How to convert units without losing the measurement

Treat the units like part of the arithmetic. They show you which factor to use, which way round it goes and whether the answer can be right.

The method that works across unit systems

Start with the value and its unit. Multiply by a fraction that is equal to one, with the unit you want to remove on the opposite side. The old unit cancels. The unit left behind belongs to the answer.

12 in × (2.54 cm / 1 in) = 30.48 cm

The fraction equals one because 1 inch and 2.54 centimetres are the same length. NIST records the international inch as exactly 25.4 millimetres. That makes the calculation exact until the original measurement or your final rounding limits it.

1. Write the starting unit

Never begin with a bare number. A value of 12 could mean inches, metres, pounds or seconds. Writing the unit stops the calculation from drifting away from the quantity it describes.

2. Choose one trusted equality

Use a definition or published conversion factor. The NIST Guide to the SI conversion tables distinguishes exact factors from rounded ones. The BIPM SI Brochure is the authoritative description of SI units and symbols.

3. Turn the equality into a cancelling fraction

If inches must disappear, put inches under the fraction. If centimetres must disappear, put centimetres under it. This rule replaces the unreliable instruction to remember whether to multiply or divide.

4. Calculate, then round once

Keep all available digits while you work. Round the final value to a precision that the starting measurement supports. A tape measurement written as 12.3 cm does not become more accurate because a calculator displays 4.842519685 inches.

Worked examples

Metres to feet

One international foot is exactly 0.3048 metres. Put metres below the factor so they cancel:

3 m × (1 ft / 0.3048 m) = 9.842519685 ft

If 3 m is an approximate measurement, write 9.84 ft or 9.8 ft to match its useful precision. If it is an exact design value, keep more digits where the work needs them.

Kilograms to pounds

One international avoirdupois pound is exactly 0.45359237 kilograms. Reversing that equality gives about 2.20462262185 pounds per kilogram.

10 kg × (1 lb / 0.45359237 kg) = 22.0462262185 lb

Miles per hour to kilometres per hour

A mile is exactly 1.609344 kilometres, and the hour already matches. Only the distance unit changes.

60 mi/h × (1.609344 km / 1 mi) = 96.56064 km/h

Area and volume: apply the factor to every dimension

A length conversion changes one dimension. Area has two dimensions and volume has three. One foot equals 0.3048 metres, but one square foot does not equal 0.3048 square metres.

1 ft² × (0.3048 m / 1 ft)² = 0.09290304 m²
1 ft³ × (0.3048 m / 1 ft)³ = 0.028316846592 m³

The units make the exponent visible. Two feet cancel in the area line and three cancel in the volume line. If only one factor appears, the calculation is dimensionally incomplete.

Temperature needs an offset

Celsius and Fahrenheit do not share zero. A ratio alone cannot convert them. First move the zero point, then change the scale.

°C = (°F − 32) × 5/9
°F = °C × 9/5 + 32

72 °F = (72 − 32) × 5/9 = 22.222... °C

Kelvin and Celsius use the same size interval, but their zeros differ by exactly 273.15. Add 273.15 to Celsius for kelvin. The kelvin symbol is K, without a degree sign.

Three checks catch most mistakes

1. Check the direction. A metre is longer than a foot, so the number of feet must be larger than the number of metres.
2. Check the units cancel. If the source unit remains in the fraction, turn the factor over.
3. Convert back. Run the answer through the reverse conversion. Apart from display rounding, you should recover the starting value.

What we verified

On 29 September 2026, we ran the converter's calculation code through twelve reference cases. The set covers linear factors, offsets, reciprocal fuel economy, binary storage and compound feet plus inches. Every result matched the stated reference value within 1 × 10⁻¹² relative error, or exactly where the expected result is zero.

The repeatable check is in docs/research/unit-converter/verify.mjs. Expected factors come from NIST Special Publication 811 and exact SI definitions. JavaScript uses IEEE 754 double-precision arithmetic, so the final displayed digit can reflect floating-point rounding.

Cases where a unit converter is not enough

Calendar months do not have one fixed duration. Currency needs a dated exchange rate. Medical doses need the substance, concentration and clinical context. A physical quantity may also need uncertainty, significant figures and calibration records. Conversion can preserve those facts, but it cannot supply them.