Physics unit conversions
Convert speed, energy, power, force, pressure, torque, temperature, length, mass, density, volume, area and angle units. Every factor is computed from the unit definitions (SI, NIST SP 811, CODATA 2022) and shown with its derivation and a table.
Length
Every formula on this site takes lengths in metres. Heights, distances and stopping distances quoted in feet, inches or miles have to be converted first — getting it wrong by a factor of 3.28 is the most common unit slip in homework.
Mass
Physics formulas take mass in kilograms. Pounds (lb) are a unit of mass; pound-force (lbf) is the weight of a pound — a different quantity, on the force page.
Speed
Kinematics and energy formulas need speed in metres per second. Road speeds come in km/h or mph, so convert before you square anything: kinetic energy goes with v², so a unit slip is squared too.
| Conversion | Rule |
|---|---|
| km/h to m/s | 1 km/h = 0.2777777778 m/s |
| m/s to km/h | 1 m/s = 3.6 km/h |
| mph to m/s | 1 mph = 0.44704 m/s |
| m/s to mph | 1 m/s = 2.236936292 mph |
| mph to km/h | 1 mph = 1.609344 km/h |
| km/h to mph | 1 km/h = 0.6213711922 mph |
| kn to km/h | 1 kn = 1.852 km/h |
| kn to mph | 1 kn = 1.150779448 mph |
| ft/s to m/s | 1 ft/s = 0.3048 m/s |
Energy
The SI unit of energy is the joule. Food labels use kilocalories, electricity bills kilowatt-hours, heating specs BTU and particle physics electronvolts — the same quantity in five costumes.
| Conversion | Rule |
|---|---|
| J to cal | 1 J = 0.2390057361 cal |
| cal to J | 1 cal = 4.184 J |
| kcal to kJ | 1 kcal = 4.184 kJ |
| kJ to kcal | 1 kJ = 0.2390057361 kcal |
| J to kWh | 1 J = 2.777777778 × 10⁻⁷ kWh |
| kWh to J | 1 kWh = 3,600,000 J |
| kWh to MJ | 1 kWh = 3.6 MJ |
| eV to J | 1 eV = 1.602176634 × 10⁻¹⁹ J |
| J to eV | 1 J = 6.241509074 × 10¹⁸ eV |
| kWh to BTU | 1 kWh = 3,412.141633 BTU |
| BTU to J | 1 BTU = 1,055.055853 J |
| ft·lbf to J | 1 ft·lbf = 1.355817948 J |
| Wh to J | 1 Wh = 3,600 J |
| kWh to kcal | 1 kWh = 860.4206501 kcal |
Power
Power is energy per second; the watt is one joule per second. Engine ratings in horsepower and air-conditioner ratings in BTU/h convert to watts with fixed factors.
| Conversion | Rule |
|---|---|
| hp to W | 1 hp = 745.6998716 W |
| W to hp | 1 W = 0.00134102209 hp |
| hp to kW | 1 hp = 0.7456998716 kW |
| kW to hp | 1 kW = 1.34102209 hp |
| PS to kW | 1 PS = 0.73549875 kW |
| PS to hp | 1 PS = 0.9863200706 hp |
| W to BTU/h | 1 W = 3.412141633 BTU/h |
| kW to BTU/h | 1 kW = 3,412.141633 BTU/h |
Force
Force in SI is the newton (kg·m/s²). Kilogram-force and pound-force are the weights of a kilogram and a pound at standard gravity — gravity's conventional value, not your local one.
Pressure
Pressure is force per area; the pascal is one newton per square metre. Tyres are quoted in psi or bar, weather in hPa, blood pressure in mmHg and gas laws in pascals or atmospheres.
| Conversion | Rule |
|---|---|
| psi to bar | 1 psi = 0.06894757293 bar |
| bar to psi | 1 bar = 14.50377377 psi |
| psi to kPa | 1 psi = 6.894757293 kPa |
| kPa to psi | 1 kPa = 0.1450377377 psi |
| bar to kPa | 1 bar = 100 kPa |
| atm to Pa | 1 atm = 101,325 Pa |
| atm to psi | 1 atm = 14.69594878 psi |
| atm to bar | 1 atm = 1.01325 bar |
| mmHg to kPa | 1 mmHg = 0.1333223874 kPa |
| mmHg to psi | 1 mmHg = 0.01933677746 psi |
| Torr to Pa | 1 Torr = 133.3223684 Pa |
| inHg to hPa | 1 inHg = 33.8638864 hPa |
| psi to MPa | 1 psi = 0.006894757293 MPa |
| hPa to mmHg | 1 hPa = 0.7500615758 mmHg |
Torque
Torque is force times lever arm, in newton-metres. Workshop manuals mix N·m, lbf·ft and lbf·in; a torque wrench set in the wrong unit over- or under-tightens by a large factor.
| Conversion | Rule |
|---|---|
| N·m to lbf·ft | 1 N·m = 0.7375621493 lbf·ft |
| lbf·ft to N·m | 1 lbf·ft = 1.355817948 N·m |
| N·m to lbf·in | 1 N·m = 8.850745791 lbf·in |
| kgf·m to N·m | 1 kgf·m = 9.80665 N·m |
Temperature
Gas laws and radiation formulas need absolute temperature in kelvin. Celsius and kelvin differ by an offset only; Fahrenheit differs in both offset and step size, so it is a formula, not a single factor.
Density
Density is mass per volume. 1 g/cm³ is exactly 1000 kg/m³ — water is close to that — and the buoyancy and pressure formulas take kg/m³.
| Conversion | Rule |
|---|---|
| g/cm³ to kg/m³ | 1 g/cm³ = 1,000 kg/m³ |
| kg/m³ to g/cm³ | 1 kg/m³ = 0.001 g/cm³ |
| lb/ft³ to kg/m³ | 1 lb/ft³ = 16.01846337 kg/m³ |
| kg/m³ to lb/ft³ | 1 kg/m³ = 0.06242796058 lb/ft³ |
| g/cm³ to lb/in³ | 1 g/cm³ = 0.036127292 lb/in³ |
Volume
The cubic metre is the SI unit of volume; the litre is exactly one thousandth of it. The US and UK gallons are different sizes, which is why a fuel-economy figure in mpg depends on which country printed it.
| Conversion | Rule |
|---|---|
| L to US gal | 1 L = 0.2641720524 US gal |
| US gal to L | 1 US gal = 3.785411784 L |
| L to UK gal | 1 L = 0.2199692483 UK gal |
| UK gal to L | 1 UK gal = 4.54609 L |
| US gal to UK gal | 1 US gal = 0.8326741846 UK gal |
| m³ to L | 1 m³ = 1,000 L |
| ft³ to L | 1 ft³ = 28.31684659 L |
| m³ to ft³ | 1 m³ = 35.31466672 ft³ |
| m³ to US gal | 1 m³ = 264.1720524 US gal |
| in³ to cm³ | 1 in³ = 16.387064 cm³ |
Area
Area in SI is the square metre. Squaring a length conversion squares its factor: 1 ft = 0.3048 m, so 1 ft² is 0.3048² m².
| Conversion | Rule |
|---|---|
| m² to ft² | 1 m² = 10.76391042 ft² |
| ft² to m² | 1 ft² = 0.09290304 m² |
| cm² to in² | 1 cm² = 0.15500031 in² |
| in² to mm² | 1 in² = 645.16 mm² |
Angle
Calculators on this site take angles in degrees, but the maths underneath runs in radians: a full turn is 360° or 2π rad.