🔬 科学与工程Science & Engineering （第 3 页）(page 3)
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.