The units of length
Length is the magnitude with the most units still in daily use, because the metric and imperial systems genuinely coexist in industry, construction and trade. The metre is the SI base unit and since 1983 it has been defined by the speed of light: the distance light travels in 1/299,792,458 of a second. Every imperial length unit is now legally defined in terms of the metre, so the two systems are exactly, not approximately, related.
| Unit | Symbol | Equals |
|---|---|---|
| Millimetres | mm | 0.001 m |
| Centimetres | cm | 0.01 m |
| Decimetres | dm | 0.1 m |
| Metres | m | 1 m |
| Kilometres | km | 1,000 m |
| Inches | in | 0.0254 m |
| Feet | ft | 0.3048 m |
| Yards | yd | 0.9144 m |
| Miles | mi | 1,609.344 m |
| Nautical miles | nmi | 1,852 m |
How to convert by hand
Every length conversion follows the same procedure: take the amount to the base unit, then from there to the target unit. In practice it is a single multiplication, because the two steps combine into one factor.
Multiply by the source unit's factor to get metres, then divide by the target unit's factor. In practice the two steps collapse into a single multiplication, which is what the conversion factor is.
The equivalents people look up most
| Conversion | Result |
|---|---|
| A standard door | 2.03 m · 6 ft 8 in |
| A football pitch | 105 m · 344.5 ft |
| A marathon | 42.195 km · 26.22 miles |
| Average adult height | 1.75 m · 5 ft 9 in |
| Cruising altitude | 11,000 m · 36,089 ft |
Common mistakes
- Treating an inch as 2.5 cm. It is exactly 2.54, and over a long run that 1.6% adds up fast.
- Confusing statute miles with nautical miles. A nautical mile is 1,852 m against 1,609.34 m, an 15% difference that matters at sea and in the air.
- Converting an area or a volume with a length factor. Areas need the factor squared, volumes cubed.
- Rounding mid-calculation. Round once, at the end, or the error compounds through every step.