MultiKitExact Unit Conversions Worth Knowing
Many conversion factors people look up are not measurements at all. They are definitions, so the result is exact and any rounding is your choice. A few others are rounded values, and it helps to know which is which.
Exact by definition
According to NIST’s table of conversion factors, these are exact:
| Conversion | Factor |
|---|---|
| 1 inch | 2.54 centimeters |
| 1 foot | 0.3048 meters |
| 1 mile | 1.609344 kilometers |
| Fahrenheit from Celsius | °F = °C × 1.8 + 32 |
The 32 and the 1.8 of the temperature formula are exact as well. The pound is defined as 0.45359237 kilograms; NIST’s table shows it rounded to 0.4535924.
Worked examples
- A person who is 5 feet 10 inches tall is 70 inches, which is 70 × 2.54 = 177.8 centimeters.
- A marathon of 42.195 kilometers is 42.195 ÷ 1.609344 = 26.2188 miles to four decimals.
- 1 kilogram is 1 ÷ 0.45359237 = 2.2046 pounds.
- Water boils at 100 °C, which is 100 × 1.8 + 32 = 212 °F. Body temperature of 37 °C is 98.6 °F.
- −40 is the same on both scales: −40 × 1.8 + 32 = −40.
- A room of 10 feet by 20 feet is 200 square feet. One square foot is 0.3048² = 0.09290304 square meters, so the room is 18.58 square meters.
Why a converter shows fewer digits than the definition
A computer holds most decimal numbers as binary approximations, so a sum that should be exactly 212 can come out as 211.99999999999994. The unit tools here use the js-quantities library, which keeps the definitions of the units, and round to 12 significant digits to remove that noise. The numbers you see are therefore correct to far more digits than you will use.
The Korean pyeong
The pyeong is a Korean unit of area. It is defined as 400/121 square meters, about 3.3058 square meters. That makes 60 square meters 18.15 pyeong, and 10 pyeong 33.058 square meters. According to Wikipedia, the unit has been officially banned since 1961 and its commercial use was made illegal from 1 July 2007, but it is still widely used, and property listings often show square meters with a pyeong equivalent.
A checklist
- Know whether a factor is a definition or a rounded value.
- Convert first and round last. Rounding in the middle adds error.
- For areas, convert the area, not the sides: a square foot is not 0.3048 square meters.
- Say which unit you mean when it matters: there is more than one kind of mile, ton and gallon in the world.