🔬 科学与工程Science & Engineering
欧姆定律计算器Ohm's Law Calculator
填写电压、电流、电阻、功率中的任意两个，计算其余两个（V=IR，P=VI）。Enter any two of voltage, current, resistance and power to get the other two (V = IR, P = VI).
色环电阻计算器Resistor Color Code Calculator
选择 4 环或 5 环电阻的颜色，计算阻值、误差范围，并显示色环图示。Pick the bands of a 4- or 5-band resistor to get resistance and tolerance, with a drawing.
分压电路计算器Voltage Divider Calculator
计算电阻分压电路的输出电压：Vout = Vin × R2 / (R1 + R2)，以及电流和功耗。Output voltage of a resistor divider: Vout = Vin × R2 / (R1 + R2), plus current and power.
LED 限流电阻计算器LED Resistor Calculator
根据电源电压、LED 正向电压和电流计算限流电阻值、功率，并推荐 E24 标准阻值。Current-limiting resistor for LEDs from supply voltage, forward voltage and current, with the nearest E24 value.
速度距离时间计算器Speed, Distance & Time Calculator
填写速度、距离、时间中的任意两个，计算第三个。Enter any two of speed, distance and time to calculate the third.
密度质量体积计算器Density, Mass & Volume Calculator
填写密度、质量、体积中的任意两个，计算第三个（ρ = m / V），并对照常见物质密度。Enter any two of density, mass and volume to find the third (ρ = m/V), with common material densities.
动能势能计算器Kinetic & Potential Energy Calculator
计算物体的动能（½mv²）和重力势能（mgh），以及从该高度落下时的着地速度。Kinetic energy (½mv²), gravitational potential energy (mgh) and impact speed from that height.
抛体运动计算器Projectile Motion Calculator
根据初速度、发射角和初始高度计算射程、最大高度和飞行时间（忽略空气阻力）。Range, maximum height and flight time from launch speed, angle and height (no air resistance).
半衰期计算器Half-Life Calculator
计算放射性衰变后剩余量：N = N₀ × (1/2)^(t/T)，或由剩余比例反推经过时间。Remaining quantity after decay, N = N₀ × (½)^(t/T), or the time elapsed from the remaining fraction.
摩尔质量计算器Molar Mass Calculator
输入化学式（如 H2O、Ca(OH)2、CuSO4·5H2O），计算摩尔质量和各元素质量分数。Molar mass and element mass percentages from a chemical formula like H2O, Ca(OH)2 or CuSO4·5H2O.
理想气体状态方程计算器Ideal Gas Law Calculator
PV = nRT：填写压强、体积、物质的量、温度中的三个，计算第四个。PV = nRT: enter three of pressure, volume, moles and temperature to solve for the fourth.
波长频率能量换算Wavelength, Frequency & Photon Energy
电磁波波长、频率和光子能量互算（c = λf，E = hf），并显示所属波段。Convert between wavelength, frequency and photon energy (c = λf, E = hf) and show the band.
溶液稀释计算器（C1V1=C2V2）Dilution Calculator (C1V1 = C2V2)
按 C1V1 = C2V2 计算溶液稀释所需体积：留空一个值即可求解。Solve C1V1 = C2V2 for any one unknown — how much stock and diluent to use.
pH 值计算器pH Calculator
由氢离子浓度 [H⁺]、氢氧根浓度 [OH⁻]、pH 或 pOH 中任意一个，计算其余值（25°C）。From [H⁺], [OH⁻], pH or pOH, calculate the others (at 25 °C).
在其他星球上的体重Weight on Other Planets
输入你在地球上的体重，看看在月球、火星、木星等星球上有多重。See what you'd weigh on the Moon, Mars, Jupiter and other planets.
电容代码换算Capacitor Code Calculator
把电容上的 3 位数字代码（如 104、472）换算为 pF/nF/µF，或反向求代码。Decode 3-digit capacitor codes (e.g. 104, 472) to pF/nF/µF, or find the code for a value.
AWG 线规换算AWG Wire Gauge Converter
美国线规 AWG 与线径(mm)、截面积(mm²)互相换算，并显示参考电阻。Convert AWG wire gauge to diameter (mm), cross-section (mm²) and resistance per km.
加速度计算器Acceleration Calculator
用速度变化与时间、力与质量，或距离与时间计算加速度，并换算为 g 值。Calculate acceleration from change in velocity over time, force and mass, or distance and time, and express it in g.
速度计算器Velocity Calculator
用位移和时间（v = d/t）或初速度、加速度和时间（v = v₀ + at）计算速度，并换算成 km/h、mph。Find velocity from displacement and time (v = d/t) or from initial velocity, acceleration and time (v = v₀ + at), in m/s, km/h and mph.
转动惯量计算器Moment of Inertia Calculator
计算实心球、空心球、圆柱、圆环、细杆、矩形板和质点绕常用转轴的转动惯量。Moment of inertia of spheres, cylinders, rings, rods, plates and point masses about common axes.
扭矩计算器Torque Calculator
由力、力臂长度和夹角计算扭矩 τ = r·F·sinθ，结果同时给出 N·m、lb·ft 和 kgf·m。Torque τ = r·F·sinθ from force, lever arm and angle, shown in N·m, lb·ft and kgf·m.
角速度计算器Angular Velocity Calculator
由转速（rpm）、转角与时间或线速度与半径计算角速度，换算 rad/s、°/s、rpm 和 Hz。Find angular velocity from rpm, angle over time, or linear speed and radius, in rad/s, °/s, rpm and Hz.
电势计算器Electric Potential Calculator
计算点电荷在距离 r 处产生的电势 V = kq/r，以及放入试探电荷时的电势能 U = kq₁q₂/r。Electric potential V = kq/r of a point charge at distance r, and the potential energy U = kq₁q₂/r with a second charge.
露点计算器Dew Point Calculator
由气温和相对湿度用 Magnus 公式计算露点温度，并给出体感舒适度提示。Calculate dew point from air temperature and relative humidity with the Magnus formula, plus a comfort hint.
体感温度（炎热指数）计算器Heat Index Calculator
按美国国家气象局（NWS）算法由气温和相对湿度计算炎热指数（体感温度）和危险等级。Heat index (feels-like temperature) from air temperature and humidity using the US National Weather Service algorithm, with risk level.
电池续航计算器Battery Life Calculator
根据电池容量（mAh 或 Wh）、设备平均电流或功率以及可用容量比例估算电池续航时间。Estimate battery runtime from capacity (mAh or Wh), average current or power draw and usable capacity.
动量计算器Momentum Calculator
p = m·v：输入任意两项求第三项（留空要求的那一项），并给出动能。p = m·v: enter any two of momentum, mass and velocity (leave the unknown blank) to solve the third, with kinetic energy.
摩擦力计算器Friction Calculator
F = μ·N：由摩擦系数和法向力（或质量与斜面角）计算摩擦力，附常见材料摩擦系数。Friction F = μ·N from the coefficient and normal force (or mass on an incline), with typical coefficients.
万有引力计算器Gravitational Force Calculator
用牛顿万有引力定律 F = G·m₁·m₂/r² 计算两物体间的引力，支持科学计数法（如 5.972e24）。Newton's law of gravitation F = G·m₁·m₂/r² between two masses; scientific notation like 5.972e24 is accepted.
时间膨胀计算器Time Dilation Calculator
按狭义相对论计算高速运动时的时间膨胀：洛伦兹因子 γ、静止参考系经过的时间和长度收缩。Special-relativity time dilation: Lorentz factor γ, elapsed time for the stationary observer and length contraction.
电压降计算器Voltage Drop Calculator
按导线材料、截面积（mm² 或 AWG）、单程长度、电流和系统电压计算线路压降和末端电压。Voltage drop and end voltage from conductor material, size (mm² or AWG), one-way length, current and system voltage.
摩尔浓度计算器Molarity Calculator
由溶质质量、摩尔质量和溶液体积计算摩尔浓度（mol/L），或反算配制所需溶质质量。Calculate molarity (mol/L) from solute mass, molar mass and solution volume, or the mass needed for a target concentration.
电子排布式计算器Electron Configuration Calculator
输入元素符号、中文/英文名称或原子序数（1–118），给出基态电子排布式、稀有气体简写、各电子层电子数和最外层（主量子数最大的电子层）电子数，并按实测数据处理铬、铜等例外；也可输入离子电荷。Enter an element symbol, name or atomic number (1–118) to get its ground-state electron configuration, noble-gas shorthand, electrons per shell and the electrons in the outermost shell (highest n) — with measured exceptions such as chromium and copper — and optionally an ion charge.
风寒指数（体感温度）计算器Wind Chill Calculator
按美国国家气象局（NWS）与加拿大环境部 2001 年联合公式，由气温和风速计算风寒温度（体感温度），并给出冻伤风险等级；支持 °C + km/h 和 °F + mph 两套单位。Calculate the wind chill temperature from air temperature and wind speed with the 2001 formula used by the US National Weather Service and Environment Canada, with a frostbite risk level, in °C with km/h or °F with mph.
产率计算器（百分产率）Percent Yield Calculator
用 实际产量 ÷ 理论产量 × 100% 计算化学反应的百分产率，也可由产率和理论产量反求实际产量，或由实际产量和产率反求理论产量。Calculate the percent yield of a reaction, actual ÷ theoretical × 100%, or solve for the actual yield or theoretical yield from the other two.
滴定计算器（求未知浓度）Titration Calculator
根据酸碱滴定的终点数据计算未知溶液的浓度：n₁·C₁·V₁ = n₂·C₂·V₂，可填写每摩尔待测物消耗的滴定剂摩尔数（如 NaOH 滴定 H₂SO₄ 填 2），体积可用 mL 或 L。Work out the concentration of an unknown solution from titration end-point data using n₁·C₁·V₁ = n₂·C₂·V₂, with the moles of titrant per mole of analyte (e.g. 2 for NaOH titrating H₂SO₄) and volumes in mL or L.
实验式（最简式）计算器Empirical Formula Calculator
由各元素的质量百分比或质量（克）计算化合物的实验式（最简式），列出摩尔数和比例；填入摩尔质量还能求出分子式。Find a compound's empirical formula from the mass percent or grams of each element, with the mole amounts and ratios; add the molar mass to get the molecular formula too.
浮力计算器（阿基米德原理）Buoyancy Calculator (Archimedes' Principle)
按阿基米德原理 F = ρ·g·V 计算物体在液体中受到的浮力，并根据物体密度判断它会漂浮还是下沉、漂浮时有多少体积浸在液体中。Calculate the buoyant force F = ρ·g·V from Archimedes' principle, and from the object's density tell whether it floats or sinks and how much of it sits below the surface.
自由落体计算器Free Fall Calculator
在忽略空气阻力的条件下，由下落高度、时间或末速度中的任意一个求出另外两个，可选择地球、月球、火星等重力加速度，并可设置初速度。Ignoring air resistance, give any one of fall height, time or final speed and get the other two, with Earth, Moon or Mars gravity and an optional initial downward speed.
声速计算器Speed of Sound Calculator
按理想气体公式 v = √(γRT/M) 计算干燥空气中随温度变化的声速，也可选水、钢等介质的典型声速；还能由声音传播时间算距离（例如看到闪电后几秒听到雷声）。Calculate the speed of sound in dry air at any temperature with v = √(γRT/M), or use typical values for water, steel and other media — and turn a delay into a distance, such as the seconds between lightning and thunder.
功的计算器（物理）Work Calculator (Physics)
按 W = F·d·cos θ 计算力对物体做的功，可求功、力或位移中的任意一个，并由做功时间算出平均功率；结果同时给出焦耳、千焦、千瓦时和卡路里。Calculate mechanical work W = F·d·cos θ — or solve for the force or distance — and the average power from the time taken, with results in joules, kilojoules, kilowatt-hours and calories.
热膨胀计算器Thermal Expansion Calculator
按 ΔL = α·L₀·ΔT 计算材料受热后的长度变化（线膨胀），或按 ΔV = β·V₀·ΔT 计算体积变化；内置钢、铝、铜、玻璃、混凝土等常见材料的典型线膨胀系数。Calculate how much a material grows when heated — linear expansion ΔL = α·L₀·ΔT, or volumetric expansion ΔV = β·V₀·ΔT — with typical coefficients for steel, aluminium, copper, glass, concrete and more.
原木重量计算器（材积公式与木材密度）Log Weight Calculator (Log Volume and Wood Density)
输入原木长度和直径（一个直径按圆柱计算，或两端直径按 Smalian 公式），选择木材状态和类别（湿材或气干材，硬木或软木）或自定义密度，算出材积和重量。支持米/厘米和英尺/英寸。本地处理。Enter the log length and diameter (one diameter for a cylinder, or both end diameters for the Smalian formula), pick the wood type and condition (green or seasoned, hardwood or softwood) or enter a density, and get the volume and weight. Works in m and cm or ft and in. Processed locally.
含水率计算器（干基/湿基互换、加水或烘干到目标）Moisture Content Calculator (Dry or Wet Basis, Water to Add or Remove)
由湿重和干重计算含水率，同时给出干基（水 ÷ 干重，木材和土壤常用）和湿基（水 ÷ 湿重，粮食和食品常用）两种结果；也可以在两种基准之间换算，或计算把一批物料调整到目标含水率需要去除或加入多少水。本地处理。Work out moisture content from wet and dry weight on both the dry basis (water / dry weight, used for wood and soil) and the wet basis (water / wet weight, used for grain and food), convert between the two, or find how much water to remove or add to bring a batch to a target moisture. Processed locally.
轨道周期计算器（开普勒第三定律，地球/太阳/月球等）Orbital Period Calculator (Kepler Third Law, Earth, Sun, Moon and More)
选择中心天体（地球、太阳、月球、火星、木星或自定义质量），输入轨道半长轴或离表面的高度，用开普勒第三定律 T = 2π√(a³/GM) 求轨道周期，并给出圆轨道速度；也可以反过来由周期求半长轴和高度（例如地球同步轨道）。本地处理。Choose the central body (Earth, Sun, Moon, Mars, Jupiter or a custom mass), enter the semi-major axis or the altitude above the surface, and get the period from Kepler third law T = 2π√(a³/GM) with the circular orbital speed, or work back from a period to the semi-major axis and altitude (such as geostationary orbit). Processed locally.
分压计算器（道尔顿分压定律，多组分与单位换算）Partial Pressure Calculator (Dalton Law, Several Gases, Unit Conversion)
按道尔顿分压定律计算：由摩尔分数和总压求分压；由各组分的物质的量（每行“名称, 摩尔数”）求每种气体的摩尔分数和分压；或由各组分分压求总压和摩尔分数。支持 Pa、kPa、atm、bar、mmHg 和 psi。本地处理。Use Dalton law to get a partial pressure from the mole fraction and total pressure; the mole fraction and partial pressure of each gas from amounts in moles (one line each: name, moles); or the total pressure and mole fractions from each partial pressure. Works in Pa, kPa, atm, bar, mmHg and psi. Processed locally.
功率重量比计算器（汽车、摩托车、骑行 W/kg）Power-to-Weight Ratio Calculator (Cars, Motorbikes, Cycling W/kg)
输入功率（W、kW、hp 或 PS）和质量（kg 或 lb），计算功率重量比：W/kg、kW/t、hp/吨、每马力承担的重量 kg/hp 和 lb/hp。车辆可选择是否加上驾驶员体重；骑行时可以直接用 FTP 和体重得到 W/kg。本地处理。Enter power (W, kW, hp or PS) and mass (kg or lb) to get the power-to-weight ratio as W/kg, kW/t and hp per tonne, plus the weight per horsepower in kg/hp and lb/hp. Add a driver for vehicles, or use FTP and body weight for cycling W/kg. Processed locally.
相对湿度计算器（露点 ↔ 相对湿度、绝对湿度）Relative Humidity Calculator (Dew Point ↔ RH, Absolute Humidity)
用 Magnus 公式在气温、露点和相对湿度之间互算：由气温和露点求相对湿度，或由气温和相对湿度求露点。同时给出饱和水汽压、实际水汽压、绝对湿度 (g/m³) 和混合比。支持 °C 和 °F。本地处理。Converts between air temperature, dew point and relative humidity with the Magnus formula: RH from temperature and dew point, or dew point from temperature and RH. Also gives saturation and actual vapour pressure, absolute humidity in g/m³ and mixing ratio. °C or °F. Processed locally.
合力计算器（分量或大小+方向，二维/三维）Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D)
把多个力合成为一个合力。可按分量输入 Fx、Fy（可选 Fz），也可按“大小 + 方向角”输入（角度从 +x 轴逆时针量）。给出合力分量、大小、方向角，以及让物体平衡所需的平衡力；输入质量可求加速度 a = F/m。本地处理。Combines several forces into one resultant. Enter components Fx, Fy (and optionally Fz), or magnitudes with direction angles measured anticlockwise from the +x axis. Gives the resultant components, magnitude and direction, the equilibrant force that would balance them, and the acceleration a = F/m if you enter a mass. Processed locally.
圆柱模板混凝土计算器（体积、袋数、多根）Sonotube Concrete Calculator (Volume, Bags, Several Tubes)
计算圆形纸管（Sonotube）柱墩的混凝土用量：输入直径、高度和数量（米或英寸/英尺），得出体积（m³、立方码、立方英尺、升），加损耗后的总量，以及需要多少袋 40/60/80 磅或 25 kg 预拌混凝土。本地处理。Works out concrete for round Sonotube piers: enter the diameter, height and number of tubes (metric or inches and feet) to get the volume in m³, cubic yards, cubic feet and litres, the total with waste, and how many 40, 60 or 80 lb or 25 kg bags of premix you need. Processed locally.
比重计算器（密度、质量与体积、水中称重）Specific Gravity Calculator (Density, Mass and Volume, Weighing in Water)
三种方法求比重 SG：由密度和参考密度（默认 4 °C 水 1000 kg/m³）；由质量和体积；或用阿基米德法（空气中重量 ÷ (空气中重量 − 水中重量)）。同时给出 g/cm³、lb/ft³ 密度，以及 API 度、波美度等换算和是否浮于水。本地处理。Three ways to get specific gravity: from density and a reference density (water at 4 °C, 1000 kg/m³, by default); from mass and volume; or by Archimedes (weight in air ÷ (weight in air − weight in water)). Also gives density in g/cm³ and lb/ft³, API gravity and Baumé degrees, and whether it floats in water. Processed locally.
比热容计算器（求热量、比热、质量或温差，含常见物质）Specific Heat Calculator (Solve for Heat, c, Mass or ΔT, With Common Materials)
用 Q = m·c·ΔT 求任意一个未知量：热量 Q、比热容 c、质量 m 或温度变化 ΔT（也可输入初温和末温）。内置水、冰、铝、铜、铁、空气等常见物质比热，结果同时给出 kJ、kcal 和 Wh。本地处理。Uses Q = m·c·ΔT to solve for any one unknown: heat Q, specific heat c, mass m or temperature change ΔT (or enter start and end temperatures). Includes specific heats of water, ice, aluminium, copper, iron, air and more, and shows results in kJ, kcal and Wh. Processed locally.
化学计量计算器（质量换算、限量反应物、产率）Stoichiometry Calculator (Mass to Mass, Limiting Reactant, Percent Yield)
按配平方程式的系数比做化学计量：由一种反应物的质量求产物的理论质量；输入两种反应物的质量找出限量反应物和过量剩余；输入实际产量求产率。可直接输入化学式自动计算摩尔质量。本地处理。Stoichiometry from the coefficients of a balanced equation: the theoretical mass of product from one reactant; the limiting reactant and leftover excess from two reactant masses; and percent yield from the actual amount obtained. Enter chemical formulas to compute molar masses automatically. Processed locally.
石料计算器（面积 × 厚度、体积、重量、袋数、费用）Stone Calculator (Area × Depth, Volume, Weight, Bags, Cost)
估算碎石、砾石、卵石、河石等石料用量：直接输入体积，或输入铺设面积和厚度（米/厘米或英尺/英寸）。按所选石料的堆积密度求重量（kg、吨、短吨），并给出立方码、袋数和费用估算。本地处理。Estimates crushed stone, gravel, pea gravel or river rock: enter a volume directly, or an area and depth in metres and centimetres or feet and inches. The bulk density of the chosen stone gives the weight in kg, tonnes and US tons, plus cubic yards, bag count and a cost estimate. Processed locally.
锥度计算器（锥度比、锥角、每英尺锥度、求未知直径）Taper Calculator (Taper Ratio, Angle, Taper per Foot, Missing Diameter)
由大端直径 D、小端直径 d 和长度 L 求锥度 (D − d)/L、1:n 锥度比、半角和全角（锥角）、每英尺锥度 (TPF) 和每英寸锥度；也可以由已知锥度或角度反求小端直径或长度。适用于车床加工、莫氏锥度等。本地处理。From the large diameter D, small diameter d and length L get the taper (D − d)/L, the 1:n taper ratio, the half angle and included angle, taper per foot (TPF) and per inch; or work back from a known taper or angle to the small diameter or the length. For lathe work, Morse tapers and similar. Processed locally.
张力计算器（竖直加速、斜拉两绳、斜面、滑轮两物体）Tension Calculator (Vertical, Two Angled Ropes, Incline, Pulley With Two Masses)
四种常见绳张力情形：竖直吊挂并加速 T = m(g + a)；两根斜绳吊挂一个物体（给出两绳与水平线的夹角）；斜面上被平行于斜面的绳拉住的物体（可含摩擦）；以及跨过定滑轮的两物体（阿特伍德机）的加速度和张力。本地处理。Four common rope tension set-ups: a hanging mass accelerating vertically, T = m(g + a); a mass hung from two angled ropes (angles from the horizontal); a mass on an incline held by a rope parallel to the slope (with optional friction); and two masses over a fixed pulley (Atwood machine) with the acceleration and tension. Processed locally.
变压器计算器（匝数比、副边电压、电流与容量）Transformer Calculator (Turns Ratio, Secondary Voltage, Current and VA)
理想变压器：Vp/Vs = Np/Ns = Is/Ip。可由匝数算副边电压，或由两侧电压算匝数比；再填容量（VA）或副边电流，得到两侧电流，并判断升压/降压。本地处理。Ideal transformer: Vp/Vs = Np/Ns = Is/Ip. Get the secondary voltage from the turns, or the turns ratio from both voltages; add the rating (VA) or the secondary current to get both currents, and see whether it steps up or down. Processed locally.
蒸气压计算器（Antoine 方程，常见液体常数）Vapor Pressure Calculator (Antoine Equation, Common Liquids)
用 Antoine 方程 log₁₀P = A − B/(C + T) 计算饱和蒸气压，内置水、乙醇、甲醇、丙酮、苯的常数（mmHg、°C），也可自填常数；结果换算成 mmHg、kPa、atm 和 bar，并提示温度是否超出常数适用范围。本地处理。Calculate the saturation vapor pressure with the Antoine equation log₁₀P = A − B/(C + T). Built-in constants (mmHg, °C) for water, ethanol, methanol, acetone and benzene, or enter your own; results in mmHg, kPa, atm and bar, with a warning when the temperature is outside the constants' valid range. Processed locally.
瓦时计算器（功率×时间、电池 V×Ah、续航时间）Watt-Hour Calculator (Power × Time, Battery V × Ah, Runtime)
计算电能：功率 × 时间，或电池电压 × 容量（Ah 或 mAh），或由 kWh 换算；结果给出 Wh、kWh、焦耳，并可填负载功率和效率估算续航时间。本地处理。Calculate energy as power × time, as battery voltage × capacity (Ah or mAh), or from kWh. Results in Wh, kWh and joules; add a load power and efficiency to estimate the runtime. Processed locally.
湿球温度计算器（干湿表方程 + Stull 公式，含露点）Wet-Bulb Temperature Calculator (Psychrometric Equation + Stull Formula, with Dew Point)
由气温、相对湿度和气压算湿球温度：用干湿表方程迭代求解（考虑气压），同时给出 Stull（2011）经验公式结果和露点，并按湿球温度提示热应激风险。本地处理。Find the wet-bulb temperature from air temperature, relative humidity and pressure: solved iteratively with the psychrometric equation (pressure included), alongside the Stull (2011) empirical formula and the dew point, with a heat-stress note based on the wet-bulb temperature. Processed locally.
导线截面积计算器（按压降选线，铜/铝，单相/三相，AWG）Wire Size Calculator (Voltage Drop, Copper/Aluminium, Single/Three Phase, AWG)
按允许电压降计算所需导线截面积：输入电流、单程长度、电压和允许压降百分比，选择铜或铝、直流/单相或三相，得到最小截面积、推荐的标准规格（mm²）和近似 AWG，以及选用该规格时的实际压降。载流量还取决于敷设方式，请同时核对规范。本地处理。Find the wire cross-section needed for an allowed voltage drop: enter current, one-way length, voltage and allowed drop %, pick copper or aluminium and DC/single phase or three phase, and get the minimum area, the recommended standard size (mm²), the nearest AWG and the actual drop with that size. Ampacity also depends on installation, so check your wiring code too. Processed locally.
弹性势能计算器（E = ½kx²，可反求 k 或 x，弹力）Elastic Potential Energy Calculator (E = ½kx², Solve for k or x, Spring Force)
胡克弹簧的弹性势能 E = ½kx²：由劲度系数和形变量求能量，或由能量反求劲度系数或形变量；同时给出弹力 F = kx。形变量可用 m、cm 或 mm。本地处理。Elastic potential energy of a Hookean spring, E = ½kx²: get the energy from the spring constant and displacement, or solve for the spring constant or displacement from the energy. Also gives the spring force F = kx. Displacement in m, cm or mm. Processed locally.
溶液浓度示意Concentration Calculator
c = n/V（mol/L）或质量浓度 m/V。本地处理。可设置「模式」、「溶质（mol 或 g）」、「溶液体积 L」。c = n/V (mol/L) or mass concentration m/V. Processed locally. Settings: Mode, Solute (mol or g), Solution volume L.
超焦距计算器（焦距、光圈、弥散圆）Hyperfocal Distance Calculator (Focal Length, f-Number, CoC)
H ≈ f²/(N·c) + f，其中 f 为焦距(mm)、N 为光圈系数、c 为弥散圆直径(mm)。再给出米制结果。本地处理。H ≈ f²/(N·c) + f with focal length f (mm), f-number N and circle of confusion c (mm), plus metres. Processed locally.
氢离子浓度 / pH 计算器Hydrogen Ion Concentration / pH Calculator
由 pH 求 [H+]=10^(-pH)（并示意 25C 的 [OH-]），或由 [H+] 求 pH。本地处理。可设置「已知」、「pH」、「[H⁺] mol/L」。From pH get [H+]=10^(-pH) (with a 25C [OH-] demo), or from [H+] get pH. Processed locally. Settings: Known, pH, [H⁺] mol/L.
稀释倍数计算器Dilution Factor Calculator
按体积比 DF = V_final / V_stock，或按浓度比 DF = C1/C2。本地处理。可设置「模式」、「原液体积」、「终体积」、「C₁」、「C₂」。By volumes DF = V_final / V_stock, or by concentrations DF = C1/C2. Processed locally. Settings: Mode, Stock volume, Final volume, C₁, C₂.
离子强度计算器Ionic Strength Calculator
I = 1/2 Sum c_i z_i^2。每行填写：浓度(mol/L) 与电荷数 z。本地处理。I = 1/2 Sum c_i z_i^2. Each line: concentration (mol/L) and charge z. Processed locally.
摩尔比计算器Molar Ratio Calculator
由两份物质的量 n1、n2 给出比值 n1/n2 与未约分的 n1 : n2。二者须大于 0。本地处理。From amounts n1 and n2 get the quotient n1/n2 and the unreduced ratio n1 : n2. Both must be greater than 0. Processed locally.
皂化值估算器（示意）Saponification Value Estimator (Demo)
示意 SV ≈ 56100 / 平均摩尔质量(g/mol)，单位 mg KOH / g 油脂。非实验滴定。本地处理。Demo SV ≈ 56100 / average molar mass (g/mol), in mg KOH per g fat. Not a lab titration. Processed locally.
真空速估算器（示意）True Airspeed Estimator (Demo)
TAS ≈ IAS × √(ρ₀/ρ) 密度比示意（简化）。本地处理。可设置「指示空速」、「密度比 ρ/ρ₀」。TAS ≈ IAS × √(ρ₀/ρ) density-ratio demo (simplified). Processed locally. Settings: Indicated airspeed, Density ratio ρ/ρ₀.
螺栓圆坐标Bolt Circle Calculator
在直径 D 的圆上均布 n 个孔的坐标（从角 0° 起）。本地处理。可设置「直径」、「孔数」、「起始角 °」。Coordinates of n holes on a circle of diameter D from angle 0°. Processed locally. Settings: Diameter, Holes, Start angle °.
酒精稀释Alcohol Dilution
C₁V₁ = C₂V₂：由浓酒兑水到目标酒精度。本地处理。可设置「原酒精度 %」、「原体积」、「目标酒精度 %」。C₁V₁ = C₂V₂: dilute strong spirit to a target ABV. Processed locally. Settings: Source ABV %, Source volume, Target ABV %.
截止频率（RC）Cutoff Frequency (RC)
f_c = 1 / (2π R C)。本地处理。可设置「电阻 Ω」、「电容 F」。f_c = 1 / (2π R C). Processed locally. Settings: Resistance Ω, Capacitance F.
树木年龄示意Tree Age (demo)
年龄 ≈ 胸径(英寸) × 生长因子。本地处理。可设置「胸径 英寸」、「生长因子」。Age ≈ diameter (inches) × growth factor. Processed locally. Settings: DBH inches, Growth factor.
切削速度与进给Speeds and Feeds
主轴转速 n = 1000 V / (π D)；进给 F = n × f × z。本地处理。可设置「切削速度 m/min」、「刀具直径 mm」、「每齿进给 mm」、「齿数」。Spindle n = 1000 V / (π D); feed F = n × f × z. Processed locally. Settings: Cutting speed m/min, Tool diameter mm, Feed per tooth mm, Flutes.
卷材长度Roll Length
长度 ≈ π × 层数 × (外径+内径)/2（示意）。本地处理。可设置「外径」、「内径」、「厚度」。Length ≈ π × layers × (OD+ID)/2 (demo). Processed locally. Settings: Outer diameter, Inner diameter, Thickness.
有效值电压RMS Voltage
正弦波 V_rms = V_peak / √2；也可由峰峰值。本地处理。可设置「已知」、「电压」。Sine V_rms = V_peak / √2; or from peak-to-peak. Processed locally. Settings: Given, Voltage.
惠斯通电桥Wheatstone Bridge
平衡：R₁/R₂ = R₃/R₄；未知 Rₓ = R₂×R₃/R₁。本地处理。可设置「R₁」、「R₂」、「R₃」。Balance R₁/R₂ = R₃/R₄; unknown Rₓ = R₂×R₃/R₁. Processed locally. Settings: R₁, R₂, R₃.
LC 谐振频率LC Resonant Frequency
f₀ = 1 / (2π √(L C))。本地处理。可设置「电感 H」、「电容 F」。f₀ = 1 / (2π √(L C)). Processed locally. Settings: Inductance H, Capacitance F.
分频点（示意）Crossover Frequency (demo)
一阶 RC：f_c = 1/(2π R C)；也可由目标 f 反推 C。本地处理。可设置「计算」、「电阻 Ω」、「电容 F」、「目标频率 Hz」。First-order RC: f_c = 1/(2π R C); or solve C from target f. Processed locally. Settings: Solve, Resistance Ω, Capacitance F, Target Hz.
压缩比Compression Ratio
CR = V_max / V_min。本地处理。可设置「最大容积」、「最小容积」。CR = V_max / V_min. Processed locally. Settings: Max volume, Min volume.
瓷砖填缝用量Grout Calculator
填缝体积示意 ≈ 缝长×缝宽×缝深。本地处理。可设置「缝总长」、「缝宽」、「缝深」。Grout volume demo ≈ length × width × depth of joints. Processed locally. Settings: Joint length, Joint width, Joint depth.
简支梁均布荷载挠度示意Simply Supported Beam Deflection (demo)
δ_max = 5 w L⁴ / (384 E I)。本地处理。可设置「均布荷载 w」、「跨度 L」、「弹性模量 E」、「惯性矩 I」。δ_max = 5 w L⁴ / (384 E I). Processed locally. Settings: UDL w, Span L, Modulus E, Inertia I.
比尔-朗伯定律Beer-Lambert Law
A = ε c l。本地处理。可设置「ε」、「浓度 c」、「光程 l」。A = ε c l. Processed locally. Settings: ε, Concentration c, Path length l.
皮带周长示意Belt Length (demo)
开口皮带 L ≈ 2C + π(D+d)/2 + (D-d)²/(4C)。本地处理。可设置「中心距 C」、「大轮直径 D」、「小轮直径 d」。Open belt L ≈ 2C + π(D+d)/2 + (D-d)²/(4C). Processed locally. Settings: Center distance C, Large pulley D, Small pulley d.
沸点海拔修正示意Boiling Point vs Altitude (demo)
示意：沸点 ≈ 100 - 海拔(m)/300（粗估）。本地处理。可设置「海拔 m」。Demo: BP ≈ 100 - altitude(m)/300 (rough). Processed locally. Settings: Altitude m.
沸点升高Boiling Point Elevation
ΔT_b = i · K_b · m。本地处理。可设置「范特霍夫 i」、「K_b」、「质量摩尔浓度 m」。ΔT_b = i · K_b · m. Processed locally. Settings: van ʼt Hoff i, K_b, Molality m.
螺栓扭矩计算器Bolt Torque Calculator
按 T = K × F × d 估算螺栓拧紧扭矩，可选力、直径和扭矩的单位（N/kN/lbf、mm/in、N·m/ft·lbf）。本地处理。Estimate bolt tightening torque with T = K × F × d, with selectable units for force, diameter and torque (N/kN/lbf, mm/in, N·m/ft·lbf). Processed locally.
相机裁切系数与等效焦距Crop Factor Calculator
裁切系数 = 全画幅对角线 43.27 mm / 传感器对角线；等效焦距 = 焦距 × 系数，等效光圈 = 光圈 × 系数。本地处理。Crop factor = 43.27 mm full-frame diagonal / sensor diagonal; equivalent focal length = focal × factor, equivalent aperture = f-number × factor. Processed locally.
德布罗意波长De Broglie Wavelength
λ = h / (m v)，h = 6.62607015×10⁻³⁴ J·s。本地处理。可设置「质量 kg」、「速度 m/s」。λ = h / (m v), with h = 6.62607015×10⁻³⁴ J·s. Processed locally. Settings: Mass kg, Velocity m/s.
多普勒效应（声波）Doppler Effect Calculator
f′ = f (v + v₀) / (v - vₛ)：观察者靠近 v₀ 取正，声源靠近 vₛ 取正（远离为负）。本地处理。f′ = f (v + v₀) / (v - vₛ): observer speed v₀ positive when approaching, source speed vₛ positive when approaching (negative when receding). Processed locally.
质能方程 E = mc²E = mc² Calculator
E = m c²，c = 299,792,458 m/s；同时换算为千瓦时和 TNT 当量。本地处理。可设置「质量 kg」。E = m c² with c = 299,792,458 m/s, also in kWh and TNT equivalent. Processed locally. Settings: Mass kg.
发动机排量Engine Displacement Calculator
排量 = π/4 × 缸径² × 行程 × 缸数。本地处理。可设置「缸径 mm」、「行程 mm」、「缸数」。Displacement = π/4 × bore² × stroke × cylinders. Processed locally. Settings: Bore mm, Stroke mm, Cylinders.
凝固点降低Freezing Point Depression Calculator
ΔT = i × Kf × m（i 范特霍夫因子，Kf 溶剂常数，m 质量摩尔浓度 mol/kg）。水的 Kf = 1.86 °C·kg/mol。本地处理。ΔT = i × Kf × m (i dissociation (van-t-Hoff) factor, Kf solvent constant, m molality in mol/kg). Water Kf = 1.86 °C·kg/mol. Processed locally.
建筑热损失Heat Loss Calculator
Q = U × A × ΔT（W）：U 为传热系数 W/(m²·K)，A 面积，ΔT 室内外温差；并估算每天耗能。本地处理。Q = U × A × ΔT (W): U-value W/(m²·K), area A and indoor-outdoor temperature difference; plus daily energy. Processed locally.
导热传热（傅里叶定律）Heat Transfer Calculator (Conduction)
Q = k × A × ΔT / d：k 导热系数 W/(m·K)，A 面积，ΔT 两侧温差，d 厚度；并给出热阻 R = d/(kA)。本地处理。Q = k × A × ΔT / d: conductivity k W/(m·K), area A, temperature difference ΔT and thickness d; plus thermal resistance R = d/(kA). Processed locally.
亨德森-哈塞尔巴尔赫方程（缓冲液 pH）Henderson-Hasselbalch Calculator
pH = pKa + log₁₀([A⁻]/[HA])；也可由目标 pH 反求所需的共轭碱/酸浓度比。本地处理。可设置「pKa」、「共轭碱 [A⁻] mol/L」、「弱酸 [HA] mol/L」、「目标 pH（可选）」。pH = pKa + log₁₀([A⁻]/[HA]); also gives the base/acid ratio needed for a target pH. Processed locally. Settings: pKa, Conjugate base [A⁻] mol/L, Weak acid [HA] mol/L, Target pH (optional).
斜面受力（含摩擦）Inclined Plane Calculator
质量 m 的物体在倾角 θ 的斜面上：沿斜面分力 mg sinθ，法向力 mg cosθ，摩擦力 μ mg cosθ，净加速度 a = g(sinθ - μ cosθ)。本地处理。For mass m on a slope of angle θ: parallel force mg sinθ, normal force mg cosθ, friction μ mg cosθ and acceleration a = g(sinθ - μ cosθ). Processed locally.
感抗 XL = 2πfLInductive Reactance Calculator
交流电路中电感的感抗 XL = 2πfL（欧姆），同时给出电流（若填电压）。本地处理。可设置「频率 Hz」、「电感 H」、「电压 V（可选）」。Inductive reactance in an AC circuit, XL = 2πfL (ohms), plus current if a voltage is given. Processed locally. Settings: Frequency Hz, Inductance H, Voltage V (optional).
kVA 视在功率kVA Calculator
单相 kVA = V × I / 1000，三相 kVA = √3 × V（线电压）× I / 1000；给出功率因数时同时算 kW。本地处理。Single-phase kVA = V × I / 1000; three-phase kVA = √3 × V (line) × I / 1000; with a power factor, kW too. Processed locally.
机械效益（理想 / 实际 / 效率）Mechanical Advantage Calculator
实际机械效益 AMA = 负载力 ÷ 施力，理想机械效益 IMA = 施力移动距离 ÷ 负载移动距离，效率 = AMA ÷ IMA。适用于杠杆、滑轮、斜面等。本地处理。Actual mechanical advantage AMA = load ÷ effort, ideal IMA = effort distance ÷ load distance, efficiency = AMA ÷ IMA. Works for levers, pulleys, ramps and more. Processed locally.
当量浓度（N）Normality Calculator
当量浓度 N = 溶质质量 ÷ 当量质量 ÷ 溶液体积，当量质量 = 摩尔质量 ÷ 当量数（酸的可电离 H⁺ 数、碱的 OH⁻ 数等）。同时给出摩尔浓度。本地处理。Normality N = solute mass ÷ equivalent weight ÷ solution volume, where equivalent weight = molar mass ÷ equivalents (H⁺ per acid, OH⁻ per base, etc.). Molarity is shown too. Processed locally.
渗透压（范特霍夫方程）Osmotic Pressure Calculator
π = i M R T：i 为解离因子，M 为摩尔浓度 mol/L，R = 0.082057 L·atm/(mol·K)，T 为绝对温度。本地处理。π = i M R T: i dissociation factor, M molarity in mol/L, R = 0.082057 L·atm/(mol·K) and T the absolute temperature. Processed locally.
PCB 走线宽度（IPC-2221）PCB Trace Width Calculator (IPC-2221)
IPC-2221：I = k × ΔT^0.44 × A^0.725（A 为截面积 mil²，外层 k = 0.048，内层 k = 0.024），由电流、允许温升和铜厚求最小线宽。本地处理。IPC-2221: I = k × ΔT^0.44 × A^0.725 (A cross-section in mil², k = 0.048 external, 0.024 internal) gives the minimum width from current, allowed temperature rise and copper weight. Processed locally.
管道流量与流速Pipe Flow Calculator
流量 Q = 截面积 × 流速，截面积 = π d² / 4；同时给出雷诺数（按 20 °C 水）判断层流或湍流。本地处理。Flow Q = cross-section × velocity, with area = π d² / 4; plus the Reynolds number (water at 20 °C) to tell laminar from turbulent. Processed locally.
串联电阻Resistors in Series Calculator
串联总电阻 R = R₁ + R₂ + …；填写电源电压时同时给出电流和每个电阻上的分压与功率。本地处理。Total series resistance R = R1 + R2 + ...; with a supply voltage, also the current and each resistor's voltage drop and power. Processed locally.
钢材重量Steel Weight Calculator
按形状和尺寸算钢材重量：钢板 = 长 × 宽 × 厚，圆钢 = π d²/4 × 长，钢管 = π (D² - d²)/4 × 长；密度默认 7850 kg/m³（不锈钢约 7930）。本地处理。Steel weight by shape: plate = length × width × thickness, round bar = π d²/4 × length, tube = π (D² - d²)/4 × length; density 7,850 kg/m³ by default (stainless ≈ 7,930). Processed locally.
刹车距离（反应 + 制动）Stopping Distance Calculator
停车距离 = 反应距离（车速 × 反应时间）+ 制动距离 v² / (2 μ g)。干燥沥青 μ ≈ 0.7，湿滑 ≈ 0.4，冰面 ≈ 0.1。本地处理。Stopping distance = reaction distance (speed × reaction time) + braking distance v² / (2 μ g). Dry asphalt μ ≈ 0.7, wet ≈ 0.4, ice ≈ 0.1. Processed locally.
功与功率Work and Power Calculator
功 W = F × d × cos θ（焦耳），功率 P = W ÷ t（瓦特），并换算为马力。本地处理。可设置「力 N」、「位移 m」、「力与位移夹角 °」、「时间 s」。Work W = F × d × cos θ (joules) and power P = W ÷ t (watts), also in horsepower. Processed locally. Settings: Force N, Displacement m, Angle between force and motion °, Time s.
角分辨率（瑞利判据）Angular Resolution Calculator
θ = 1.22 λ / D（弧度），λ 为波长、D 为口径；换算成角秒，并给出 Dawes 极限 116/D(mm) 角秒作为参考。本地处理。θ = 1.22 λ / D (radians) for wavelength λ and aperture D, in arcseconds too, with the Dawes limit 116 / D(mm) arcsec for reference. Processed locally.
望远镜口径面积与集光力Aperture Area Calculator
口径面积 = π D² / 4；集光力与面积成正比，和人眼瞳孔（默认 7 mm）比较；有中央遮挡时扣除副镜面积。本地处理。Aperture area = π D² / 4; light grasp scales with area, compared with a dark-adapted pupil (7 mm by default); a central obstruction is subtracted. Processed locally.
空气阻力（阻力方程）Drag Equation Calculator
F = ½ ρ v² C_d A：ρ 流体密度（空气 1.225 kg/m³），v 速度，C_d 阻力系数，A 迎风面积；并给出克服阻力所需功率 P = F v。本地处理。F = ½ ρ v² C_d A: fluid density ρ (air 1.225 kg/m³), speed v, drag coefficient C_d and frontal area A; plus the power to overcome it, P = F v. Processed locally.
弗劳德数Froude Number Calculator
Fr = v / √(g L)：v 流速，L 特征长度（明渠为水深）。Fr < 1 缓流（亚临界），= 1 临界，> 1 急流（超临界）。本地处理。Fr = v / √(g L): flow speed v and characteristic length L (water depth for open channels). Fr < 1 subcritical, = 1 critical, > 1 supercritical. Processed locally.
传热系数 hHeat Transfer Coefficient Calculator
对流传热系数 h = Q ÷ (A × ΔT)（W/(m²·K)）；也可由 h 反算热流。同时给出对应的热阻 1/(hA)。本地处理。Convective heat transfer coefficient h = Q ÷ (A × ΔT) in W/(m²·K), with the matching thermal resistance 1/(hA). Processed locally.
液压压力与输出力（帕斯卡原理）Hydraulic Pressure Calculator
压力 P = F ÷ A（A = π d²/4）；按帕斯卡原理，大活塞输出力 F₂ = P × A₂ = F₁ × (d₂/d₁)²。本地处理。Pressure P = F ÷ A (A = π d²/4); by Pascal's principle the output force is F₂ = P × A₂ = F₁ × (d₂/d₁)². Processed locally.
液体静压力Hydrostatic Pressure Calculator
P = ρ g h：液体密度 ρ（淡水 1000，海水约 1025 kg/m³）、深度 h；同时给出加上大气压后的绝对压力。本地处理。P = ρ g h for fluid density ρ (fresh water 1000, seawater about 1025 kg/m³) and depth h; plus the absolute pressure including the atmosphere. Processed locally.
努森数Knudsen Number Calculator
Kn = λ / L：分子平均自由程 λ 与特征长度 L 之比。Kn < 0.01 连续介质，0.01-0.1 滑移流，0.1-10 过渡区，> 10 自由分子流。本地处理。Kn = λ / L: mean free path λ over characteristic length L. Kn < 0.01 continuum, 0.01-0.1 slip, 0.1-10 transition, > 10 free-molecular. Processed locally.
长度收缩（相对论）Length Contraction Calculator
运动物体沿运动方向的长度 L = L₀ √(1 - v²/c²)，L₀ 为固有长度；同时给出洛伦兹因子 γ。本地处理。Length along the motion L = L₀ √(1 - v²/c²) for rest length L₀; the Lorentz factor γ is shown too. Processed locally.
雷电距离（声光时差）Lightning Distance Calculator
看到闪电到听到雷声的秒数 × 声速 ≈ 距离。声速用 331.3 + 0.606 × T(°C) m/s，或近似"秒数 ÷ 3 ≈ 公里"。本地处理。Seconds between flash and thunder × speed of sound ≈ distance. Sound speed is 331.3 + 0.606 × T(°C) m/s, or roughly "seconds ÷ 3 ≈ kilometres". Processed locally.
马赫数Mach Number Calculator
马赫数 Ma = v / a，当地声速 a = √(γ R T)，空气 γ = 1.4、R = 287.05 J/(kg·K)。Ma < 0.8 亚音速，0.8-1.2 跨音速，> 1 超音速，> 5 高超音速。本地处理。Mach number Ma = v / a with local speed of sound a = √(γ R T); for air γ = 1.4 and R = 287.05 J/(kg·K). Ma < 0.8 subsonic, 0.8-1.2 transonic, > 1 supersonic, > 5 hypersonic. Processed locally.
加速度大小（矢量）Magnitude of Acceleration
三维加速度矢量的大小 |a| = √(aₓ² + aᵧ² + aᵤ²)；也可用初速度、末速度和时间计算平均加速度。本地处理。Magnitude of a 3-D acceleration vector |a| = √(aₓ² + aᵧ² + aᵤ²); or the average acceleration from initial and final velocity and time. Processed locally.
马吕斯定律（偏振光透过）Malus Law Calculator
透过检偏器的光强 I = I₀ cos²θ，θ 为起偏器与检偏器透振方向的夹角；两个检偏器串联时用夹角差。本地处理。Intensity through an analyser I = I₀ cos²θ for the angle θ between polariser and analyser; for two analysers in series use the angle between them. Processed locally.
约化质量Reduced Mass Calculator
两体问题约化质量 μ = m₁ m₂ / (m₁ + m₂)，使相对运动等价于质量 μ 绕固定中心的运动。本地处理。Two-body reduced mass μ = m₁ m₂ / (m₁ + m₂), so relative motion equals mass μ orbiting a fixed centre. Processed locally.
转动动能Rotational Kinetic Energy Calculator
E = ½ I ω²：I 为转动惯量，ω 为角速度（可用 rpm 换算）；常见物体的 I 也可由质量和尺寸估算。本地处理。E = ½ I ω² for moment of inertia I and angular speed ω (rpm supported); I can also be estimated from mass and size for common shapes. Processed locally.
应力与应变Stress Calculator
正应力 σ = F / A，剪应力 τ = F / A；给出应变 ε = σ / E（弹性模量）和伸长量 ΔL = ε L₀。本地处理。Normal stress σ = F / A and shear stress τ = F / A; plus strain ε = σ / E (Young's modulus) and elongation ΔL = ε L₀. Processed locally.
表面张力（毛细管 / 液滴）Surface Tension Calculator
毛细管上升：γ = ρ g h r / (2 cos θ)；液滴重量法：γ = mg / (2 π r)。结果用 N/m = J/m²。本地处理。Capillary rise: γ = ρ g h r / (2 cos θ); drop-weight: γ = mg / (2 π r). Result in N/m = J/m². Processed locally.
导热系数（由测量反算）Thermal Conductivity Calculator
平板稳态导热：k = Q d / (A ΔT)，单位 W/(m·K)。常见材料参考：空气 0.026、水 0.6、玻璃 1、铝 205、铜 400。本地处理。Steady conduction through a slab: k = Q d / (A ΔT) in W/(m·K). Rough references: air 0.026, water 0.6, glass 1, aluminium 205, copper 400. Processed locally.
热阻（单层 / 多层）Thermal Resistance Calculator
单层热阻 R = d / (k A)；多层串联把各层 R 相加，总传热 Q = ΔT / R_total。每行一层：厚度(m) 导热系数 面积(m²，可省略共用)。本地处理。Single-layer resistance R = d / (k A); layers in series add; heat flow Q = ΔT / R_total. One line per layer: thickness(m) conductivity area(m², optional shared). Processed locally.
瓦特转安培Watts to Amps Calculator
直流 / 单相：I = P ÷ V；三相：I = P ÷ (√3 × V × PF)。可设置「功率 W」、「电压 V」、「类型」、「功率因数」。DC / single-phase: I = P ÷ V; 3-phase: I = P ÷ (√3 × V × PF). Settings: Power W, Voltage V, Type, Power factor.
安培转瓦特Amps to Watts Calculator
P = V × I（三相 × √3 × PF）。可设置「电流 A」、「电压 V」、「类型」、「功率因数」。P = V × I (× √3 × PF for 3-phase). Settings: Current A, Voltage V, Type, Power factor.
克转摩尔Grams to Moles Calculator
n = m / M。可设置「质量 g」、「摩尔质量 g/mol」。n = m / M. Settings: Mass g, Molar mass g/mol.
dBm 转瓦特dBm to Watts
P(W)=10^((dBm-30)/10)。可设置「方向」、「数值」。P(W)=10^((dBm-30)/10). Settings: Direction, Value.
伏特转焦耳Volts to Joules Calculator
电容能量 E = ½ C V²（也可由 E、C 求 V）。可设置「已知」、「电压 V」、「电容 F」、「能量 J」。Capacitor energy E = ½ C V² (or V from E, C). Settings: Given, Voltage V, Capacitance F, Energy J.
摩尔分数计算器Mole Fraction Calculator
输入混合物中各组分的物质的量（mol），或化学式和质量（g），计算每个组分的摩尔分数 χ、摩尔百分比和总物质的量。Enter each component of a mixture as moles, or as a formula and mass in grams, to get each mole fraction χ, mole percent and the total moles.
理论产量计算器Theoretical Yield Calculator
由限量反应物的质量和化学式、反应方程式中的系数和产物化学式，按化学计量关系计算产物的理论产量（物质的量和质量）；填入实际产量还能求百分产率。Work out the theoretical yield of a product, in moles and grams, from the limiting reactant's mass and formula, the equation coefficients and the product formula; add the actual yield for the percent yield.
质量摩尔浓度计算器Molality Calculator
按 b = 溶质物质的量 ÷ 溶剂质量（kg）计算溶液的质量摩尔浓度（mol/kg）；溶质可输入物质的量，或化学式加质量。Calculate molality, b = moles of solute ÷ kilograms of solvent (mol/kg); give the solute as moles, or as a formula and mass.
质量分数（质量百分比）计算器Mass Percent Calculator
计算溶液或混合物中某组分的质量分数 = 组分质量 ÷ 总质量 × 100%；也可以输入化学式，求每种元素在化合物中的质量百分比。Calculate mass percent = component mass ÷ total mass × 100% for a solution or mixture, or enter a formula to get the mass percent of each element in a compound.
物质的量（摩尔）计算器Mole Calculator
在质量、物质的量和粒子数之间换算：n = m ÷ M，N = n × Nₐ；摩尔质量可直接输入，也可由化学式自动算出。Convert between mass, moles and number of particles with n = m ÷ M and N = n × Nₐ; enter the molar mass or let a formula supply it.
平均原子质量计算器Average Atomic Mass Calculator
输入一种元素各同位素的质量（u）和丰度（%），计算加权平均原子质量；丰度之和不等于 100% 时会提示并按比例归一。Enter the mass (u) and abundance (%) of each isotope of an element to get the weighted average atomic mass; if the abundances do not add up to 100% the tool says so and normalises them.
原子质量计算器（质子、中子、电子）Atomic Mass Calculator (Protons, Neutrons, Electrons)
输入元素（符号、名称或原子序数）和中子数，给出质子数、电子数（可含离子电荷）、质量数 A = Z + N、近似原子质量和该元素的标准原子量。Enter an element (symbol, name or atomic number) and a neutron count to get the protons, electrons (with an optional ion charge), mass number A = Z + N, approximate atomic mass and the element's standard atomic weight.
能斯特方程计算器Nernst Equation Calculator
按能斯特方程 E = E° − (RT/nF)·ln Q 计算非标准条件下的电极电势或电池电动势，可直接输入反应商 Q，或输入氧化态、还原态的浓度。Calculate an electrode or cell potential under non-standard conditions with the Nernst equation, E = E° − (RT/nF)·ln Q, from the reaction quotient Q or from the oxidised and reduced concentrations.
活化能计算器（阿伦尼乌斯方程）Activation Energy Calculator (Arrhenius)
由两个温度下的速率常数，按阿伦尼乌斯方程 ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂) 计算活化能 Eₐ 和指前因子 A；也可由 Eₐ 预测另一温度下的速率常数。Calculate the activation energy Eₐ and pre-exponential factor A from rate constants at two temperatures with the Arrhenius equation ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂), or predict a rate constant at another temperature from Eₐ.
熵变计算器Entropy Change Calculator
计算三类常见过程的熵变 ΔS：可逆等温过程 ΔS = q/T，物质加热或冷却 ΔS = m·c·ln(T₂/T₁)，理想气体等温膨胀 ΔS = nR·ln(V₂/V₁)。Calculate the entropy change ΔS for three common processes: reversible isothermal heat transfer ΔS = q/T, heating or cooling a substance ΔS = m·c·ln(T₂/T₁), and isothermal ideal-gas expansion ΔS = nR·ln(V₂/V₁).
量热计算器（q = mcΔT）Calorimetry Calculator (q = mcΔT)
按 q = m·c·ΔT 计算吸收或放出的热量，或由热量反求质量、比热容或温度变化；还可以计算两种物质混合后的最终温度（不考虑热损失和相变）。Use q = m·c·ΔT to find the heat absorbed or released, or solve for mass, specific heat or temperature change; or find the final temperature when two substances are mixed (no heat loss or phase change).
键级计算器Bond Order Calculator
按分子轨道理论计算键级 =（成键电子数 − 反键电子数）÷ 2：可输入第一、二周期元素组成的双原子分子或离子（如 O2、N2+、NO、CO），自动给出分子轨道排布和未成对电子数；也可直接输入电子数。Calculate bond order = (bonding − antibonding electrons) ÷ 2 with molecular orbital theory. Enter a diatomic molecule or ion of period 1–2 elements (such as O2, N2+, NO or CO) for its MO configuration and unpaired electrons, or enter the electron counts directly.
量子数计算器Quantum Number Calculator
输入主量子数 n，列出所有允许的角量子数 l、磁量子数 mₗ 范围、轨道名称、轨道数和最多容纳的电子数；也可以检查一组 (n, l, mₗ, mₛ) 是否合法。Enter the principal quantum number n to list the allowed l values, the mₗ range, subshell names, orbital counts and maximum electrons, or check whether a set (n, l, mₗ, mₛ) is allowed.
终端速度计算器Terminal Velocity Calculator
按 v = √(2mg ÷ (ρ·A·C_d)) 计算物体在空气（或其他流体）中下落的终端速度，可选常见形状的阻力系数，结果给出 m/s、km/h 和 mph，以及达到约 95% 终端速度所需的大致时间。Calculate the terminal velocity of a falling object, v = √(2mg ÷ (ρ·A·C_d)), with drag coefficients for common shapes, in m/s, km/h and mph, plus the rough time to reach about 95% of it.
向心力计算器Centripetal Force Calculator
由质量、半径和线速度（或角速度、转速）计算圆周运动的向心力 F = mv²/r 和向心加速度，并换算成重力加速度的倍数（g 值）。Calculate the centripetal force F = mv²/r and centripetal acceleration of circular motion from mass, radius and linear speed (or angular speed or rpm), with the acceleration in g.
并联电阻计算器Parallel Resistor Calculator
输入多个电阻值，计算并联后的等效电阻 1/R = Σ(1/Rᵢ)，同时给出串联总电阻作对比；填入电压还能算出每个支路的电流和功率。Enter several resistor values to get the equivalent parallel resistance 1/R = Σ(1/Rᵢ), with the series total for comparison; add a voltage for each branch's current and power.
折射率计算器Index of Refraction Calculator
由光在介质中的速度计算折射率 n = c/v，或用斯涅尔定律 n₁·sin θ₁ = n₂·sin θ₂ 求折射角，并给出全反射临界角；内置空气、水、玻璃、钻石等常见介质的折射率。Calculate the refractive index n = c/v from the speed of light in a medium, or use Snell's law n₁·sin θ₁ = n₂·sin θ₂ to find the refraction angle and the critical angle for total internal reflection, with common media built in.
逃逸速度计算器Escape Velocity Calculator
按 v = √(2GM ÷ r) 计算从地球、月球、火星、木星、太阳或自定义天体表面（或某高度）逃逸所需的速度，同时给出该高度的圆轨道速度。Calculate the escape velocity v = √(2GM ÷ r) from the surface (or an altitude) of Earth, the Moon, Mars, Jupiter, the Sun or a custom body, with the circular orbit speed at that height.
法向力（支持力）计算器Normal Force Calculator
计算物体在水平面或斜面上受到的法向力（支持力）N = mg·cos θ，可加上垂直于表面向下压或向上拉的外力，并给出沿斜面的重力分量。Calculate the normal force N = mg·cos θ on an object on a flat or inclined surface, with an optional extra force pressing into or pulling away from the surface, plus the weight component along the slope.
雷诺数计算器Reynolds Number Calculator
按 Re = ρ·v·D ÷ μ（或 v·D ÷ ν）计算流体的雷诺数并判断管流是层流、过渡还是湍流；内置 20 °C 水和空气的密度与黏度。Calculate the Reynolds number Re = ρ·v·D ÷ μ (or v·D ÷ ν) and whether pipe flow is laminar, transitional or turbulent, with the density and viscosity of water and air at 20 °C built in.
流量计算器Flow Rate Calculator
由管道内径和流速按 Q = A·v 计算体积流量，或由流量反求流速；结果同时给出 L/s、L/min、m³/h 和美制加仑每分钟（GPM）。Calculate volumetric flow Q = A·v from pipe inner diameter and flow speed, or the speed from a flow rate, in L/s, L/min, m³/h and US gallons per minute (GPM).
管道摩阻损失计算器（达西公式）Pipe Friction Loss Calculator (Darcy–Weisbach)
按达西–魏斯巴赫公式 h_f = f·(L/D)·v²/(2g) 计算水在圆管中流动的沿程水头损失和压降，摩擦系数用 Swamee–Jain 公式（湍流）或 64/Re（层流）求得，内置常见管材的粗糙度。Calculate head loss and pressure drop for water flowing in a round pipe with the Darcy–Weisbach equation h_f = f·(L/D)·v²/(2g); the friction factor comes from Swamee–Jain (turbulent) or 64/Re (laminar), with roughness for common pipe materials.
电容计算器Capacitance Calculator
计算电容：由电荷和电压 C = Q/V，平行板电容 C = ε₀·εᵣ·A/d，或多个电容串联、并联的总电容；同时给出储存的能量 ½CV²。Calculate capacitance from charge and voltage (C = Q/V), for a parallel-plate capacitor (C = ε₀·εᵣ·A/d), or for capacitors in series or parallel, with the stored energy ½CV².
效率计算器Efficiency Calculator
按 效率 = 有用输出 ÷ 输入 × 100% 计算机器、电机、电源等的效率和损耗，也可以由效率反求输出或所需输入；输入和输出用同一单位（W、J、kWh 等）。Calculate efficiency = useful output ÷ input × 100% for a machine, motor or power supply, with the losses, or solve for output or required input from the efficiency; use the same unit for input and output (W, J, kWh, …).
太阳能板数量计算器Solar Panel Calculator
根据每月或每日用电量、当地峰值日照时数、单块组件功率和系统损耗，估算所需的光伏系统容量（kW）、组件数量和年发电量。日照时数和损耗都是示例值，请按当地数据修改。Estimate the solar array size (kW), number of panels and yearly output from your monthly or daily electricity use, local peak sun hours, panel wattage and system losses. Sun hours and losses are example values; change them for your location.
管道容积计算器Pipe Volume Calculator
由管道内径和长度计算管内容积（π·r²·L），结果给出升、立方米和美制加仑，并可按液体密度估算管内液体的质量；也可输入外径和壁厚。Calculate the volume inside a pipe (π·r²·L) from its inner diameter and length, in litres, cubic metres and US gallons, with the mass of liquid inside for a given density; or enter the outer diameter and wall thickness.
化学方程式配平Chemical Equation Balancer
输入未配平的化学方程式（如 Fe + O2 = Fe2O3），用线性代数精确求出最小整数系数，支持括号、结晶水（CuSO4·5H2O）和离子电荷（Ag^+、SO4^2-），并列出两边各元素的原子数核对。Enter an unbalanced chemical equation such as Fe + O2 = Fe2O3 to get the smallest whole-number coefficients by exact linear algebra — with parentheses, hydrates (CuSO4·5H2O) and ionic charges (Ag^+, SO4^2-) — and an atom count for each side to check.
元素周期表（118 种元素：原子量、电子排布、电负性）Periodic Table of Elements
交互式元素周期表：118 种元素按族和周期排列，可按类别或分区着色；点击元素或输入原子序数、符号、中英文名称，查看 IUPAC/CIAAW 2024 标准原子量、电子排布、电负性、族、周期和类别。An interactive periodic table of all 118 elements by group and period, colored by category or block. Click an element or search by atomic number, symbol or name to see its IUPAC/CIAAW 2024 standard atomic weight, electron configuration, electronegativity, group, period and category.
基尼系数计算器Gini Coefficient Calculator
输入一组收入、财富或任意非负数值，计算基尼系数 G（0 = 完全平等，1 = 极度不平等）及小样本修正值，并画出洛伦兹曲线、给出累计份额。Enter a list of incomes, wealth or any non-negative values to get the Gini coefficient G (0 = perfect equality, 1 = maximal inequality) and its small-sample corrected value, with a Lorenz curve and cumulative shares.
单摆周期计算器Pendulum Period Calculator
由摆长和重力加速度计算单摆周期 T = 2π√(L/g) 和频率，并可按摆角给出大摆角下的精确周期（算术–几何平均法）；也能由周期反求摆长。Calculate a simple pendulum's period T = 2π√(L/g) and frequency from its length and gravity, with the exact large-amplitude period for a given swing angle (via the arithmetic–geometric mean) — or work back from a period to the length.
冲量与动量计算器Impulse and Momentum Calculator
按冲量定理 J = F·Δt = Δp = m(v₂ − v₁) 计算冲量：可由力和作用时间求冲量及速度变化，也可由质量和前后速度求冲量、动量和平均作用力。Calculate impulse with the impulse–momentum theorem J = F·Δt = Δp = m(v₂ − v₁) — from a force and its duration (with the velocity change), or from mass and the velocities before and after (with momentum and the average force).
功率因数计算器Power Factor Calculator
由有功功率和视在功率，或由有功功率、电压和电流（单相或三相）计算功率因数 cos φ、相位角、无功功率，并估算提高到目标功率因数所需的补偿电容无功容量。Find the power factor cos φ, phase angle and reactive power from real and apparent power, or from real power, voltage and current (single- or three-phase) — and the capacitor kvar needed to correct to a target power factor.
伯努利方程计算器Bernoulli Equation Calculator
按伯努利方程 P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂，由其余量求截面 2 的压力、流速、高度，或截面 1 的压力，并给出总水头。Solve Bernoulli's equation P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ for the pressure, velocity or height at point 2, or the pressure at point 1, from the other values — with the total head.
查理定律计算器（K / °C / °F）Charles's Law Calculator (K, °C, °F)
查理定律 V₁/T₁ = V₂/T₂（压力和物质的量不变）：求 V₂ 或 T₂，温度可用 K、°C 或 °F 输入，内部换算为开尔文计算，并拒绝不高于绝对零度的温度。本地处理。Charles's law V₁/T₁ = V₂/T₂ (constant pressure and amount of gas): solve for V₂ or T₂, with temperatures in K, °C or °F converted to kelvin internally; temperatures at or below absolute zero are rejected. Processed locally.
等位基因频率与 Hardy–Weinberg 检验Allele Frequency & Hardy–Weinberg Calculator
由 AA / Aa / aa 基因型计数算等位基因频率 p、q，给出 Hardy–Weinberg 平衡下的期望 p²、2pq、q²（频率和人数），并做卡方检验（自由度 1）。本地处理。Allele frequencies p and q from AA / Aa / aa genotype counts, the Hardy–Weinberg expected p², 2pq and q² (frequencies and counts), and a chi-square test (1 degree of freedom). Processed locally.
水粘度示意Water Viscosity (demo)
按温度查表示意动力粘度（近似）。本地处理。可设置「温度 °C」。Lookup-style dynamic viscosity vs temperature (approx). Processed locally. Settings: Temp °C.
焓变计算器（生成焓、q = mcΔT、ΔH = ΔU + PΔV）Enthalpy Change Calculator (Formation, q = mcΔT, ΔH = ΔU + PΔV)
三种方法计算焓变：按标准生成焓 ΔH = ΣΔHf(产物) − ΣΔHf(反应物)（每行“系数 生成焓”），按热量 q = m·c·ΔT，或按 ΔH = ΔU + PΔV。可选 J、kJ、cal、kcal，并判断放热、吸热或热中性。本地处理。Enthalpy change three ways: from standard enthalpies of formation, ΔH = ΣΔHf(products) − ΣΔHf(reactants) (one "coefficient value" per line), from heat q = m·c·ΔT, or from ΔH = ΔU + PΔV. Choose J, kJ, cal or kcal; the page says whether the change is exothermic, endothermic or thermoneutral. Processed locally.
齿轮比计算器（转速、扭矩、多级齿轮）Gear Ratio Calculator (Speed, Torque, Gear Trains)
齿轮比 = 从动齿数 ÷ 主动齿数，可加更多级组成齿轮系；可选输入转速和扭矩，算出输出转速和理想输出扭矩，并给出最简整数比。本地处理。Gear ratio = driven teeth ÷ drive teeth, with optional extra stages for a gear train. Add an input speed and torque to get the output speed and ideal output torque, plus the ratio in lowest terms. Processed locally.
斯涅尔定律计算器（折射角、折射率、临界角）Snell's Law Calculator (Refraction Angle, Index, Critical Angle)
按 n₁ sin θ₁ = n₂ sin θ₂ 求折射角、入射角或任一侧的折射率；光从高折射率进入低折射率时给出临界角，并判断是否发生全反射。角度从法线量起。本地处理。Solve n₁ sin θ₁ = n₂ sin θ₂ for the refraction angle, the incidence angle or either refractive index. Going from a higher to a lower index it also gives the critical angle and flags total internal reflection. Angles are measured from the normal. Processed locally.
平衡常数计算器（Kc、Kp、反应商 Q）Equilibrium Constant Calculator (Kc, Kp, Q)
输入平衡时各反应物和产物的浓度及化学计量数，算出 Kc = Π[产物]^系数 ÷ Π[反应物]^系数；可选温度换算 Kp = Kc(RT)^Δn，或输入已知 K，把这些浓度当作反应商 Q 判断反应方向。本地处理。Enter the equilibrium concentrations and stoichiometric coefficients of the reactants and products to get Kc = Π[products]^coeff ÷ Π[reactants]^coeff. Optionally convert to Kp = Kc(RT)^Δn at a temperature, or enter a known K to treat the values as a reaction quotient Q and see which way the reaction shifts. Processed locally.
吉布斯自由能计算器（ΔG = ΔH − TΔS）Gibbs Free Energy Calculator (ΔG = ΔH − TΔS)
由 ΔH（kJ/mol）、ΔS（J/(mol·K) 或 kJ/(mol·K)）和温度（K 或 °C）算出 ΔG，判断是否自发，给出转变温度 T = ΔH/ΔS 和平衡常数 K = e^(−ΔG/RT)。本地处理。Work out ΔG from ΔH (kJ/mol), ΔS (J/(mol·K) or kJ/(mol·K)) and the temperature (K or °C), see whether the reaction is spontaneous, and get the crossover temperature T = ΔH/ΔS and the equilibrium constant K = e^(−ΔG/RT). Processed locally.
速率常数计算器（零级、一级、二级与阿伦尼乌斯）Rate Constant Calculator (Zero, First, Second Order & Arrhenius)
由浓度随时间的变化按积分速率方程求零级、一级或二级反应的速率常数 k 和半衰期；也可用阿伦尼乌斯方程 k = A·e^(−Ea/RT) 求 k，或由一个温度下的 k 换算另一温度下的 k。本地处理。Find the rate constant k and half-life of a zero-, first- or second-order reaction from how the concentration changes over time (integrated rate laws), or get k from the Arrhenius equation k = A·e^(−Ea/RT), or convert a known k to another temperature. Processed locally.
溶液稀释计算器（C₁V₁ = C₂V₂）Solution Dilution Calculator (C₁V₁ = C₂V₂)
按 C₁V₁ = C₂V₂ 求最终体积、最终浓度、所需原液体积或原液浓度中的任意一个，并给出稀释倍数和需要加入的溶剂量。浓度和体积的单位只要两边一致即可。本地处理。Solve C₁V₁ = C₂V₂ for the final volume, final concentration, stock volume or stock concentration, with the dilution factor and how much solvent to add. Any units work as long as both sides use the same ones. Processed locally.
空气密度计算器（含湿度）Air Density Calculator (with Humidity)
由气温、气压和相对湿度计算湿空气密度：把气压分成干空气分压和水汽分压分别用理想气体定律计算后相加，饱和水汽压用 Tetens 公式。可用 °C/°F 和 hPa、kPa、inHg、mmHg，结果给出 kg/m³ 和 lb/ft³。本地处理。Work out the density of humid air from temperature, pressure and relative humidity: the pressure is split into dry-air and water-vapour parts, each goes through the ideal gas law, and the two are added, with saturation vapour pressure from the Tetens formula. Use °C or °F and hPa, kPa, inHg or mmHg; results are in kg/m³ and lb/ft³. Processed locally.
折射角计算器（斯涅尔定律，含常见介质）Angle of Refraction Calculator (Law of Refraction, Common Media)
选择或填写两种介质的折射率和入射角，用 n₁ sin θ₁ = n₂ sin θ₂ 求折射角，并给出偏折角、临界角和是否发生全反射。本地处理。Pick or type the refractive indices of the two media and the angle of incidence to get the angle of refraction from n₁ sin θ₁ = n₂ sin θ₂, plus the deviation, the critical angle and whether total internal reflection happens. Processed locally.
梁挠度计算器（简支梁/悬臂梁，集中/均布荷载）Beam Deflection Calculator (Simply Supported or Cantilever, Point or Uniform Load)
选择支承和荷载形式（简支梁跨中集中力、简支梁均布荷载、悬臂梁端部集中力、悬臂梁均布荷载），输入荷载、跨度、弹性模量 E 和惯性矩 I（或矩形截面宽高），得到最大挠度、最大弯矩、支座反力和挠跨比 L/δ。本地处理。Choose supports and load (simply supported with a central point load or uniform load, cantilever with an end load or uniform load), enter the load, span, modulus E and second moment of area I (or a rectangular width and depth) and get the maximum deflection, maximum bending moment, support reaction and the span-to-deflection ratio L/δ. Processed locally.
风量 CFM 计算器（风管、换气次数、单位换算）CFM Calculator (Duct Airflow, Air Changes, Unit Conversion)
三种算法：由风管尺寸（圆形直径或矩形宽高）和风速 fpm 求风量 CFM；由房间尺寸和每小时换气次数 ACH 求所需 CFM；或在 CFM、m³/h、L/s、m³/min 之间换算。本地处理。Three ways: airflow in CFM from a duct size (round diameter or rectangular width and height) and air velocity in fpm, the CFM a room needs from its size and air changes per hour (ACH), or converting between CFM, m³/h, L/s and m³/min. Processed locally.
混凝土砌块计算器（墙体、门窗扣除、损耗）Concrete Block Calculator (Wall, Openings, Waste)
输入墙长和墙高（或直接输入面积），扣除门窗洞口，按所选砌块规格（含灰缝）算出需要的砌块数、加损耗后的订购数和行数，支持公制和英制。本地处理。Enter the wall length and height (or the area), take off door and window openings, and get the number of blocks for the chosen size including mortar joints, the order quantity with waste and the number of courses, in metric or imperial. Processed locally.
直流线径计算器（按压降选线，mm² / AWG）DC Wire Size Calculator (by Voltage Drop, mm² and AWG)
输入直流电压、电流、单程线长、允许压降百分比和导体材料（铜或铝），按往返回路电阻算出所需的最小截面积，并推荐下一档标准公制截面和 AWG 线号，同时给出实际压降和线损功率。适用于太阳能、汽车、房车等低压直流线路。本地处理。Enter the DC voltage, current, one-way cable length, allowed voltage drop and conductor (copper or aluminium) to get the minimum cross-section from the round-trip resistance, the next standard metric size and AWG gauge, and the resulting voltage drop and power loss. For solar, automotive, RV and other low-voltage DC runs. Processed locally.
密度高度计算器（含高度表拨正、露点）Density Altitude Calculator (with Altimeter Setting and Dew Point)
输入机场标高、高度表拨正值和气温（可选露点），先求气压高度，再按国际标准大气从空气密度求出密度高度；同时给出常用的“每高于标准温度 1 °C 加 120 英尺”经验值和 ISA 温度偏差。仅供学习，飞行请使用经批准的性能资料。本地处理。Enter the field elevation, altimeter setting and temperature (and optionally the dew point) to get the pressure altitude and then the density altitude from the air density in the International Standard Atmosphere, alongside the common 120 ft per °C rule of thumb and the ISA deviation. For learning; use approved performance data for flight. Processed locally.
稀释比例计算器（1:n 配比、C₁V₁ = C₂V₂）Dilution Ratio Calculator (1:n Mixing, C₁V₁ = C₂V₂)
三种算法：按 1:n 的稀释比和想要的总量算出原液和水各需多少（可选“1 份原液 + n 份水”或“原液占总量 1/n”两种说法）；由已知原液和水的体积求比例与浓度；或用 C₁V₁ = C₂V₂ 求需要的原液体积。本地处理。Three ways: from a 1:n ratio and the total you want, get how much concentrate and water to use (as 1 part concentrate plus n parts water, or concentrate as 1/n of the total); from known volumes, get the ratio and strength; or use C₁V₁ = C₂V₂ to find the concentrate volume. Processed locally.
位移计算器（匀加速运动四种公式）Displacement Calculator (Constant Acceleration, Four Equations)
匀加速直线运动的位移：由初速度、加速度和时间 (s = v₀t + ½at²)；由初速度、末速度和时间 (s = (v₀ + v)t/2)；由初速度、末速度和加速度 (s = (v² − v₀²)/2a)；或由末速度、加速度和时间。同时补齐其余未知量。本地处理。Displacement under constant acceleration from initial velocity, acceleration and time (s = v₀t + ½at²), from initial and final velocity and time (s = (v₀ + v)t/2), from both velocities and acceleration (s = (v² − v₀²)/2a), or from final velocity, acceleration and time, filling in the other unknowns too. Processed locally.
墙体龙骨计算器（立柱、上下梁板、门窗、转角）Wall Framing Calculator (Studs, Plates, Openings, Corners)
输入墙长、立柱间距（16/24 英寸或 400/600 毫米）、门窗洞口数和转角数，估算需要的立柱数量、上下梁板（单底板 + 双顶板）总长度和所需板材根数，并加上损耗。支持英尺和米。本地处理。Enter the wall length, stud spacing (16 or 24 in, or 400 or 600 mm), the number of openings and corners to estimate the studs, the total plate length (single bottom plate plus double top plate), the number of plate boards and waste. Works in feet or metres. Processed locally.