How unit conversions stay exact, and when they cannot.
Why an inch is exactly 2.54 cm, why a kilogram in pounds never ends, and how a converter can be exact without rounding factors from a table.
By Suraj Kumar4 min read
Most conversion tables print factors rounded to a few digits, and most converters multiply by them. The customary units were defined in metric terms long ago, so the exact factors are known.
Feet, pounds and gallons are defined in metric terms.
Since 1959 the inch has been exactly 25.4 mm and the pound exactly 0.45359237 kg. Everything else follows: a foot is 0.3048 m, a mile 1,609.344 m, an ounce 28.349523125 g. The US gallon is 231 cubic inches, which makes it exactly 3.785411784 litres; the UK gallon is defined as 4.54609 litres.
KeepSimp's Unit converter builds every factor from these definitions and works with exact fractions, so 5 ft 11 in is exactly 180.34 cm.
When an answer has to be rounded.
Going the other way usually means dividing: 70 kg is 70 ÷ 0.45359237 pounds, a decimal that never ends. The converter keeps it exact and rounds only to show it, says about, and gives 6 significant digits unless you ask for more.
Conversions that need a second fact.
Cups to grams needs what is in the cup, temperatures need an offset as well as a factor, and fuel economy turns round from miles a gallon to litres per 100 km. The converter handles all three, and says which fact it used.
Further reading
Topics: unit converter · unit conversion · exact conversion factors · metric conversion · imperial to metric · conversion calculator
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