Eight Units, Four Exact Definitions
The metric units are powers of ten of the meter. The imperial units are all defined from the meter too, through four exact numbers, so every length conversion can be done without rounding until the final answer.
| Unit | Symbol | In meters | Defined as |
|---|
| Millimeter | mm | 0.001 | 1/1000 m |
| Centimeter | cm | 0.01 | 1/100 m |
| Meter | m | 1 | SI base unit |
| Kilometer | km | 1000 | 1000 m |
| Inch | in | 0.0254 | 2.54 cm exactly |
| Foot | ft | 0.3048 | 12 in = 0.3048 m |
| Yard | yd | 0.9144 | 3 ft = 0.9144 m |
| Mile | mi | 1609.344 | 1,760 yd = 1,609.344 m |
How the Inch Became Exactly 2.54 cm
Until the 1950s the US inch and the British inch were very slightly different, because each country defined its yard from its own standards. In 1959 the US, UK, Canada, Australia, New Zealand and South Africa agreed on an international yard of exactly 0.9144 meters.
That single agreement fixed the inch at 2.54 cm, the foot at 30.48 cm and the mile at 1,609.344 m. It is why these converters can give exact answers rather than approximations.
Mental Shortcuts and How Far Off They Are
When you need a rough answer without a calculator, these rules are close enough for everyday use. The error column shows how far each one is from the exact value.
| Conversion | Shortcut | Exact factor | Error |
|---|
| cm → in | × 0.4 | 0.393701 | +1.6% |
| in → cm | × 2.5 | 2.54 | −1.6% |
| m → ft | × 3.3 | 3.28084 | +0.6% |
| ft → m | × 0.3 | 0.3048 | −1.6% |
| km → mi | × 0.6 | 0.621371 | −3.4% |
| mi → km | × 1.6 | 1.609344 | −0.6% |
| m → yd | × 1.1 | 1.093613 | +0.6% |