Mathematics

Calculate the combined capacitance of two capacitors in series using the product-over-sum rule — C = (C1 × C2) ÷ (C1 + C2).

Calculate the total resistance of two resistors in series — they simply add: R = R1 + R2.

Convert shoe sizes between EU, UK, US (Men), US (Women), and foot length in centimetres — instantly, using the documented foot-length method.

Round any number to a chosen count of significant figures, with a worked explanation of how the rounding place is found.

Calculate the skin depth of an AC current in a conductor from the frequency, resistivity, and relative permeability — δ = √(ρ / (π × f × µ₀ × µr)).

Calculate the slope (gradient) and y-intercept of the line through two points — slope = (y2 − y1) ÷ (x2 − x1) and y = mx + b.

Calculate the angle of refraction with Snell's law (n1·sin θ1 = n2·sin θ2) from the two refractive indices and the angle of incidence.

Calculate the daily energy output (kWh) of a solar panel or array from its wattage, the site's peak sun hours, and a performance ratio.

Calculate the stock volume needed and the diluent to add using C₁V₁ = C₂V₂ when diluting a solution to a target concentration and final volume.

Calculate the sound intensity level in decibels (L = 10 · log₁₀(I/I₀), with I₀ = 1e-12 W/m²) from a measured sound intensity in watts per square metre.

Calculate how a point source's sound pressure level drops with distance in a free field — L2 = L1 − 20·log10(d2/d1). Doubling the distance lowers the level by about 6 dB.

Calculate the specific gravity (relative density) of a substance from its density and a reference density such as water at 4 °C (1000 kg/m³).

Calculate the specific heat capacity c = Q / (m·ΔT) in J/(kg·K) from the heat energy added, the mass, and the temperature change of a sample.

Calculate the specific impulse (Isp) of a rocket engine in seconds from its thrust and propellant mass flow rate.

Calculate the specific weight (weight density, γ = ρ·g) of a material in N/m³ from its density and the local gravitational acceleration.

Convert speed between metric, imperial, and nautical units — metres per second, kilometres per hour, miles per hour, feet per second, and knots.

Calculate the speed of sound in dry air from the air temperature — v = 331.3 + 0.606 × T (T in °C), about 343 m/s at 20 °C.

Calculate average speed in km/h and pace in minutes per kilometre from a distance in kilometres and a time in hours.

Calculate the surface area of a sphere from its radius using A = 4 × π × r², plus the volume, in any unit you choose.

Calculate the volume and surface area of a sphere from its radius using V = 4/3 × π × r³ and A = 4 × π × r².

Calculate the curved surface, base radius, and total surface area of a spherical cap from the sphere radius and cap height — curved surface = 2πRh, base radius = √(h(2R−h)).

Calculate the volume, curved surface area, and base radius of a spherical cap from the sphere radius and cap height — volume = (πh²/3)(3R−h), curved surface = 2πRh, base radius = √(h(2R−h)).

Calculate the volume of a spherical sector from the sphere radius and the cap height — volume = (2/3)πR²h.

Calculate the volume of a spherical segment (a zone of a sphere between two parallel planes) from the two base radii and the height — volume = (πh/6)(3a² + 3b² + h²).

Calculate the volume of a spherical wedge (an orange slice) from the sphere radius and the wedge angle in degrees — volume = (2/3)·R³·α, with α in radians.

Calculate the period and frequency of a mass-spring oscillator from its mass and spring constant — period = 2π√(m ÷ k) and frequency = 1 ÷ period.

Calculate the elastic potential energy (PE = ½kx²) in joules stored in a stretched or compressed spring from its spring constant and displacement.

Convert square feet to linear feet, or square metres to running metres. Enter the area and the material width — the width is what makes the conversion possible.

Calculate the total square footage of a rectangular area from its length and width, with the result shown in square feet and square metres.

Calculate the radiated power of an ideal blackbody (P = σAT⁴) in watts from its surface area and absolute temperature using the Stefan-Boltzmann law.

Calculate a vehicle's total stopping distance from its speed, reaction time, and tyre–road friction — stopping distance = reaction distance (v·t) + braking distance (v²/(2·μ·g)).

Calculate the surface gravity (g = G·M/r²) in m/s² of a planet or moon from its mass and radius, plus how many Earth gravities that is.

Calculate the surface (cutting) speed (v = π × d × n) in metres per minute of a rotating part from its diameter and rotational speed.

Solve a 2×2 system of linear equations by Cramer's rule. Enter the six coefficients and get x and y instantly, with the determinant shown.

Calculate the tangential (linear) velocity (v = ω × r) in metres per second of a point on a rotating body from its angular velocity and radius.

Find the capacity of a cylindrical, rectangular, or capsule tank in litres, US gallons, imperial gallons, and cubic metres.

Convert temperature between Celsius, Fahrenheit, and Kelvin — instantly and with exact, offset-based scale definitions.

Calculate the terminal velocity of a falling object, v = √(2mg / ρACd), in metres per second from its mass, area, drag coefficient, and fluid density.

Calculate your test grade as a percentage and a US A–F letter grade from the points you earned out of the total possible points.

Calculate the linear thermal expansion (ΔL = α·L₀·ΔT) of a solid — the change in length and the final length from its expansion coefficient, original length, and temperature change.

Calculate the conductive thermal resistance (R = L ÷ kA) in K/W of a flat layer from its thickness, thermal conductivity, and area.

Solve the thin-lens equation (1/f = 1/dₒ + 1/dᵢ) for the image distance and magnification from a focal length and object distance.

Calculate the real, apparent, and reactive power of a balanced three-phase AC system from line voltage, line current, and power factor — P = √3 × V_L × I_L × pf.

Calculate the thrust-to-weight ratio (TWR = thrust ÷ (mass × g)) of a rocket, drone, or jet from its thrust and mass — a ratio above 1 means it can lift off.

Calculate torque (τ = F × r) in newton-metres from a force and a lever-arm length, with the force applied perpendicular to the lever arm.

Convert torque between newton-metre, pound-foot, pound-inch, kilogram-force metre, and more — instantly and with exact, newton-metre-based conversion factors.

Convert engine torque (lb-ft) and rpm to power in horsepower and kilowatts — horsepower = (torque × rpm) / 5252, kilowatts = horsepower × 0.7457.

Calculate the efflux speed of fluid leaving an opening below the surface with Torricelli's law — v = √(2gh). The exit speed equals a free fall from the same height and ignores fluid density.

Calculate the surface area and volume of a torus (ring/donut) from its major and minor radius — surface = 4π²Rr, volume = 2π²Rr².

Calculate the volume and surface area of a torus (a donut) from its major radius R and minor radius r — volume = 2π²Rr², surface area = 4π²Rr.