Mathematics

Calculate molality (b = moles of solute divided by kilograms of solvent) in mol/kg from the moles of solute and the mass of the solvent.

Calculate molarity from moles and volume — molarity = moles ÷ litres of solution, in moles per litre (mol/L, also written M).

Calculate the mole fraction of each component in a two-part mixture from the amount in moles — x_A = nA / (nA + nB), with both fractions summing to 1.

Convert a mass into the amount of substance (n = m / M) in moles and the number of molecules from the mass and molar mass.

Calculate the moment of inertia (I = m·r²) of a point mass about an axis of rotation in kg·m² from its mass and its distance from the axis.

Calculate the linear momentum (p = mv) in kg·m/s and the kinetic energy of a moving object from its mass and velocity.

Calculate the output frequency, duty cycle, and high/low times of a 555 timer in astable mode from R1, R2, and the timing capacitor — f = 1.44 / ((R1 + 2·R2) × C).

Calculate the output pulse width of a 555 timer in monostable (one-shot) mode from its timing resistor and capacitor — T = 1.1 × R × C.

Calculate the net force on an object from its mass and acceleration using Newton's second law — force = mass × acceleration (F = m × a).

Calculate the nth root of a number, ⁿ√x = x^(1/n), from the radicand and the degree — square roots, cube roots, and any higher root.

Calculate the area, perimeter, apothem, and circumradius of a regular octagon from its side length — area = 2(1+√2)s², perimeter = 8s, apothem = ((1+√2)/2)s, circumradius = (√(4+2√2)/2)s.

Calculate the volume, cross-section area, and surface area of a regular octagonal prism from the side length and prism length — volume = 2(1+√2)·s²·L.

The complete Ohm's law solver. Pick which two of voltage (V), current (I), resistance (R), and power (P) you know, enter them, and get the other two instantly — V = I × R, P = V × I, and every rearrangement.

Calculate the orbital period (Kepler's third law, T = 2π·√(a³/GM)) in seconds and days from the semi-major axis and the central mass.

Calculate the circular orbital velocity (v = √(GM/r)) in m/s and km/s of a body orbiting a central mass from the mass and orbital radius.

Calculate the volumetric flow rate through a sharp-edged orifice — Q = Cd·A·√(2gh). The discharge coefficient Cd (~0.62) accounts for the vena contracta.

Calculate the osmotic pressure (Π = iMRT) in atmospheres and kilopascals of a solution from the van 't Hoff factor, the molar concentration, and the temperature.

Calculate the distance to a star in parsecs and light-years from its annual parallax angle in arcseconds, using d = 1 / p.

Calculate the moment of inertia about a parallel axis with the parallel axis theorem: I = I_cm + m·d² in kg·m².

Calculate the total capacitance of two capacitors in parallel — they simply add: C = C1 + C2.

Calculate the equivalent inductance of two inductors in parallel, L_eq = (L1·L2)/(L1+L2), in henries from the two coil inductances.

Calculate the combined resistance of two resistors in parallel using the product-over-sum rule — Rp = (R1 × R2) ÷ (R1 + R2).

Calculate the capacitance of a parallel-plate capacitor from its plate area, plate separation, and dielectric constant — C = ε₀ × εr × A / d.

Calculate the area of any parallelogram from its base and perpendicular height using the formula area = base × height.

Calculate the partial pressure of a gas using Dalton's law (P_i = mole fraction × total pressure) in kilopascals.

Calculate the output force of a hydraulic press with Pascal's principle (F2 = F1 × A2 / A1) from the input force and the two piston areas.

Work out your new pay and the size of the increase from a raise percentage — currency-agnostic, works for hourly or annual pay, and handles pay cuts too.

Calculate the period and frequency of a simple pendulum from its length — period = 2π√(L ÷ g) and frequency = 1 ÷ period.

Calculate the area, perimeter, apothem, and circumradius of a regular pentagon from its side length — area = ¼√(5(5+2√5))s², perimeter = 5s, apothem = s/(2·tan36°), circumradius = s/(2·sin36°).

Calculate the volume, cross-section area, and surface area of a regular pentagonal prism from the side length and prism length — volume = ¼√(5(5+2√5))·s²·L.

Calculate percent error between an experimental (measured) value and a theoretical (true) value — percent error = |measured − true| ÷ |true| × 100%.

Calculate the percent yield of a chemical reaction from the actual yield and the theoretical yield predicted by stoichiometry.

Calculate percentages in three modes: find a percentage of a number, find what percent one number is of another, or calculate percentage change between two values.

Calculate the percentage increase or decrease between an original value and a new value, with the absolute difference shown alongside.

Calculate the percentage difference between two values — a symmetric comparison relative to their average.

Calculate the percent error between a measured value and the accepted (true) value, plus the absolute error.

Calculate the pH (pH = −log₁₀([H⁺])) of an aqueous solution from its hydrogen-ion concentration, plus the matching pOH.

Calculate the energy of a photon (E = h·c / λ) in electronvolts and joules from its wavelength using the Planck–Einstein relation.

Calculate the momentum of a photon (p = h / λ) in kg·m/s from its wavelength in nanometres, using the Planck constant.

Work out the weight of any straight pipe run from its outside diameter, wall thickness, length and material. Metric and imperial, seven materials.

Convert pixels to inches, centimetres, millimetres or points at any DPI — and back. Free, instant, and it shows the pixel density the answer depends on.

Convert a point between polar and rectangular coordinates in either direction, in degrees or radians.

Calculate each interior angle of a regular polygon ((n − 2)·180 / n) and the sum of all interior angles ((n − 2)·180) from the number of sides.

Calculate the gravitational potential energy of an object from its mass and height — PE = m × g × h, with g = 9.80665 m/s², in joules.

Calculate power from work and time — power = work ÷ time, in watts (W), with the equivalent in horsepower (hp).

Convert power between metric, imperial, and thermal units — watts, kilowatts, megawatts, mechanical horsepower, metric horsepower (PS), and BTU per hour.

Calculate the power dissipated by a resistor (P = I²R) in watts and the voltage drop across it from the current and resistance.

Calculate the power factor, phase angle, and reactive power of an AC circuit from its real and apparent power — PF = P / S, φ = arccos(P / S), Q = √(S² − P²).

Calculate power-to-weight ratio in watts per kilogram and horsepower per tonne and per pound, for cars, bikes, and cycling.

Calculate the pixel density (PPI) and dot pitch of any display from its pixel resolution and physical diagonal in inches.