科學與工程

使用歐姆定律計算電壓、電流、電阻與功率——輸入任意兩個值。

使用 PE = m·g·h（g = 9.80665 m/s²），從質量與高度計算重力位能。結果以焦耳與千焦耳表示。

換算任何恆星的視星等、絕對星等與距離。

使用 a = (vf − vi) / t，從速度在時間內的變化計算加速度。以 m/s² 與 g 的倍數給出結果。

由天體的實際大小與距離計算其角大小，或反向求解任一未知量。

由週期、頻率或線速度計算角速度（rad/s 及 RPM）。

利用 Arrhenius 方程及其雙溫度形式計算活化能或速率常數。

Find the number of protons, neutrons and electrons in any atom or ion, plus nuclear binding energy from the Bethe-Weizsäcker formula.

利用 Bohr 模型計算類氫原子的能級、軌道半徑及躍遷光子能量。

由鍵焓估算反應焓：斷鍵能量減去成鍵能量。

利用 q = mcΔT，由質量、比熱和溫度變化計算吸收或釋放的熱能。

由電容和施加電壓求電容器儲存的電荷量和能量。

由電容值列表求電容器串聯和並聯組合的總電容。

由高溫和低溫熱源的溫度求熱機的最大理論效率。

由速度和半徑計算向心（徑向）加速度，a=v²/r=ω²r。

圓周運動的向心力，F=mv²/r，並輸出加速度。

利用庫侖定律，由電荷量和間距求兩個點電荷之間的靜電力。

由兩個折射率求全內反射的臨界角。

Convert between decibel (dB) gain and power or amplitude ratios. Enter dB to find ratio, or ratio to find dB.

利用 λ = h/(mv) 由粒子的質量和速度計算其物質波波長。

利用 L = 10·log10(I/I0) 換算聲音強度與分貝，或由 dB 值求強度。

使用 密度 = 質量 / 體積，從質量與體積計算密度。對固體、液體與氣體立即以 kg/m³ 與 g/cm³ 給出結果。

使用溶質的莫耳質量，將溶液的密度和質量百分比轉換為莫耳濃度。

使用 M1V1 = M2V2 解決溶液稀釋問題。即時找出缺少的濃度或體積。

以秒差距和光年為單位，在距離模數與距離之間相互轉換。

使用都卜勒公式計算移動聲源和觀察者的觀測頻率位移。

根據電流、載子密度和截面積計算導體中電荷載子的漂移速度。

Apply Einstein's E = mc² to any mass in kg, g, lb or oz — get rest energy in joules, kWh and TNT equivalents with step-by-step working.

Calculate EIRP (dBm, dBW, and watts) from transmitter power, antenna gain, and cable loss, plus optional power density at a given range.

保守動量和能量的一維彈性碰撞後的最終速度。

計算點電荷在給定距離處的電場強度，並查看電場如何隨距離衰減。

計算點電荷在某距離處產生的電位（電壓）以及試驗電荷在該點的能量。

從元素質量百分比或質量確定化合物的實驗式。

使用 Hess 定律和標準生成熱計算標準反應焓 ΔH。

從產物和反應物的標準莫耳熵計算標準反應熵 ΔS。

從平衡濃度和化學計量係數計算平衡常數 Kc。

離開行星或恆星的最小速度，v=√(2GM/R)，附預設值。

Apply the fan affinity laws to predict new flow rate, pressure, and shaft power when fan speed changes — ideal for VFD-controlled HVAC fans.

使用法拉第定律計算電解過程中沉積的物質質量和莫耳數。

從線圈匝數和磁通量變化率計算線圈中的感應電動勢。

Calculate Feed Conversion Ratio (FCR) for livestock, aquaculture, and poultry — how many kg of feed produce 1 kg of live weight gain.

從速率常數求一級反應的半衰期和剩餘濃度。

使用牛頓第二定律 F = m × a，從質量與加速度計算力。立即以牛頓、千牛頓與公斤力給出結果。

根據落下高度計算自由落體時間、撞擊速度和距離。

由摩擦係數和法向力利用 f=μN 計算靜摩擦力或動摩擦力。

Calculate Growing Degree Units (GDU/GDD) from daily temperatures and a base temperature. Predict crop development stages.

由焓變、熵變和溫度計算 Gibbs 自由能變化 ΔG，並判斷反應自發性。

利用物質的莫耳質量將質量（克）換算為莫耳數。

由恆星光度計算恆星宜居帶（金髮姑娘區）的內外邊界距離。

由熱量輸入和功輸出，或由輸入熱和排放熱，計算實際熱機的熱效率。

利用 Henderson-Hasselbalch 方程式，由 pKa 和共軛鹼與酸的濃度比計算緩衝液 pH 值。

由彈簧常數和位移利用 F=kx 計算彈簧力；求解任意變數。

利用哈伯定律由星系退行速度估算其距離。

利用理想氣體定律 PV = nRT 求解壓力、體積、莫耳數或溫度。

由力和時間或動量變化求衝量，J=FΔt=mΔv。

帶選擇性摩擦力的斜面上質量的受力和加速度。

換算酸解離常數 Ka 與 pKa（及反向換算），以及共軛 Kb 和 pKb 值。

利用克卜勒第三定律由軌道半長軸和中心天體質量計算軌道週期。

求解速度、時間、位移或加速度的等加速度運動。

使用 KE = ½mv²，從運動物體的質量與速度計算其動能。結果以焦耳、千焦耳與千卡表示。

使用 Kp = Kc(RT)^Δn 在氣相平衡常數 Kp 與 Kc 之間相互轉換。

Convert Kc to Kp using Kp = Kc × (RT)^Δn and calculate ΔG° from the equilibrium constant at a given temperature.

對任意 AxBy 化學計量的鹽，從 Ksp 求摩爾溶解度（或從溶解度求 Ksp）。

Calculate apparent power (kVA), real power (kW), reactive power (kVAR) and power factor for AC electrical systems.

使用 Q = mL 以熔化或沸騰的潛熱計算熱量。

Calculate the series resistor value needed for an LED circuit from supply voltage, LED forward voltage and desired current — with E24 nearest standard value.

在光年、秒差距、天文單位、千米和米之間轉換天文距離。

根據反應物質量和方程式係數確定限量反應物及過量量。

Calculate the Log Mean Temperature Difference (LMTD) for counterflow and parallel-flow heat exchangers from hot and cold inlet/outlet temperatures.

根據電荷的電場和磁場向量及其速度向量計算完整勞侖茲力。

根據磁場強度、面積和與法線的夾角計算穿過表面的磁通量。

根據電流、長度、磁場和角度求在磁場中載流導線所受的磁力。

使用 F = qvB sin(theta) 計算帶電粒子在磁場中運動所受的磁力。

根據溶質質量和溶液總質量計算溶液中溶質的質量百分比。

用愛因斯坦的 E = mc² 將質量轉換為能量。輸入質量以焦耳、kWh 和百萬噸當量表示等效能量。

Calculate 1 MOA size at any shooting distance and find the scope clicks needed to correct point-of-impact error.

根據溶質的莫耳數和以千克計的溶劑質量計算重量莫耳濃度（mol/kg）。

根據化學式（如 H2O、C6H12O6 或 Ca(OH)2）求任何化合物的摩爾質量（g/mol）。

根據溶質的莫耳數或克數和溶液體積計算摩爾濃度（mol/L）。

Convert between grams, moles, and number of molecules using molar mass and Avogadro's number.

從各組分的莫耳數或質量計算混合物中每個組分的莫耳分率。

從實驗式和化合物的莫耳質量求分子式。

使用亞佛加厥數將莫耳換算為粒子數（原子、分子、離子），以及反向換算。

使用莫耳質量將物質的莫耳數轉換為公克數。快速莫耳到克的換算。

從質量和尺寸計算常見形狀（球體、圓盤、桿）的轉動慣量。

計算線性動量 p=mv，或從動量求解質量或速度。

從 E°、轉移電子數和反應商 Q 求非標準電池電位 E。

從像距和物距或高度計算透鏡和反射鏡的放大率。

從中心天體質量和軌道半徑求圓形軌道的速度和周期。

從板面積、間距和介電常數計算平行板電容器的電容。

從化學式求化合物中每個元素的質量百分比。

從 Ka 和初始濃度計算弱酸的電離百分率、[H+] 和 pH。

從實際產率和理論產率計算反應的百分率產率。

在週期、頻率和角頻率之間轉換。輸入週期或頻率，即時得到 T、f 和 ω。

求溶液的 pH、pOH、[H+] 和 [OH-]。即時將氫離子濃度轉換為 pH 及反向轉換。

求光電效應中發射電子的最大動能、截止電壓和臨界頻率。

使用 E = hf = hc/λ 從光子的頻率或波長計算其能量，以焦耳和電子伏特表示。

Convert Ka to pKa, calculate buffer pH with Henderson-Hasselbalch, and find % ionization of a weak acid.

從氫氧根離子濃度計算 pOH，並在 25°C 下於 pOH、pH、[OH-] 和 [H+] 之間互相換算。

使用 P = W / t，以功除以時間計算功率。立即以瓦、千瓦與機械馬力給出結果。

在稀溶液中對 ppm、ppb、mg/L 和質量百分比進行換算。

使用 P = F / A，從力與面積計算壓力。立即以帕、千帕、psi 與巴給出結果。

由速度、角度和發射高度計算拋體的射程、最大高度和飛行時間。

Calculate the Q10 coefficient — how much a biological or chemical reaction rate changes per 10 °C temperature rise — from two rate–temperature pairs.

利用 N = N0·(1/2)^(t/T) 計算放射性衰變的剩餘量、已過時間或半衰期。

由速率定律 rate = k[A]^m[B]^n 計算反應速率，並求總反應級數。

求電阻-電容電路的 RC 時間常數，並繪製充電曲線。

由光譜線計算星系的宇宙學紅移 z 和退行速度。

使用勞侖茲收縮 L = L0/γ 計算高速運動物體的收縮長度。

計算以光速分數運動的物體之相對論性時間膨脹和勞倫茲因子。

由逗號分隔的電阻列表，計算任意數量電阻串聯和並聯的總等效電阻。

求 RLC 電路的諧振頻率，並查看感抗和容抗曲線隨頻率的變化。

Convert actual flow rate (ACFM) to standard cubic feet per minute (SCFM) using actual pressure and temperature. Also outputs SCMH.

由黑洞質量計算其事件視界（史瓦西）半徑。

應用二級積分速率定律求半衰期和任意時刻的濃度。

由擺長和重力加速度計算單擺週期和頻率，T=2π√(L/g)。

Calculate a sled's acceleration, net force, and friction on a slope given mass, angle, and kinetic friction coefficient.

應用斯涅爾定律 n1·sinθ1 = n2·sinθ2 求折射角、折射率或臨界角。

Calculate soil bulk density, porosity, void ratio, and optional water content from dry mass, total volume, and particle density.

由螺線管的匝數、長度和電流計算其內部磁場。

求混合兩種不同濃度和體積的溶液後的最終濃度。

利用 Q = mcΔT，以質量、比熱和溫度變化計算改變物質溫度所需的熱能。

由彈簧剛度和伸縮量計算彈簧儲存的彈性位能，PE=½kx²。

從陰極與陽極還原電位計算標準電池電位 E°cell，並判斷反應自發性。

根據恆星相對於太陽的質量估算其主序列壽命。

使用 Stefan-Boltzmann 定律，根據恆星半徑與表面溫度求其光度。

利用莫耳比和莫耳質量，將反應物質量換算為產物質量。

根據行星、衛星或恆星的質量和半徑計算其表面重力。

根據兩個軌道天體的恆星軌道週期計算其會合週期。

Convert electrical conductivity (EC) to TDS in ppm and check water quality against EPA and WHO drinking water limits.

根據焦距和口徑計算望遠鏡放大率、焦比和出瞳直徑。

根據口徑求望遠鏡的分辨率、集光力和極限星等。

根據質量、面積、阻力係數和空氣密度計算下落物體的終端速度。

根據反應物量、莫耳比和莫耳質量計算產物的理論產量。

根據溫度變化和膨脹係數計算線性、面積或體積熱膨脹量。

使用 1/f = 1/do + 1/di，求透鏡和鏡面的像距、焦距或物距。

計算遠方質量對天體施加的差分潮汐力和加速度。

根據力、力臂和角度計算旋轉力矩，τ=rF·sinθ。

根據初級值計算理想變壓器的次級電壓、電流和匝數比。

依牛頓萬有引力定律計算兩質量間的引力，F=Gm₁m₂/r²。

使用 v = d / t，從距離與時間計算平均速度。立即以每秒公尺、每小時公里與每小時英里給出結果。

Calculate electrical power in watts from any two of voltage, current or resistance using P = V × I, P = V²/R or P = I²R.

使用 v = f × λ 求波速、頻率或波長，輸入任意兩個值即可求解第三個。

使用 λ = v / f，從波速與頻率計算波長。適用於光、聲與無線電波，結果以公尺、公分與奈米表示。

以 W=mg 換算地球、月球、火星及其他天體上的質量與重力。

查看您在月球、火星、木星及太陽系其他所有行星上的體重。

由黑體溫度求其峰值輻射波長，反之亦然。

使用 W = F·d·cos(θ)，從力、距離與兩者間的夾角計算機械功。結果以焦耳、千焦耳與千卡表示。

由質量與速度以 W=½m(v²−u²) 計算合力做的功（動能變化）。

Find the correct AWG copper wire gauge for a 12 V DC circuit based on current, wire length, and acceptable voltage drop.

Find the correct AWG copper wire gauge for 220 V / 230 V / 240 V circuits based on current, run length, and allowed voltage drop.

Find the correct AWG copper wire gauge for a 24 V DC circuit based on current, one-way wire length, and acceptable voltage drop.

Calculate the full-load line current of a 3-phase AC motor from its rated kW, supply voltage, power factor and efficiency.

Convert air temperature and relative humidity into absolute humidity (g/m³), dew point and saturation vapour pressure.

Calculate real power (W), apparent power (VA) and reactive power (VAR) for single- or three-phase AC circuits from voltage, current and power factor.

Calculate acceleration from net force and mass using Newton's second law: a = F ÷ m, with results in m/s² and g-units.

Calculate gravitational acceleration g = GM/r² at the surface or any altitude of Earth, Moon, Mars or any body.

Calculate the acceleration a = qE/m of a charged particle (proton, electron, ion) in a uniform electric field.

Calculate acoustic impedance (Z = ρc) for two media and find the intensity reflection and transmission coefficients at the interface.

Calculate agricultural field coverage in acres per hour from ground speed, implement width and field efficiency. Also shows hectares/hr and daily acreage.

Calculate activation energy Ea from two rate constants at two temperatures using the two-point Arrhenius equation.

Calculate the mean ionic activity coefficient γ± for electrolyte solutions using the Debye–Hückel limiting law or the Davies equation.

Calculate percent yield from actual and theoretical yield — a core chemistry lab calculation for reaction efficiency.

Estimate the water consumed by your AI queries. Based on 2023 research: a GPT-4-class prompt uses ~50 mL of data-centre cooling water.

Calculate moist air density (kg/m³) from temperature, atmospheric pressure and relative humidity using the ideal-gas law and Magnus formula.

Calculate atmospheric pressure, temperature, and air density at any altitude using the International Standard Atmosphere (ISA) model.

Calculate the air-fuel ratio (AFR) and lambda (λ) for any fuel — see whether the mixture is rich, lean or stoichiometric.

Calculate the Alfvén velocity in a magnetized plasma from the magnetic field strength B and plasma mass density ρ.

Estimate the number of technologically communicating extraterrestrial civilizations in the Milky Way using the Drake Equation.

Calculate allele and genotype frequencies (p², 2pq, q²) for a two-allele locus under Hardy–Weinberg equilibrium.

Use the alligation alternate method to find the volumes of two solutions needed to produce a mixture at a desired concentration.

Calculate air temperature, pressure and density at any altitude using the International Standard Atmosphere (ISA) model up to 32,000 m.

Find the minimum AWG or kcmil wire size for a given amperage load using NEC 2020 Table 310.15(B)(16) ampacity values for copper or aluminum conductors.

Calculate the angle of incidence from source height and horizontal offset, plus reflected angle and grazing angle for any flat surface.

Calculate the angle of refraction using Snell's law for any two media, with total internal reflection check and critical angle.

Calculate the angle of repose for sand, gravel, soil and other granular materials from the coefficient of static friction.

Calculate the torsional angle of twist for solid and hollow circular shafts using the formula φ = TL/(GJ), with max shear stress.

Calculate angular acceleration (α) in rad/s² from Δω/t, net torque and moment of inertia, or tangential acceleration and radius.

Calculate angular displacement θ in radians, degrees and revolutions from arc length/radius, kinematic equations, or average angular velocity.

Calculate angular frequency ω (rad/s) from period, ordinary frequency, a spring–mass system, or a simple pendulum length.

Calculate angular momentum (L) in kg·m²/s from I·ω, shape/mass/radius, or point-mass orbital motion m·v·r.

Calculate minimum resolvable angle for telescopes (Rayleigh criterion, Dawes' limit) or minimum detail for microscopes (Abbe limit).

Calculate crude and annual mortality rates, survival rate, and deaths per 1,000 for any animal population study.

Calculate PCR primer melting temperature (Tm) and annealing temperature from base composition using Wallace rule or empirical formula.

Calculate the physical aperture area of a circular lens, mirror, or camera from its diameter or focal length and f-number.

Convert between API gravity (°API) and specific gravity for petroleum liquids. Classifies crude as extra-heavy, heavy, medium, light, or very light.

Calculate the buoyant (upthrust) force on a submerged object using Archimedes' principle: F = ρ × V × g.

Calculate arrow speed (fps & m/s), kinetic energy and momentum from draw weight, draw length, arrow weight and bow efficiency.

Calculate atom economy for any reaction: the percentage of reactant atoms that end up in the desired product versus waste by-products.

Calculate the weighted average atomic mass of an element from its isotope masses and natural abundances — up to four isotopes.

Calculate signal attenuation in decibels (dB) from input and output power or amplitude, plus attenuation coefficient and half-power distance.

Calculate the average atomic mass of an element from its isotope masses and natural abundances — up to 4 isotopes supported.

Convert between moles, number of particles and mass using Avogadro's constant (6.022 × 10²³). Covers atoms, molecules and formula units.

Calculate bacterial population after any elapsed time using the exponential doubling formula N = N₀ × 2^(t/g), with growth rate constant and fold increase.

Calculate the G1 ballistic coefficient (BC) and sectional density of a bullet from its mass in grains, diameter, and form factor.

Calculate the ideal bank angle for a vehicle or aircraft in a circular turn — eliminates lateral slip at any speed and radius.

Explore the barn-pole (ladder) paradox of special relativity: compute Lorentz contraction in each reference frame and the simultaneity shift that resolves the contradiction.

Calculate tree basal area (m²) from diameter at breast height (DBH) and stand basal area per hectare for forestry surveys.

Calculate the beat frequency and beat period when two close-frequency sound waves interfere. Shows the amplitude envelope with the number of beats per second.

Solve the Beer–Lambert law A = ε·c·l for absorbance, concentration, molar absorptivity, or path length with transmittance output.

Calculate the exact length of an open or crossed drive belt from the two pulley diameters and centre distance, with wrap angles and speed ratio.

Calculate bend allowance, bend deduction and outside set-back for sheet metal fabrication using the standard K-factor formula.

Estimate excess lifetime cancer risk from benzo[a]pyrene (B[a]P) in air using the WHO inhalation unit risk factor.

Calculate downstream pressure P₂ using Bernoulli's equation. Enter upstream pressure, velocities, elevations and fluid density.

Calculate how far binoculars can identify a target, plus exit pupil, relative brightness and twilight factor for any magnification and objective lens.

Calculate the Biot number (Bi = h·Lc/k) and check whether lumped capacitance is valid for transient heat transfer analysis.

Convert your bird's age to a human-equivalent age using the proportional lifespan method for 10 common pet bird species.

Calculate a black hole's Schwarzschild radius, event horizon area, photon sphere and ISCO from its mass in solar masses.

Calculate the Hawking temperature, luminosity and evaporation time of a black hole of any mass using CODATA 2018 constants.

Calculate peak wavelength, radiated intensity and total power for a blackbody using Wien's displacement law and the Stefan-Boltzmann equation.

Estimate fireball and blast damage zone radii for a nuclear weapon yield using Glasstone cube-root scaling. Educational reference only.

Calculate how much bleach and water to mix to reach a target sodium hypochlorite concentration using the dilution formula C₁V₁ = C₂V₂.

Calculate Brake Mean Effective Pressure from engine torque and displacement for 4-stroke or 2-stroke engines, with power output.

Calculate the boiling point of water at any altitude (0–11 000 m) using the ISA atmosphere and Clausius–Clapeyron equation.

Calculate the boiling point of water, ethanol, acetone and other common substances at any pressure using the Clausius–Clapeyron equation.

Calculate how much a dissolved solute raises the boiling point of a solvent using ΔTb = Kb × m × i (colligative property).

Calculate the Boltzmann factor exp(−E/kT) and thermal energy kT for any energy barrier and temperature — fundamental to thermodynamics, kinetics and statistical mechanics.

Calculate bond order from bonding and antibonding molecular orbital electron counts using MO theory.

Compare the lifetime CO₂ footprint of reading physical books versus an e-reader — find the break-even point where the e-reader wins.

Calculate duty cycle, input current, power loss and efficiency for a boost (step-up) DC–DC converter from V_in, V_out, load current and efficiency.

Calculate the unknown pressure or volume using Boyle's Law P₁V₁ = P₂V₂. Enter any three of the four values.

Solve Bragg's law (nλ = 2d·sin θ) for X-ray wavelength, interplanar spacing, or Bragg angle from any two known values.

Calculate the correct circuit breaker ampere rating for any electrical load using NEC 80% continuous-load rule and standard breaker sizes.

Calculate Brewster's angle for any two optical media using their refractive indices — with refracted ray angle, reflectance, and an interactive n₂/n₁ plot.

Calculate the DC output voltage, ripple, PIV and efficiency of a full-wave bridge rectifier from AC input voltage and diode parameters.

Calculate the Brinell Hardness Number (HB) from the applied load, ball indenter diameter and measured indentation diameter using the ISO 6506 formula.

Calculate the discharge over a broad-crested weir using the standard hydraulic formula Q = Cd × 1.705 × L × H^(3/2), with critical depth and velocity.

Convert between BTU/hr, tons of refrigeration, kilowatts, watts and kcal/hr for HVAC and refrigeration capacity. 1 ton = 12,000 BTU/hr = 3.517 kW.

Calculate output voltage, power loss, and minimum inductance for a step-down (buck) DC-DC converter from duty cycle and switching frequency.

Calculate the Euler critical buckling load for a slender column given Young's modulus, moment of inertia, length, and end conditions.

Calculate the Van Slyke buffer capacity β (mol/L per pH unit) for a weak acid/base buffer at a given pH, pKa, and total concentration.

Compute the pH of a weak acid/conjugate base buffer using the Henderson–Hasselbalch equation from pKa and component concentrations.

Explore the special-relativity bug-rivet paradox: compute Lorentz contraction and see how length and simultaneity differ between inertial frames.

Calculate how many flower bulbs fit in a rectangular planting bed at a chosen centre-to-centre spacing — rows, columns and total count.

Calculate the bulk modulus K and compressibility β of a material from the applied pressure change and volumetric strain.

Calculate the muzzle energy of a bullet in joules and ft·lbf from its mass and velocity, plus momentum and IPSC power factor.

Calculate the buoyant force on a submerged object using Archimedes' principle: F = ρ × V × g.

Determine buoyant force, displaced volume, and object density from a spring-scale experiment: weigh in air, then in fluid.

Calculate buoyant force, object weight, and net force to determine whether an object floats or sinks in a fluid.

Fit a linear calibration curve (y = mx + b) to standard concentration–response data and determine unknown sample concentrations.

Calculate the capacitance of a parallel plate capacitor using C = ε₀εᵣA/d, plus stored charge and energy for a given voltage.

Calculate capacitive reactance Xc from frequency and capacitance, with optional RMS current and reactive power for AC circuit analysis.

Calculate capacitive reactance, load current and output power for a mains-connected capacitor dropper (transformerless) power supply.

Calculate stored charge, stored energy and capacitive reactance from capacitance, voltage and frequency.

Calculate how long an RC circuit takes to charge a capacitor to any target voltage using the time constant τ = RC.

Find the capacitance you need from stored energy, stored charge, power-supply ripple, or a target capacitive reactance.

Calculate the equivalent capacitance of any number of capacitors connected in series — result is always less than the smallest capacitor.

Find a car's longitudinal centre of gravity from front and rear axle loads and wheelbase, and calculate the front/rear weight distribution.

Calculate the impact force, g-force and kinetic energy in a car crash from vehicle mass, speed and stopping distance.

Calculate how far a car travels through the air after launching off a ramp: jump distance, air time and peak height using projectile motion.

Compare the annual cost, CO₂ emissions and commute time of driving a car versus cycling for your daily commute.

Calculate the radiocarbon age of a sample from its remaining C-14 fraction using the radioactive decay equation.

Calculate the carburetor CFM rating for a 4-stroke engine from displacement, peak RPM and volumetric efficiency.

Calculate population size at any time using the logistic growth model — enter carrying capacity K, initial population, intrinsic growth rate and time.

Convert your cat's age to the equivalent human age using the AAFP non-linear feline age conversion scale.

Assess your cat's weight by comparing it to the vet-set ideal — rated on the 1–9 Body Condition Score (BCS) scale.

Calculate how many calories your cat needs per day using the veterinary RER formula, adjusted for life stage and activity level.

Calculate days remaining to your cat's due date, track weekly gestation progress, and see key developmental milestones.

Score your cat's quality of life using the veterinary HHHHHMM scale (Hurt, Hunger, Hydration, Hygiene, Happiness, Mobility, More). Total ≥ 35/70 indicates acceptable QoL.

Calculate how many cattle an acre of pasture can support using forage yield, utilization rate and grazing season length.

Calculate cell dilutions using C₁V₁ = C₂V₂ — find final volume, final concentration, stock volume or initial concentration from any three values.

Calculate cell population doubling time and growth rate from initial count, final count and elapsed time. For cell culture and microbiology.

Calculate centrifugal (centripetal) force, g-force, and linear velocity for a rotating object from mass, radius and RPM or angular velocity.

Convert centrifuge speed between RPM and RCF (relative centrifugal force) using rotor radius. Find RPM for a target g-force.

Apply Charles's Law (V₁/T₁ = V₂/T₂) to find the final volume or temperature of a gas at constant pressure. Temperatures converted to Kelvin automatically.

Automatically balance a chemical equation by entering element symbols — uses matrix Gaussian elimination to find the smallest integer stoichiometric coefficients.

Generate the IUPAC name and formula for binary ionic or covalent compounds by selecting two elements and their subscripts.

Calculate COD in mg/L from dichromate back-titration results using Standard Method 5220C (FAS blank and sample volumes, normality, sample size).

Estimate the number, weight, and volume of cigarette butts discarded by a group of smokers over any time period.

Calculate linear velocity, angular velocity, frequency, centripetal acceleration and centripetal force for uniform circular motion.

Estimate cumulus cloud base height (lifted condensation level) from surface temperature and dew point using the standard 400-ft rule.

Calculate how much CO₂ a person exhales per breath, minute, hour, day and year from breathing rate and tidal volume.

Calculate how much CO₂ you need to add to a grow room to reach a target ppm from ambient levels.

Calculate the coefficient of discharge Cd = Q_actual / Q_theoretical for an orifice using Torricelli's theorem.

Calculate the COP for a refrigerator or heat pump and compare it to the theoretical Carnot maximum using cold-side heat, work input, and reservoir temperatures.

Determine the empirical formula of an organic compound from combustion analysis data: CO₂, H₂O, N₂, and SO₂ masses.

Balance the complete combustion equation for any hydrocarbon (CₙHₘ) and calculate masses of CO₂, H₂O, and O₂ from a given fuel mass.

Calculate the carbon-to-nitrogen (C:N) ratio of your compost pile and learn if you need more browns or greens.

Calculate volumetric compressibility (κ) and bulk modulus from initial volume, final volume, and applied pressure.

Calculate the Compton wavelength shift, scattered photon wavelength, and electron recoil energy for any photon wavelength and scattering angle.

Calculate the Compton wavelength and reduced Compton wavelength of the electron, proton, neutron, muon, or tau particle.

Calculate solution molarity (mol/L) from the mass of solute, molar mass, and volume of solution. Also shows mass concentration and mole amount.

Convert electrical conductivity (S/m) to resistivity (Ω·m) using ρ = 1/σ, with unit conversions to Ω·cm, μΩ·m, mS/m and S/cm.

Calculate final velocities for elastic or perfectly inelastic 1D collisions using conservation of momentum. Energy loss shown for inelastic case.

Convert spectacle prescription to contact lens power using the vertex distance formula Vc = Vs / (1 − d·Vs). Rounds to nearest 0.25 D.

Calculate the weight of solid copper wire by diameter (mm) or AWG gauge and length. Includes cross-section area and DC resistance.

Calculate the Coriolis acceleration and force on a moving object at any latitude on Earth.

Estimate corn (maize) yield in bushels per acre using the yield component method: plant population, ears, and kernels.

Estimate the annual and lifetime cost of owning a dog — food, vet, grooming, insurance, boarding, and more.

Estimate how much NO₂, PM2.5 and CO₂ emissions fell during COVID-19 lockdowns based on traffic and industrial activity reduction.

Calculate expected calving date and gestation progress for cattle. Supports 9 breed-specific gestation lengths from 278 to 292 days.

Calculate the crawl ratio of any 4WD vehicle from transmission, transfer case and axle ratios. Includes ground speed at idle and off-road capability rating.

Estimate temperature from cricket chirp rate using Dolbear's Law — count chirps per minute and convert to °F, °C and K.

Calculate the damping ratio, critical damping coefficient, natural frequency, and step response for a spring-mass-damper system.

Calculate inductor and capacitor values for a 1st- or 2nd-order speaker crossover at any crossover frequency and speaker impedance.

Calculate crude protein content (%) from nitrogen (%) using the Jones conversion factor — supports food, feed and agronomic samples.

Estimate the energy use (kWh) and CO₂ emissions of cryptocurrency transactions — Bitcoin, Ethereum, and more — with editable 2024 estimates.

Calculate the density of a cube from its mass and side length. Get density in g/cm³, kg/m³ and lb/ft³ with unit conversion.

Calculate atomic radius, packing efficiency, atoms per cell and coordination number for simple cubic, BCC and FCC crystal structures.

Calculate the Curie constant, effective magnetic moment, and molar susceptibility for a paramagnetic material given the g-factor, J, and temperature.

Calculate the magnetic susceptibility and magnetization of a paramagnetic material with Curie's law χ = C/T.

Find how current splits across two parallel resistors: I₁ = I × R₂/(R₁+R₂) and I₂ = I × R₁/(R₁+R₂).

Calculate the cutoff (−3 dB) frequency for RC, RL, and LC passive filters from component values.

Calculate valve flow coefficient (Cv or Kv) from flow rate, pressure drop, and specific gravity — or solve for any unknown.

Calculate cyclotron frequency, angular frequency and orbital period for a charged particle in a uniform magnetic field using f = qB / (2πm).

Calculate the density of a cylindrical object from its mass, radius and height — outputs g/cm³, kg/m³, volume and surface area.

Calculate DLI (mol/m²/day) from PPFD and photoperiod. See how much light plants receive daily and whether it meets crop requirements.

Calculate the damping ratio ζ, critical damping, natural frequency and free-vibration response of a spring-mass-damper system.

Calculate the Darcy–Weisbach friction factor for pipe flow from Reynolds number, pipe diameter, and wall roughness (Swamee–Jain method).

Calculate pipe pressure drop (ΔP) and head loss using the Darcy-Weisbach equation with the Swamee-Jain friction factor. Covers laminar and turbulent flow.

Calculate porous-media flow rate with Darcy's law: Q = K × A × (Δh / L). Get volumetric flow, Darcy flux and hydraulic gradient.

Calculate hours of daylight, approximate sunrise and sunset times for any latitude and date — using solar declination and the sunrise hour-angle formula.

Calculate decibel (dB) gain or attenuation from input and output voltage, current or power values.

Calculate the minimum wire cross-section (mm²) and AWG gauge for a DC circuit based on current, length and allowable voltage drop.

Calculate the Debye screening length in electrolytes and plasmas — the distance over which a point charge's electric field is exponentially suppressed.

Calculate the degree of unsaturation (index of hydrogen deficiency, IHD) for any organic molecular formula — identifies double bonds, triple bonds and rings.

Calculate a rocket's delta-v from initial mass, dry mass and specific impulse using the Tsiolkovsky rocket equation.

Convert resistor networks between Delta (Δ) and Wye (Y / Star) configurations in both directions for circuit analysis.

Calculate density altitude from field elevation, altimeter setting and outside air temperature for aviation takeoff and climb performance.

Calculate density, mass, or volume from any two known values using the triangle formula ρ = m ÷ V.

Calculate the mass of an object from its density and volume using m = ρ × V. Results in kg, grams, and tonnes.

Calculate the weight (gravitational force) of an object from its density and volume. Results in Newtons, kgf, and lbf.

Calculate hydraulic detention time (HRT) for water and wastewater treatment tanks: HDT = Volume ÷ Flow rate.

Calculate the dew point temperature from air temperature and relative humidity using the August-Roche-Magnus approximation.

Calculate differential pressure (P1 − P2) across any two points with instant conversion to Pa, kPa, bar, psi, mmHg, inH₂O and more.

Calculate diffraction angles for a grating or single slit using d·sin θ = mλ. Enter wavelength, spacing, and order.

Calculate the diffusion coefficient of a spherical particle in a liquid using the Stokes-Einstein equation D = k_BT/(6πηr).

Build a 4×4 dihybrid Punnett square for two genes and get the genotype and phenotype ratios for all 16 offspring combinations.

Calculate the dilution factor, final concentration, and diluent volume using C₁V₁ = C₂V₂. Supports any concentration unit.

Convert between diopters and focal length, and find the image distance for a lens of any optical power.

Calculate the length of a half-wave dipole antenna from frequency and velocity factor for ham radio, broadcast, and RF work.

Calculate the electric dipole moment from charge and separation distance, in both Debye and SI units (C·m).

Calculate displacement from initial velocity, acceleration, and time using the kinematic equation s = ut + ½at². Also finds final velocity and average velocity.

Calculate how sound pressure level or light intensity decreases with distance using the inverse square law: L₂ = L₁ + 20·log₁₀(d₁/d₂).

Calculate how far the horizon is from an observer at a given height above sea level using the geometric horizon formula.

Calculate DNA or RNA concentration from A260 absorbance using Beer-Lambert extinction coefficients. Includes A260/A280 purity ratio and total yield.

Calculate the number of DNA molecules (copies) in a sample from mass in nanograms and fragment length in base pairs.

Calculate the mass of insert DNA needed for a ligation reaction given vector mass, sizes, and the desired insert:vector molar ratio.

Convert a DNA sequence to its mRNA transcript. Supports template or coding strand input, shows GC content and codon count.

Convert your dog's age to the human equivalent using a size-based model. More accurate than the popular multiply-by-7 rule.

Calculate your dog's body mass index from weight and shoulder height. A rough screening tool — BCS is the clinical standard for dogs.

Calculate your dog's daily calorie needs using the veterinary RER × lifestyle-factor formula. Covers all life stages and activity levels.

Find the right crate size for your dog by entering its body length and standing height.

Calculate how much food your dog needs each day based on weight, age, and activity level.

Find the right harness size for your dog by entering the chest girth circumference.

Predict when your dog will next come into heat and identify the fertile window.

Estimate your dog's life expectancy and human-age equivalent based on breed size class.

Calculate your dog's due date and key pregnancy milestones from the mating date.

Assess your dog's quality of life using the veterinary HHHHHMM scale. Score seven criteria to get a total out of 70 with an actionable verdict.

Predict your puppy's adult weight from current age (weeks) and weight using a breed-size growth model. Results within ±20–30 % for most dogs.

Calculate the double bond equivalent (DBE / degrees of unsaturation) from a molecular formula: C, H, N, X counts.

Calculate aerodynamic drag force using F_D = ½ρv²C_D A — enter velocity, drag coefficient, frontal area and fluid density.

Estimate the number of communicating civilizations in the Milky Way using the Drake equation: N = R* × f_p × n_e × f_l × f_i × f_c × L.

Calculate how much water a dripping faucet wastes per day and per year in litres and gallons, plus the annual cost.

Calculate dry matter percentage, moisture content and water loss from fresh and dry weight measurements. Essential for agriculture, food science and forage analysis.

Calculate how much Earth's surface curves over a distance, the hidden height below the horizon, and your horizon distance from any observer height.

Calculate orbital velocity, period, revolutions per day, and escape velocity for any circular orbit around Earth by altitude.

Estimate how many plastic bags you avoid and how much CO₂ you save by switching to reusable bags, accounting for bag manufacturing.

Calculate the effective nuclear charge Z_eff felt by an electron in any atomic orbital using Slater's rules — enter the atomic number and choose the orbital.

Calculate efficiency as useful output divided by total input, and compare against the Carnot efficiency limit for heat engines operating between two temperatures.

Convert between Young's modulus, shear modulus, bulk modulus and Poisson's ratio for isotropic linear-elastic materials.

Calculate shaft torque, angular velocity and full-load current for an electric motor from rated power, speed and efficiency.

Calculate carrier mobility μ from drift velocity and electric field, then derive conductivity and resistivity from carrier density.

Solve for electrical power, voltage, current or resistance — enter any two of the four quantities and get the rest instantly.

Calculate the mass deposited or dissolved during electrolysis using Faraday's first and second laws: m = (M × I × t) / (n × F).

Calculate the EMF of a battery or cell from terminal voltage, current and internal resistance using ε = V_t + I·r.

Find the electron configuration of any element (Z = 1–118) using the Aufbau principle — orbital notation plus shell-by-shell electron count.

Calculate the drift velocity of electrons in a conductor from current, wire diameter and material using v = I / (n·A·e).

Calculate the electronegativity difference (ΔEN) between two atoms to predict bond type: nonpolar covalent, polar covalent or ionic.

Calculate percentage elongation, engineering strain, true strain and reduction of area from tensile test gauge-length measurements.

Calculate the energy density stored in electric and magnetic fields using uₑ = ε₀E²/2 and u_B = B²/(2μ₀).

Convert photon energy (eV, meV, keV or J) to wavelength (nm, m) and frequency using the Planck relation λ = hc/E.

Calculate engine displacement in cc, litres and cubic inches from bore, stroke and cylinder count using V = (π/4) × bore² × stroke × cylinders.

Calculate enthalpy change for heating or cooling any substance using ΔH = m × cₚ × ΔT, with built-in specific heat values for common materials.

Calculate entropy change ΔS for isothermal heat transfer, heating or cooling a substance, or ideal gas expansion — three standard thermodynamic formulas.

Calculate enzyme activity in U/mL and specific activity in U/mg from a spectrophotometric assay using the Beer-Lambert law.

Estimate the vapor-pressure driven evaporation rate (mm/day) from water surface temperature, air temperature, humidity and wind speed.

Find the number of excess electrons from a net charge using Q = n × e, where e = 1.602176634 × 10⁻¹⁹ C.

Calculate the minimum exhaust pipe internal diameter for a 4-stroke engine from displacement, RPM, volumetric efficiency and exhaust temperature.

Calculate exoplanet orbital period, equilibrium temperature, transit depth and transit probability from stellar and orbital parameters.

Calculate relativistic travel time to any exoplanet: Earth-frame and ship-frame duration, Lorentz factor, length contraction, and time dilation.

Calculate the factor of safety (FOS) by dividing the failure load by the applied load, with engineering category guidance.

Calculate the mass deposited or dissolved in electrolysis using Faraday's laws: m = (M × I × t) / (z × F).

Calculate the Fermi energy level position in intrinsic, n-type, and p-type semiconductors from temperature, bandgap, and doping concentration.

Estimate your weekly methylmercury intake from fish consumption and compare it with the EPA reference dose for your body weight.

Calculate horizon distance and curvature drop on a spherical Earth; compare to the flat-Earth prediction of zero drop at any distance.

Estimate the CO₂ equivalent emissions of a flight per passenger, by distance and cabin class, compared to car and train alternatives.

Calculate volumetric flow rate through a circular pipe from inner diameter and mean velocity in GPM, L/min, m³/s, and cfs, plus Reynolds number.

Design a flyback DC-DC converter: CCM duty cycle, peak primary/secondary currents, critical inductance, and MOSFET voltage stress.

Calculate the kinetic energy stored in a spinning flywheel from its mass, radius, RPM and geometry using E = ½Iω².

Calculate work or energy in foot-pounds (ft·lbf) from force (lbf) and distance (ft), then convert to joules, BTU, calories and kWh.

Calculate the output voltage of a single-transistor forward converter from its input voltage, duty cycle, and transformer turns ratio.

Calculate free-space path loss (FSPL) in dB from distance and frequency using the Friis transmission equation for wireless link budgets.

Calculate the freezing point depression of a solution using ΔTf = Kf × m × i for water, benzene, cyclohexane and more.

Calculate bandwidth, centre frequency, Q factor and fractional bandwidth from two cutoff frequencies for any filter or RF system.

Convert wavelength (nm) to frequency (THz), period (fs), photon energy (eV) and wavenumber (cm⁻¹) using c = f × λ and E = hf.

Convert any EM wave frequency (Hz to THz) to wavelength in metres, cm and nm using λ = c / f, the speed of light.

Calculate the nth Fresnel zone radius for a radio link to determine the required line-of-sight clearance for Wi-Fi, microwave and wireless links.

Calculate the coefficient of friction (μ) from measured forces, mass and applied force, or the incline angle at which an object just slides.

Calculate friction force, normal force and net acceleration on a flat or inclined surface using F = μN. Includes common surface presets.

Calculate pipe friction head loss and pressure drop using the Darcy–Weisbach equation from friction factor, pipe length, diameter and flow velocity.

Calculate the Froude number for open-channel flow and classify the regime as subcritical, critical or supercritical from velocity and flow depth.

Calculate effort force, load, or arm lengths for a lever. Uses the principle of moments: Effort × Effort Arm = Load × Load Arm.

Convert acceleration (m/s²) to g-force, or calculate the g-force in a turn from speed and radius, with human tolerance reference bands.

Calculate the density of any gas at a given temperature and pressure using the ideal gas law ρ = PM/RT.

Calculate electric flux and the electric field at a Gaussian surface radius using Gauss's law Φ = Q/ε₀.

Solve Gay-Lussac's law P₁/T₁ = P₂/T₂ for any unknown pressure or temperature of a gas at constant volume.

Calculate the gear ratio from driver and driven gear tooth counts, with output speed and torque multiplication.

Find output shaft RPM from input RPM and gear ratio. A curve plots output speed across the full ratio range.

Calculate vehicle speed (km/h, mph) from engine RPM, transmission gear ratio, final drive ratio, and tyre diameter.

Calculate gear ratio, output speed, output torque and mechanical power for any gear, chain or belt-drive transmission.

Calculate real power (kW), apparent power (kVA) and reactive power (VAR) for single-phase, three-phase or DC generators from voltage, current and power factor.

Estimate global plastic waste leakage and model policy impacts — production cuts and recycling increases — using editable 2022 baseline figures.

Calculate the expected kidding (birth) date for a goat from the breeding date. Goats average 150 days gestation (range 145–155 days).

Calculate the pure gold content and market value of a gold piece from its weight, karatage, and current spot price.

Calculate the diffusion and effusion rate ratio of two gases using Graham's Law: Rate₁/Rate₂ = √(M₂/M₁).

Calculate grain bin storage capacity in bushels and tonnes from diameter, eave height, and grain type (corn, wheat, soybeans and more).

Convert grain quantities between US bushels, pounds, kilograms, metric tonnes, short tons, and hundredweight for corn, wheat, soybeans, and more.

Calculate density in g/cc (g/cm³) from mass and volume, or find mass or volume when density is known.

Calculate the gravitational attraction between two masses using F = G·m₁·m₂/r². Defaults show the Earth–Moon system.

Calculate aircraft ground speed from true airspeed and wind using the wind triangle. Shows headwind, crosswind and wind correction angle.

Convert your guinea pig's age to the human equivalent. Shows the life stage from baby to geriatric and age relative to typical lifespan.

Track a guinea pig pregnancy: enter days since mating to see days remaining, progress percentage and whether the due date has passed.

Calculate the diameter of a human hair from single-slit laser diffraction: enter the wavelength, screen distance and dark fringe position.

Calculate the Hall coefficient R_H from Hall voltage, sample thickness, current and magnetic field, plus carrier density and type.

Convert your hamster's age in months to a human age equivalent, with life stage and remaining lifespan for five common species.

Compare annual CO₂ emissions and costs of electric hand dryers versus paper towels using lifecycle data and your local electricity grid intensity.

Calculate wave speed, period, angular frequency and wave number from amplitude, frequency, wavelength and phase using y = A sin(kx − ωt + φ).

Calculate heat energy absorbed or released by a substance using Q = mcΔT. Includes specific heat values for 14 common materials.

Calculate heat exchanger effectiveness from NTU and capacity ratio using the ε–NTU method for counter-flow or parallel-flow arrangements.

Calculate the apparent temperature ("feels like") from air temperature and humidity using the NOAA Rothfusz heat index equation.

Calculate the heat released by burning a fuel using its lower heating value (LHV). Covers common fuels — natural gas, petrol, diesel, hydrogen, coal and more.

Calculate the heat absorbed or released by a substance using Q = mcΔT. Choose from common materials or enter a custom specific heat capacity.

Calculate the overall heat transfer coefficient (U-value) and thermal resistances for a flat wall with convection on both sides using 1/U = 1/h_i + d/k + 1/h_o.

Calculate the minimum uncertainty in momentum (Δp) or time (Δt) from a known position (Δx) or energy (ΔE) spread using Heisenberg's principle: Δx·Δp ≥ ℏ/2.

Calculate the wire length and inductance of a single-layer helical coil from its number of turns, mean diameter and coil length.

Calculate the resonant frequency of a Helmholtz resonator (bottle, cavity, bass reflex port) from its volume, neck length and radius.

Calculate the cutoff frequency and time constant of an RC high-pass filter from resistance and capacitance.

Calculate the two delta-v burns and transfer time for a Hohmann orbital transfer between two co-planar circular orbits around Earth, Moon, Mars, or the Sun.

Calculate hoop (circumferential) and longitudinal stress in a thin-walled cylindrical pressure vessel using σ = Pr/t.

Calculate the expected foaling date and gestation progress for a mare from the breeding date. Average equine gestation is 340 days.

Estimate a horse's weight using Caslick's formula: (Heart Girth² × Body Length) / 330. No scale needed — just a measuring tape.

Estimate your kitten's adult size from its current age and weight using a veterinary growth curve. Includes breed-size and sex adjustments.

Convert horsepower to amperes for DC, single-phase or three-phase AC motors using NEC standard formulas — enter HP, voltage, efficiency and power factor.

Calculate soil hydraulic conductivity K from constant-head or falling-head permeameter test data using Darcy's law.

Calculate the hydraulic gradient i = Δh/L and Darcy seepage velocity/flow rate for groundwater or pipe flow.

Calculate the sequent depth, Froude numbers, energy loss and power dissipated in a hydraulic jump in an open rectangular channel.

Calculate hydrostatic pressure at a given depth in any fluid using P = ρgh, with results in Pa, kPa, bar, psi and atm.

Calculate the hydraulic radius R_h = A/P for rectangular, circular and trapezoidal channels, then apply Manning's equation for velocity and flow rate.

Calculate HRT = V/Q for wastewater treatment reactors, ponds or tanks in days, hours, minutes and seconds.

Calculate hydroelectric power output P = η·ρ·g·Q·H and annual energy generation from head, flow rate and turbine efficiency.

Convert pH to [H⁺] concentration or vice versa — get pOH, [OH⁻], and acid/base classification instantly.

Calculate Bohr energy levels, orbital radii, and emission wavelengths for hydrogen-like ions using the Rydberg formula.

Calculate gauge and absolute pressure at any depth in water, seawater, mercury or a custom fluid using P = ρgh.

Calculate the density of any ideal gas from pressure, temperature and molar mass using ρ = PM/(RT). Outputs kg/m³, g/L and molar volume.

Calculate the pressure of an ideal gas from moles, temperature and volume using PV = nRT. Outputs in Pa, atm, kPa, bar and psi.

Find the temperature of an ideal gas from pressure, volume, and moles. Outputs Kelvin, Celsius, and Fahrenheit.

Calculate the volume of an ideal gas from pressure, temperature, and moles using PV = nRT. Outputs litres and cubic metres.

Calculate rocket delta-v using Δv = Isp × g₀ × ln(m₀/mf). Enter wet mass, dry mass, and specific impulse.

Calculate secondary voltage, current, and turns ratio for an ideal transformer. Enter V₁, N₁, N₂, and optionally I₁.

Calculate the apparent weight of any fully-submerged object using Archimedes' principle and compare buoyancy to actual weight.

Calculate the kinetic energy at impact from mass and velocity, or from free-fall drop height. Optionally compute average impact force from stopping distance.

Calculate the energy absorbed by a material specimen in a Charpy or Izod pendulum impact test and compute impact toughness (J/mm²).

Calculate impulse, change in momentum, average force or contact time using the impulse-momentum theorem J = F·Δt = m·Δv.

Calculate the index of refraction from the speed of light in a medium (n = c/v) or using Snell's law from angles of incidence and refraction.

Calculate inductive reactance of an inductor in AC circuits. Enter frequency (Hz) and inductance (H) to get X_L in ohms.

Calculate the energy stored in an inductor's magnetic field. Enter inductance (H) and current (A) to get energy in joules.

Calculate insertion loss in dB from power or voltage ratios. Enter input and output values to get insertion loss and the power/voltage ratio.

Calculate the internal resistance of a battery or power source from its EMF, terminal voltage and load current.

Calculate the intrinsic carrier concentration nᵢ of silicon, germanium or GaAs at any temperature using the effective density-of-states model.

Calculate how intensity changes with distance using the inverse square law: I₂ = I₁ × (r₁/r₂)². Covers light, sound, gravity and radiation.

Calculate output voltage, inductor currents and ripple for an inverting buck-boost DC-DC converter from duty cycle and component values.

Calculate ionic strength I = ½ Σ cᵢzᵢ² for any electrolyte solution and estimate the mean activity coefficient via the Davies equation.

Compute isentropic flow ratios T/T₀, P/P₀, ρ/ρ₀ and A/A* for any Mach number and ratio of specific heats (γ).

Calculate the isoelectric point (pI) of an amino acid from its pKa values and plot net charge versus pH.

Calculate J-pole antenna dimensions — radiating element, matching stub, gap and feed point — for any frequency and velocity factor.

Calculate the heat energy dissipated by an electric current through a resistor using Joule's law: Q = I² × R × t.

Decompose CO₂ emissions into population, GDP per capita, energy intensity and carbon intensity using the Kaya Identity. Model any country or scenario.

Convert kilograms (mass) to Newtons (weight force) using F = m × g. Includes Earth, Moon, Mars and custom gravity values.

Calculate the kinematic viscosity of air at any temperature and pressure using Sutherland's law and the ideal-gas equation.

Calculate the Knudsen number (Kn = λ/L) from temperature, pressure, molecular diameter and length scale to identify the gas flow regime.

Convert kVA (apparent power) to amps for single-phase and three-phase systems. Shows active power at common power factors.

Calculate equilibrium adsorption capacity using the Langmuir isotherm model: q = qmax·KL·C / (1 + KL·C).

Calculate laser beam divergence, Rayleigh range, and beam radius at any distance using Gaussian beam propagation.

Calculate the output beam diameter and divergence of a laser beam expander from magnification M: D_out = M·D_in, θ_out = θ_in/M.

Calculate laser brightness (radiance) B = P/(A·Ω) in W/(cm²·sr) from power, beam radius, far-field divergence and M² beam quality.

Convert laser frequency linewidth Δν (MHz) to wavelength linewidth Δλ (nm) and compute coherence length and coherence time at any center wavelength.

Calculate the focused spot size, Rayleigh range and depth of focus for a Gaussian laser beam through a thin lens using M²·λ·f/(π·w).

Calculate ionic crystal lattice energy using the Born-Landé equation from the Madelung constant, ion charges, interionic distance and Born exponent.

Calculate the resonant frequency, characteristic impedance and reactance of an LC filter or tank circuit. Supports H, mH, μH, nH and F, μF, nF, pF.

Calculate the resonant frequency, period, and characteristic impedance of an LC tank circuit from inductance and capacitance.

Compute a thin lens's focal length and optical power from its refractive index and radii of curvature using the lensmaker's equation.

Calculate effort force, load force, arm lengths and mechanical advantage for any lever. Enter three values and solve for the fourth.

Calculate the lift coefficient (CL) or lift force from air density, airspeed and wing area using the fundamental aerodynamic lift equation.

Calculate how far away a lightning strike was by timing the delay between the flash and the thunder, with temperature-corrected speed of sound.

Calculate the push (extension) and pull (retraction) force of a hydraulic or pneumatic cylinder from pressure and bore/rod diameters.

Calculate the density of liquid ethylene (C₂H₄) at any temperature from −103.77 °C to 9.20 °C using the Rackett equation.

Calculate fence perimeter, number of posts and total wire or rail needed for a rectangular or circular livestock enclosure.

Calculate pack weight capacity and daily dry-matter feed requirements for llamas based on body weight, trip length, and herd size.

Calculate the log reduction in microbial count after disinfection or sterilisation, plus the percentage reduction and surviving fraction.

Compute the equilibrium populations, cycle period, and phase portrait for the Lotka–Volterra predator–prey model from its four rate parameters.

Calculate the −3 dB cutoff frequency, time constant and Bode plot of a first-order RC low-pass filter from R and C values.

Convert lumens to lux (illuminance), calculate luminous efficacy (lm/W), and find how many lumens a room needs for a target brightness.

Calculate the luminosity of any star from its radius and surface temperature using the Stefan-Boltzmann law (L = 4πR²σT⁴).

Instantly convert between lux (lm/m²) and foot-candles (lm/ft²) — exact SI and imperial illuminance unit conversion with a reference scale.

Calculate Mach number from object speed and air temperature, with subsonic, transonic, supersonic and hypersonic classification.

Convert a compass (magnetic) bearing to a true geographic bearing using your local magnetic declination, or reverse the correction.

Calculate the magnetic dipole moment of a current loop and the resulting far-field B on axis and at the equator.

Find the magnetic field at a perpendicular distance from a long straight current-carrying wire using Ampere's law.

Calculate the magnetic force per unit length between two parallel current-carrying wires — attractive for same-direction currents, repulsive for opposite.

Calculate the magnetic moment of a multi-turn coil and the resulting torque and potential energy when placed in a magnetic field.

Calculate absolute permeability, magnetic flux density B, and susceptibility from relative permeability μr and field intensity H.

Calculate the magnitude and direction of an acceleration vector from its x, y (and optional z) components.

Calculate the Magnus force on a spinning ball or cylinder: the sideways lift that curves a football, baseball or cricket ball in flight.

Calculate transmitted light intensity through a polariser using Malus's law: I = I₀ cos²(θ).

Calculate gauge and absolute pressure from a fluid column in a manometer using P = ρgh, with conversion to Pa, kPa, bar, psi, mmHg or atm.

Calculate density from mass and volume, or solve for mass or volume when density is known. Supports g, kg, lb, cm³, L, m³.

Calculate the mean free path of gas molecules (λ = k_B T / (√2 π d² P)) for common gases at any temperature and pressure.

Estimate your annual CO₂e emissions from weekly meat consumption (beef, pork, chicken, lamb, fish) using 2018 global median emission factors.

Calculate the ideal mechanical advantage of a lever, inclined plane, wheel-and-axle, or pulley from its dimensions.

Calculate the reaction rate v from Vmax, Km and substrate concentration [S] using the Michaelis-Menten equation of enzyme kinetics.

Calculate interplanar spacing d and Bragg diffraction angle 2θ for any (hkl) plane in a cubic crystal lattice.

Solve the mirror equation 1/f = 1/dₒ + 1/dᵢ for concave or convex mirrors — enter any two values to find the third.

Calculate mixed air dry-bulb temperature, humidity ratio and enthalpy for HVAC systems mixing outdoor and return air streams.

Calculate the resulting temperature when two air streams of different flow rates and temperatures are mixed — for HVAC and ventilation.

Calculate the mixing ratio of two substances: get the simplified ratio, percentage share of each component and parts per unit.

Calculate the atmospheric mixing ratio (g/kg), relative humidity, specific humidity and vapour pressure from temperature, dew point and pressure.

Calculate MLVSS from MLSS and volatile fraction, plus F/M ratio, hydraulic retention time and organic loading rate for activated-sludge systems.

Calculate AM or FM modulation index, Carson bandwidth, sideband frequencies, and AM power efficiency from carrier and message parameters.

Find principal stresses, maximum shear stress and principal-plane angle from a 2D stress state (σx, σy, τxy) with Mohr's circle.

Calculate the moisture content of any material on a wet basis and dry basis from wet and oven-dried masses.

Calculate the molar ratio of two substances from their masses and molar masses — essential for stoichiometry and limiting-reagent problems.

Calculate the molar mass of any compound by typing its chemical formula — supports parentheses and 60+ elements.

Convert moles to atoms or molecules using Avogadro's constant, and optionally convert to grams with molar mass.

Calculate NMOS MOSFET drain current I_D in cutoff, triode and saturation regions given V_GS, V_th, V_DS and transconductance parameter k_n.

Calculate MOSFET threshold voltage V_th from substrate doping N_A, oxide thickness t_ox and flat-band voltage V_fb using long-channel device physics.

Estimate lawn mowing cost per session and annually from area, mowing speed, labour rate, fuel cost and number of sessions per year.

Calculate muzzle energy in ft-lb and joules, SI momentum, IPSC power factor, and a projectile trajectory arc from bullet mass and velocity.

Calculate the natural frequency, angular frequency, and period of a spring-mass system, simple pendulum, or LC resonant circuit.

Calculate the output frequency, period, high/low times and duty cycle of an NE555 timer wired in astable (free-running oscillator) mode.

Derive net ionic equations from balanced molecular equations for common acid–base, precipitation, and gas-forming reactions in step-by-step detail.

Calculate the volume of base needed to neutralize an acid (or vice-versa) using acid–base stoichiometry and molar equivalents.

Calculate the temperature of a cooling (or heating) object at any elapsed time using Newton's law of cooling: T(t) = T∞ + (T₀ − T∞) × e^(−kt).

Solve Newton's second law F = m × a for force, mass, or acceleration. Enter any two values to calculate the third, plus weight and impulse.

Apply Newton's third law: for every action force there is an equal and opposite reaction force. Enter the force and both masses to find accelerations.

Compute cascaded noise figure, noise factor and noise temperature for a two-stage RF amplifier chain using the Friis formula.

Calculate the normal force on an inclined plane: N = mg cos θ. Optionally add friction force and net force along the slope.

Calculate the normality of a solution from mass, molar mass, n-factor and volume, and convert between normality and molarity.

Calculate NPSH available for a pump system and check the cavitation margin against NPSH required.

Calculate particle number density from N/V, mass density and molar mass, or ideal-gas pressure and temperature.

Calculate the Nusselt number by definition (Nu = hL/k), flat-plate correlation, or Dittus-Boelter pipe-flow formula.

Calculate shock wave angle, post-shock Mach number, pressure, temperature and density ratios for an oblique shock wave.

Calculate the fraction of night sky covered by stars and explore why an infinite universe still has a dark sky.

Estimate the carbon footprint of attending the Olympic Games covering flights, accommodation and local transport.

Calculate how much combined EPA+DHA your dog needs daily based on body weight and dosing level, and convert to fish oil capsules.

Calculate discharge, velocity and Froude number for a rectangular open channel using Manning's equation (SI units).

Calculate absorbance, transmittance, concentration, or molar absorptivity using the Beer-Lambert law (A = εlc) for spectrophotometry.

Calculate the orbital period of any body using Kepler's Third Law: T = 2π √(a³ / GM). Works for planets, moons and satellites.

Calculate volumetric flow rate through a circular orifice using the Torricelli / orifice-flow equation Q = Cd·A·√(2gh).

Calculate osmotic pressure of a solution using the van't Hoff equation π = iMRT. Enter molarity, temperature and solute type.

Calculate stellar distances in parsecs and light-years from an annual parallax angle, or find object distance from a terrestrial baseline and parallax angle.

Calculate the equivalent inductance of 2–4 inductors connected in parallel. Uses the reciprocal-sum formula, assuming no mutual coupling.

Calculate the partial pressure of each gas in a mixture using Dalton's Law (P_i = x_i × P_total). Supports kPa, atm, bar, psi, mmHg.

Calculate the RMS speed, mean speed and most probable speed of gas particles using the kinetic theory of ideal gases — for any gas and temperature.

Estimate a building's annual specific heating demand (kWh/m²·year) and check compliance with the Passive House standard of ≤ 15 kWh/m²·year.

Calculate the oscillation frequency of a simple pendulum from its length and local gravity. Includes period and angular frequency.

Calculate the maximum kinetic energy and speed of a pendulum bob at the bottom of its swing from mass, length, and release angle.

Calculate the period of a simple pendulum from length, gravity, and swing angle — includes large-angle correction beyond the small-angle formula.

Calculate the percent ionic character of a chemical bond from the electronegativity difference using the Pauling formula.

Calculate the concentration of a solution as a percentage — mass/volume %(w/v), mass/mass %(w/w), or volume/volume %(v/v).

Convert % w/w or % w/v concentration to molarity (mol/L) — enter percentage, molar mass, and density.

Estimate pet-sitting costs for dog walks, drop-in visits, overnight stays or day boarding — with multi-pet surcharges and a weekly total.

Calculate the degrees of freedom (F) of a chemical system using the Gibbs Phase Rule F = C − P + 2, or the condensed form F = C − P + 1.

Calculate plug-in hybrid (PHEV) combined fuel economy (MPGe), annual fuel cost, and the electric vs gasoline mileage split based on your daily driving habits.

Calculate the oscillation period, frequency and angular frequency of a physical (compound) pendulum using T = 2π√(I/mgd).

Calculate how many bales of pine straw you need to cover a garden bed at a chosen depth, with area, volume and cost estimate.

Calculate pipe flow rate, Reynolds number, friction factor and pressure drop using the Darcy–Weisbach equation and Swamee–Jain approximation.

Calculate the average fluid velocity in a pipe from flow rate and internal diameter — with Reynolds number and flow regime.

Calculate the extend and retract force of a hydraulic or pneumatic cylinder from bore, rod diameter and operating pressure.

Calculate mean and peak piston speed from stroke length and engine RPM — in m/s, ft/min and km/h.

Calculate the total plant population, plants per hectare and plants per acre for any field from row and plant spacings.

Estimate a plant's daily water requirement and gross photosynthesis (O₂/CO₂) from pot size, leaf area, light and temperature.

Estimate your annual single-use plastic waste in kg from weekly usage of bags, bottles, containers and packaging.

Calculate push and pull force of a pneumatic cylinder from bore diameter, rod diameter and operating pressure in bar.

Convert between dynamic viscosity (Poise, cP, Pa·s) and kinematic viscosity (Stokes, cSt, m²/s) using fluid density.

Calculate volumetric flow rate through a tube using the Hagen-Poiseuille equation: Q = πr⁴ΔP / (8ηL).

Calculate Poisson's ratio from axial and lateral strain, plus bulk and shear moduli when Young's modulus is known.

Calculate the polar moment of inertia (J) for solid and hollow circles and rectangles. Used in torsion, shaft, and beam design.

Calculate rock or soil porosity (φ = Vv/Vt) and intrinsic permeability in Darcy, millidarcy and m² using Darcy's law.

Calculate how many bags of potting soil you need for containers, raised beds or planters — rectangular or round pots, any bag size.

Convert mass flow rates between lb/min, lb/hr, lb/s, kg/min, kg/hr and g/s. See cumulative weight over 60 minutes at any rate.

Calculate pressure in PSI from force (lbf) and area (in²), then convert to Pa, kPa, MPa, bar, atm and mmHg.

Calculate power dissipated in a resistive element. Enter any two of voltage, current or resistance to get watts plus daily energy consumption.

Calculate power factor, true power, reactive power and apparent power for AC circuits. Visualises the kW–kVAR–kVA power triangle.

Calculate power-to-weight ratio in W/kg, kW/tonne and hp/ton from any power unit (kW, hp, PS) and mass unit (kg, lbs).

Convert concentration from ppm (mg/kg) to molarity (mol/L, mM, μM, nM) using the solute molar mass and solution density.

Calculate the Prandtl number from dynamic viscosity, specific heat, and thermal conductivity — or from kinematic viscosity and thermal diffusivity.

Calculate the downstream Mach number and isentropic property ratios for a Prandtl-Meyer expansion fan given upstream Mach number and turning angle.

Calculate principal stresses σ₁ and σ₂, maximum shear stress, principal plane angle, and Von Mises stress from a 2D stress state.

Calculate theoretical boat top speed from propeller pitch, engine RPM and gear ratio. Find prop shaft RPM and speed in mph, knots and km/h.

Calculate propeller slip percentage from engine RPM, pitch, gear ratio and actual GPS speed. Find effective pitch and compare theoretical vs actual advance.

Calculate protein concentration in mg/mL, µg/mL and µM from dissolved mass and solution volume.

Estimate protein molecular weight from residue count using the 110 Da average residue mass, with disulfide bond and Stokes radius output.

Estimate protein solubility relative to the optimal pH using the isoelectric point, buffer pH, and NaCl ionic strength via Cohn–Hofmeister principles.

Calculate dew point, wet-bulb temperature, humidity ratio, enthalpy and specific volume from dry-bulb temperature and relative humidity.

Calculate the mechanical advantage, required effort force, rope length to haul, and efficiency of a block-and-tackle pulley system.

Calculate water horsepower, brake horsepower and motor power required for a pump given flow rate, total head, specific gravity and efficiencies.

Calculate offspring genotype and phenotype probabilities for a monohybrid genetic cross using a 2×2 Punnett square.

Calculate PCR amplification efficiency from the standard curve slope: E = 10^(−1/slope) − 1. Acceptable range is 90–110%.

For a given shell n, find all allowed l and ml values, subshell names, electrons per subshell, shell capacity, and the hydrogen energy level.

Estimate quarter-mile elapsed time and trap speed from vehicle weight and horsepower using the Lawlor drag-racing formula.

Calculate the minimum cage size your rabbit needs based on body length, shoulder height and breed — based on RWAF and House Rabbit Society guidelines.

Predict offspring coat colours from two parent rabbits using A-locus (agouti/self) and B-locus (black/chocolate) Mendelian genetics.