Length Converter

Rather than storing a factor for every possible pair of units, which would mean 72 separate numbers for nine units, the converter uses a single base. Each unit is defined by how many metres it contains, and every conversion runs in two steps: multiply the input by the source unit's metre factor to get a length in metres, then divide by the destination unit's metre factor to get the answer.

The metric factors are decimal by definition: a millimetre is 0.001 metres, a centimetre is 0.01, and a kilometre is 1000. The imperial factors come from the international agreement of 1959, which defined the yard as exactly 0.9144 metres. Everything else follows from it: a foot is exactly 0.3048 metres, an inch is exactly 0.0254 metres, and a statute mile of 1760 yards is exactly 1609.344 metres. The nautical mile is separately defined as exactly 1852 metres.

Because all of these are exact definitions rather than measured approximations, the two-step route introduces no error beyond ordinary floating-point rounding.

Enter 5, set the source unit to kilometre and the destination to mile.

Step one converts to the base unit: 5 kilometres multiplied by 1000 metres per kilometre gives 5000 metres. Step two divides by the mile factor: 5000 divided by 1609.344 equals 3.106856 miles, usually shown as 3.1069 or rounded to 3.11 for everyday use.

The all-units table then shows the same 5000 metres expressed everywhere else. In feet, 5000 divided by 0.3048 is 16404.2 feet. In yards, 5000 divided by 0.9144 is 5468.07 yards. In inches, 5000 divided by 0.0254 is 196850.4 inches. In nautical miles, 5000 divided by 1852 is 2.6998.

A quick sanity check in the other direction: a marathon of 26.2 miles multiplied by 1609.344 gives 42164.8 metres, close to the official 42195 metres, because the official distance is 26 miles and 385 yards rather than a round 26.2.

Decide how many figures your task actually needs. Converted values rarely land on round numbers, and quoting 3.106856 miles for a distance you paced out on a phone implies a precision you do not have. A reasonable rule is to keep the same number of significant figures you started with, so a measurement of 5 kilometres becomes about 3.1 miles rather than 3.106856.

For workshop and construction jobs, round in the direction that matters. Cutting timber to a converted length usually means rounding up and trimming, since material can be removed but not added.

Two look-alikes cause real errors. The nautical mile of 1852 metres is used in aviation and at sea and is about 15 per cent longer than the statute mile of 1609.344 metres, so mixing them up on a chart is serious. And the US survey foot, used in some older American land records, is very slightly longer than the international foot of 0.3048 metres; the difference is tiny per foot but grows to a couple of centimetres over a kilometre of surveying.