Unit Converter

Nearly every unit conversion — whether you are converting kilometres, kilograms, kilojoules or kilopascals — is the same two-step move: scale the input to one agreed base unit, then scale back out to the target. That single idea is why one tool can handle thirteen different kinds of quantity. The only thing that changes between length and mass and pressure is the conversion factor, and for temperature, an added offset; the procedure underneath is identical. So instead of memorising a separate rule for feet-to-metres, pounds-to-kilograms and psi-to-bar, you learn it once and it applies everywhere.

This calculator puts all thirteen quantities on one canonical URL: length (13 units, millimetre to parsec), mass (12 units, milligram to carat), temperature (5 scales, kelvin to Réaumur), volume (12 units, millilitre to UK gallon), area (10 units, square millimetre to square mile), pressure (12 units, pascal to inch of water), energy (11 units, joule to electronvolt), power (9 units, watt to mechanical horsepower), force (8 units, newton to short ton-force), torque (7 units, newton-metre to ounce-inch), angle (7 units, radian to arcsecond), time (12 units, nanosecond to decade) and data storage (14 units, bit to exbibyte) — 132 units in all. Each quantity routes through a single SI base unit: metre, kilogram, kelvin, cubic metre, square metre, pascal, joule, watt, newton, newton-metre, radian, second and byte. The factor tables come straight from NIST SP 811 Appendix B.8, the BIPM SI Brochure 9th edition, ISO 80000-3 through 80000-5, the 1959 International Yard and Pound Agreement, and the relevant IAU resolutions.

Twelve of the thirteen quantities are purely multiplicative, because their zero points coincide: 0 m, 0 kg, 0 J and 0 Pa all mean "nothing". Temperature is the one exception. Celsius and Fahrenheit start counting from a shifted zero relative to the absolute Kelvin scale, so their conversion is affine — multiply by the slope, then add the offset — rather than a plain ratio. That single offset is also the source of the most common temperature trap: a change of 5 °C is not 41 °F (that would be the reading at 5 °C), it is a change of 9 °F, because the offset of 32 cancels in differences but not in absolute readings. No other quantity behaves this way, which is exactly why the calculator switches to the offset-aware formula the moment you pick a temperature scale and leaves every other quantity on the simple ratio.

Most casual converters merge every category into one giant dropdown of 2,000 entries and treat every factor as equally trustworthy. This one does the opposite: it groups units by physical quantity, exposes the SI pivot, and labels every result exact or approximate. Metre ↔ inch is exact (both factors are finite binary fractions fixed by the 1959 agreement); Celsius ↔ Fahrenheit is tagged approximate because the 5/9 slope never terminates in IEEE-754 binary, even though it is symbolically exact by the 13th CGPM 1967 Resolution 4; degree ↔ radian is approximate because π/180 is irrational and any 64-bit double rounds it at the 16th digit. That honesty about exact-versus-approximate is what separates a converter built for engineers from one built for ad impressions. The second difference is shareable state: every choice — category, source, target, value, precision — is encoded in the URL as ?cat=length&from=meter&to=foot&v=1&p=auto, so there is no per-pair URL explosion (no /miles-to-kilometers route). The canonical URL is /tools/unit-converter and every conversion is a query-string permutation of it, which means an engineering wiki, a lab manual or a Stack Overflow comment can link to the exact conversion the reader needs.

Every conversion in this tool is two operations through a single SI base unit per category. For purely multiplicative quantities (length, mass, volume, area, pressure, energy, power, force, torque, angle, time, data storage) the formula is:

where x is your input value, a_from is the source unit's factor to the SI base, and a_to is the target unit's factor to the same base. For temperature — the only quantity with non-zero zero points relative to its absolute scale — the formula adds an offset and becomes affine:

To do it by hand, follow the same four steps regardless of category:

1. Look up the source-to-base factor. For feet to metres, a_from = 0.3048. For psi to pascals, a_from = 6894.757293168361. For Btu (IT) to joules, a_from = 1055.05585262.

2. Multiply the input by that factor to get the value in the SI base unit. 100 ft × 0.3048 = 30.48 m. 50 psi × 6894.757293168361 = 344,737.86 Pa. 1 Btu × 1055.05585262 = 1055.05585262 J.

3. Look up the target-to-base factor. For metres to inches, a_to = 0.0254. For pascals to bar, a_to = 100,000. For joules to kilowatt-hours, a_to = 3,600,000.

4. Divide the base value by the target factor. 30.48 m ÷ 0.0254 = 1200 in. 344,737.86 Pa ÷ 100,000 = 3.4474 bar. 1055.05585262 J ÷ 3,600,000 = 0.00029307 kWh.

The same procedure works for every supported unit in every category. The one trap is temperature: a 5 °C change is not 41 °F (which would be the value at 5 °C); it is a 9 °F change, because the offset cancels in differences but not in absolute readings. The calculator handles this correctly by routing through the offset-aware affine formula.

To use this calculator, pick a measurement category from the sticky category strip at the top — Length, Mass, Temperature, Volume, Area, Pressure, Energy, Power, Force, Torque, Angle, Time or Data storage. Pick a source unit from the From searchable dropdown, type a value, then pick a target unit from the To dropdown. The result updates on every keystroke; no Convert button. Click the hero result card to copy the converted value to the clipboard. Use the precision selector to switch between auto (6 significant figures, scientific notation outside the 10⁻³ to 10¹² range), or a fixed 0, 2, 4, 6, 10 or 15 decimals. The exact badge appears next to the result whenever both the source and target units are definitionally exact and the conversion does not lose information in IEEE-754; approximate fires when the slope or factor is irrational in binary (5/9 for Fahrenheit and Rankine, π/180 for degree, π/200 for gradian, π/648000 for arcsecond) or when one endpoint is too large to fit a 64-bit double without rounding (light-year, parsec).

The general multiplicative formula above covers twelve of the thirteen supported categories (length, mass, volume, area, pressure, energy, power, force, torque, angle, time, data storage). The thirteenth — temperature — uses an affine form because Celsius, Fahrenheit and Réaumur have non-zero zero points relative to the absolute (Kelvin) scale: T_out = ((T_in × a_from + b_from) − b_to) / a_to. Every factor table this calculator uses is sourced from primary metrology references:

The exact badge fires only when both endpoints are factors representable bit-perfectly as 64-bit doubles. So metre ↔ inch is exact (both factors are finite binary fractions), psi ↔ kPa is exact, joule ↔ kilowatt-hour is exact. But degree ↔ radian is approximate (π/180 is irrational), Celsius ↔ Fahrenheit is approximate (5/9 is non-terminating in binary), and light-year ↔ kilometre is approximate (the integer metre value of a light-year is too large to fit a double without rounding the last digit). The badge is informational honesty, not a quality complaint.