Physics Calculators and Formulas
One calculator for each core physics formula, from Newton’s laws and motion to optics, electricity, heat and modern physics. Each solves for any variable, accepts SI or US units and shows the working.
38 calculators · 21 converters · common conversions
Forces and Newton’s Laws
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Gravitational Force Calculator
F = G m₁ m₂ / r²
G = 6.67430 × 10⁻¹¹ N·m²/kg², m₁ and m₂ the masses, r the distance between their centres
Example: Earth (5.972 × 10²⁴ kg) and the Moon (7.348 × 10²² kg) 384,400 km apart: Gravitational force F = 1.98211 × 10²⁰ N.
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Newton's Second Law Calculator
F = m a
F net force (N), m mass (kg), a acceleration (m/s²)
Example: A 12 kg trolley accelerating at 2.5 m/s²: Net force F = 30 N.
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- Weight Calculator – Mass and a planet (or any g) → weight in N, kgf and lbf, with a table for every planet.
- Centripetal Force Calculator – Mass, speed and radius → centripetal force and acceleration; or solve for any one of them.
- Hooke's Law Calculator – Any two of spring force, spring constant and extension → the third, plus stored energy.
- Young's Modulus Calculator – Stress and strain → Young's modulus, or E with one of them → the other (Hooke's law).
- Tensile Stress Calculator – Load + round, rectangular or tube section → tensile or yield stress in MPa, N/mm², psi, ksi.
Motion
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Speed Distance Time Calculator
v = d / t
v average speed, d distance, t time; d = v × t, t = d / v
Example: A 150 km drive that takes 2 hours 30 minutes: Speed v = 60 km/h.
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Acceleration Calculator
a = (v − u) / t
a acceleration, v final velocity, u initial velocity, t time taken
Example: A car that speeds up from 5 m/s to 25 m/s in 10 s: Acceleration a = 2 m/s².
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- Equations of Motion (SUVAT) Calculator – Any three of displacement, initial and final velocity, acceleration and time → the other two.
- Free Fall Calculator – Height or fall time → the other, plus impact speed, on Earth or any g.
- Projectile Motion Calculator – Launch speed, angle and height → range, maximum height, flight time and impact velocity.
- Pendulum Period Calculator – Length and g → period and frequency; or the length for a period, or g from a measurement.
Energy, Work and Momentum
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Kinetic Energy Calculator
KE = ½ m v²
KE kinetic energy (J), m mass (kg), v speed (m/s)
Example: A 20 kg object moving at 10 m/s: Kinetic energy KE = 1000 J.
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Potential Energy Calculator
PE = m g h
PE potential energy (J), m mass, g gravitational acceleration, h height above the reference level
Example: Lifting a 10 kg box 10 m on Earth: Potential energy PE = 980.665 J.
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- Work Calculator – Force, displacement and the angle between them → work; or the force, distance or angle.
- Power Calculator – Work (energy) and time → power in W, kW or hp; or the energy or time.
- Momentum Calculator – Mass and velocity → momentum; or the mass or velocity for a given momentum.
- Impulse Calculator – Average force and contact time → impulse; or the force or time for an impulse.
Fluids, Pressure and Density
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Pressure Calculator
P = F / A
P pressure (Pa = N/m²), F force normal to the surface, A area
Example: A 500 N force spread over 0.01 m² (10 cm × 10 cm): Pressure P = 50000 Pa.
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Density Calculator
ρ = m / V
ρ density, m mass, V volume; specific gravity = ρ / ρ(water)
Example: A 2.7 kg block with a volume of 1 litre (0.001 m³): Density ρ = 2700 kg/m³.
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- Buoyancy Calculator – Fluid density and displaced volume → buoyant force; or the volume or density.
- Reynolds Number Calculator – Velocity, diameter, density and viscosity in any units → Re and flow regime.
Gravitation and Orbits
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Escape Velocity Calculator
vₑ = √(2GM / R)
G gravitational constant, M mass of the body, R distance from its centre (the radius at the surface)
Example: Escaping Earth from its surface (GM = 3.986004418 × 10¹⁴ m³/s², R = 6371 km): Escape velocity from Earth vₑ = 11.1861 km/s.
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Orbital Velocity Calculator
v = √(GM / r), T = 2π √(r³ / GM)
r = R + altitude, the distance from the body’s centre; GM the gravitational parameter
Example: The International Space Station about 420 km above Earth: Orbital speed v = 7.66129 km/s.
Waves and Optics
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Wave Speed Calculator
v = f λ
v wave speed, f frequency (Hz), λ wavelength; period T = 1/f
Example: Concert A (440 Hz) travelling through air at 343 m/s: Wavelength λ = 0.779545 m.
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Snell's Law Calculator
n₁ sin θ₁ = n₂ sin θ₂
n refractive index of each medium, θ angle measured from the normal; critical angle θc = arcsin(n₂/n₁)
Example: Light passing from air (n = 1) into water (n = 1.333) at 30° to the normal: Angle of refraction θ₂ = 22.0301 °.
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Lens and Mirror Equation Calculator
1/f = 1/dₒ + 1/dᵢ, m = −dᵢ/dₒ
f focal length, dₒ object distance, dᵢ image distance (real-is-positive convention); m magnification
Example: An object 15 cm from a converging lens with f = 10 cm: Image distance dᵢ = 30 m.
Electricity
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Coulomb's Law Calculator
F = k |q₁ q₂| / r²
k = 1/(4πε₀) = 8.9875517923 × 10⁹ N·m²/C², q the charges, r the distance between them
Example: Two +1 µC charges 10 cm apart in vacuum: Electrostatic force F = 0.898755 N.
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Ohm's Law Calculator
V = I R, P = V I
V voltage, I current, R resistance, P power
Example: 12 V across 4 Ω drives 3 A and dissipates 36 W.
Heat and Gases
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Specific Heat Calculator
Q = m c ΔT
Q heat (J), m mass (kg), c specific heat capacity (J/(kg·K)), ΔT temperature change (K or °C)
Example: Heating 1 kg of water by 10 °C: Heat energy Q = 41840 J.
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Combined Gas Law Calculator
P₁V₁ / T₁ = P₂V₂ / T₂
P pressure, V volume, T absolute temperature (K) for a fixed amount of gas
Example: 2 L of gas at 1 atm and 20 °C heated to 100 °C while the pressure doubles to 2 atm: Final volume V₂ = 1.2729 L.
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- Ideal Gas Law Calculator – Solve PV = nRT for P, V, n or T in any pressure, volume and temperature units.
- Thermal Expansion Calculator – Material or α + length + temperature change → expansion ΔL and new length.
Modern Physics
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E = mc² Calculator
E = m c²
E energy (J), m mass (kg), c = 299,792,458 m/s exactly
Example: Converting 1 gram of mass entirely into energy: Energy E = 89875500000000 J.
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Photon Energy Calculator
E = h f = h c / λ
h = 6.62607015 × 10⁻³⁴ J·s, c = 299,792,458 m/s (both exact), f frequency, λ wavelength
Example: A photon of green light with a wavelength of 500 nm: Photon energy E = 2.47968 eV.
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- de Broglie Wavelength Calculator – A particle and its speed, energy or accelerating voltage → its matter wavelength.
- Half-Life Calculator – Initial amount, half-life and time → amount left; or the age, half-life or starting amount.
Unit Converters for Physics
- Length Converter – m, km, cm, mm, µm, ft, in, mi, yd, nmi
- Weight and Mass Converter – kg, g, mg, lb, oz, st, t, ton, oz t, ct
- Time Converter – ms, s, min, h, day
- Temperature Converter – °C, °F, K, °R
- Speed Converter – km/h, mph, m/s, ft/s, knots
- Angle Converter – degrees, radians, gradians, arcminutes
- Frequency & RPM Converter – Hz, kHz, MHz, GHz, rpm, rad/s
- Energy Converter – J, kJ, kWh, kcal, cal, BTU, therm, eV
- Power Converter – W, kW, MW, hp, PS, BTU/h, TR, kcal/h
- Force Converter – N, kN, lbf, kgf, kip, dyn, ozf, gf
- Pressure Converter – Pa, kPa, psi, bar, inH₂O, mmHg, torr, atm
- Density Converter – kg/m³, g/cm³, g/mL, lb/ft³, lb/gal, mg/L
- Radioactivity Converter – Bq, MBq, Ci, mCi, µCi, pCi, dpm
- Absorbed Radiation Dose Converter – Gy, mGy, cGy, rad, kGy
- Radiation Dose Converter (Sv, rem) – Sv, mSv, µSv, rem, mrem
- Illuminance Converter (Lux, Foot-candle) – lux, foot-candles, klx, phot
- Luminance Converter (Nits, cd/m²) – nits, cd/m², foot-lamberts, stilb
- Thermal Conductivity Converter – W/(m·K), mW/(m·K), BTU/(h·ft·°F), k-value, kcal/(h·m·°C)
- Magnetic Flux Density Converter – T, mT, µT, nT, G, mG, kG
- Magnetic Field Strength Converter – A/m, kA/m, A/cm, Oe, kOe
- Magnetic Flux Converter – Wb, mWb, µWb, Mx
Common Physics Conversions
Using these physics calculators
The calculators here apply the core relations of school and engineering physics, one formula per tool: Newton’s laws and gravitation, the equations of motion and projectiles, work, energy, power and momentum, pressure and buoyancy, waves and optics, Coulomb’s and Ohm’s laws, heat and the gas laws, and the photon, de Broglie and half-life relations of modern physics. Each shows the formula with your numbers substituted, so you can check the working as well as the result.
Most tools solve for any variable in their equation. Pick what you want to find, enter the rest in the units you have (kilograms or pounds, metres, kilometres or miles, km/h or mph) and choose the unit of the answer; every input is converted to SI before the formula runs, and the step-by-step working shows each conversion.
Physical constants are entered exactly where they are defined exactly. The gas constant R = 8.314462618 J/(mol·K) is exact in the revised SI, as are the conversion factors between SI, CGS and US units used by the converters. Temperatures in gas calculations must be absolute (kelvin), and pressures must be absolute, not gauge.
Results are given in full and can be cut to the number of decimals you need. Report the answer to the precision of your least precise input: a temperature known to the nearest degree does not justify a volume to ten significant figures.