group every 4 bits. Handy for learning binary subtraction, two's complement and digital-logic exercises. Processed locally.
十六进制加法计算器Add Hex Numbers
把两个或多个十六进制数相加：每行一个或用空格、逗号、加号分隔，支持任意位数、负数和 0x 前缀；可同时显示十进制和二进制结果，设置最少位数补 0。适合学习十六进制运算和检查作业，数据在本地处理。Add two or more hexadecimal numbers. One per line or separated by spaces, commas or plus signs; any length, negatives and 0x prefixes work. Also show decimal and binary, pad to a minimum width. Handy for learning hex arithmetic and checking homework. Processed locally.
十六进制乘法计算器Multiply Hex Numbers
把两个或多个十六进制数相乘：每行一个或用空格、逗号、*、× 分隔，支持任意位数、负数和 0x 前缀；可同时显示十进制结果。适合学习十六进制运算，数据在本地处理。Multiply two or more hexadecimal numbers. One per line or separated by spaces, commas, * or x; any length, negatives and 0x. Optionally show decimal. Handy for hex arithmetic. Processed locally.
十六进制转罗马数字Convert Hex to Roman Numeral
把十六进制整数（1–0xF9F，即 1–3999）转换成罗马数字，每行一个；可同时显示十进制。适合铭文、编号和教学，数据在本地处理。Convert hexadecimal integers (1-0xF9F, i.e. 1-3999) into Roman numerals, one per line; optionally show decimal too. Handy for inscriptions, numbering and teaching. Processed locally.
罗马数字转十六进制Convert Roman Numeral to Hex
把规范罗马数字（I–MMMCMXCIX）转换成十六进制，每行一个；可同时显示十进制。适合铭文解读和编号转换，数据在本地处理。Convert standard Roman numerals (I-MMMCMXCIX) into hexadecimal, one per line; optionally show decimal too. Handy for reading inscriptions and converting numbers. Processed locally.
整数分析（个数、求和、平均、奇偶等）Analyze Integers
分析一串整数：个数、最小值、最大值、求和、平均值、中位数、偶数/奇数个数、正负零个数。适合快速摸清数据分布，本地处理。Analyze a list of integers: count, min, max, sum, mean, median, even/odd counts, and positive/negative/zero counts. Handy for a quick look at a dataset. Processed locally.
更改整数正负号Change Integer Sign
批量更改整数的正负号：全部取相反数、全部变正、全部变负，或去掉符号。适合整理数据，本地处理。Change the sign of integers in bulk: negate all, make all positive, make all negative, or strip signs. Handy for cleaning data. Processed locally.
整数转回文数Convert Integer to Palindrome
把整数变成回文数：在末尾追加反转数字（保留符号），或仅反转数字。适合趣味数学和练习，本地处理。Turn integers into palindromes by appending the reversed digits (keeping the sign), or only reverse the digits. Handy for recreational math. Processed locally.
整数转英文 / 中文读法Convert Integers to Words
把整数写成英文（one hundred twenty-three）或中文（一百二十三）读法，支持正负和很大的数。适合支票、朗读稿和教学，本地处理。Write integers in English (one hundred twenty-three) or Chinese reading forms, including negatives and large values. Handy for cheques, scripts and teaching. Processed locally.
英文 / 中文数字词转整数Convert Words to Integers
把英文或中文数字读法还原为整数（one hundred → 100，一百二十三 → 123）。每行一个短语，本地处理。Turn English or Chinese number words back into integers (one hundred -> 100). One phrase per line. Processed locally.
从文本中提取整数Extract Integers from Data
从任意文本中提取整数（含负数、千位逗号），按出现顺序列出。适合从日志、表格粘贴中捞数字，本地处理。Extract integers (including negatives and thousands commas) from arbitrary text, in order of appearance. Handy for pulling numbers from logs or pasted tables. Processed locally.
找出最大整数Find Max Integer
从一串整数中找出最大值（可同时显示位置）。本地处理。可设置「显示位置」、「千位逗号」。Find the maximum in a list of integers (optionally with its position). Processed locally. Settings: Show position, Thousands commas.
找出最小整数Find Min Integer
从一串整数中找出最小值（可同时显示位置）。本地处理。可设置「显示位置」、「千位逗号」。Find the minimum in a list of integers (optionally with its position). Processed locally. Settings: Show position, Thousands commas.
整数累计求和Find Running Total
计算整数序列的累计和（前缀和），每一步显示到目前为止的总和。本地处理。可设置「显示加数」、「千位逗号」。Compute the running (prefix) sum of a sequence of integers, showing the total so far at each step. Processed locally. Settings: Show addends, Thousands commas.
整数累计求积Find Running Product
计算整数序列的累计积，每一步显示到目前为止的乘积。本地处理。可设置「显示乘数」、「千位逗号」。Compute the running product of a sequence of integers, showing the product so far at each step. Processed locally. Settings: Show factors, Thousands commas.
连接整数列表Join Integers
把多个整数用指定分隔符连接成一行（或保持每行一个）。可加千位逗号。本地处理。可设置「分隔」、「千位逗号」。Join integers with a chosen separator into one line (or keep one per line). Optional thousands commas. Processed locally. Settings: Separator, Thousands commas.
整数各位数字相乘Multiply Integer Digits
把每个整数的各位数字相乘（忽略符号与前导零处理按数字本身），可反复乘到只剩一位（数字根相关）。本地处理。Multiply the digits of each integer together (sign ignored for the product of digits). Optionally repeat until a single digit remains. Processed locally.