Which factors are exact and which are not
The distinction matters when a converted figure is carried into further calculation. An exact factor introduces no error at all; a defined-but-irrational relationship or a measured constant does.
| Relationship | Status | Value |
|---|---|---|
| Inch to metre | Exact by definition (1959) | 0.0254 |
| Pound to kilogram | Exact by definition (1959) | 0.45359237 |
| Mile to metre | Exact by definition | 1609.344 |
| US gallon to litre | Exact (231 cubic inches) | 3.785411784 |
| Imperial gallon to litre | Exact by definition (1985) | 4.54609 |
| Mile per hour to metre per second | Exact | 0.44704 |
| Nautical mile to metre | Exact by international agreement | 1852 |
- Mass and weight are distinct physical quantities. The kilogram and the pound used here are units of mass; a kilogram-force or pound-force is a unit of force and is not interchangeable with them.
- US and imperial liquid measures share names but not sizes: a US gallon is 3.785411784 litres and an imperial gallon is 4.54609 litres, a difference of about 20%. The same applies to pints and fluid ounces.
What a unit conversion actually is
A unit conversion multiplies a measurement by a ratio equal to one. Because 1 inch and 25.4 millimetres are the same length, the fraction 25.4 mm / 1 in has a value of one, and multiplying by it changes the units without changing the quantity.
Most of the imperial-to-metric factors in everyday use are exact rather than approximate. Since the international yard and pound agreement of 1959, the yard is defined as exactly 0.9144 metres and the pound as exactly 0.45359237 kilograms, and every derived factor — inches, feet, miles, ounces — follows from those definitions. NIST Special Publication 811 marks such factors as exact.
This converter works through the SI base unit for each quantity: the value is converted into metres, kilograms, cubic metres, square metres or metres per second, and then out again into every unit on the list. That keeps a single source of truth for each factor rather than a table of every pair.
How to use the unit converter
- Choose the quantity you are converting — length, mass, volume, area or speed.
- Pick the unit your value is currently in.
- Enter the value. Every other unit of that quantity updates at once.
- Read whichever line you need; the unit you entered is highlighted so you can check it against the rest.
The formulae behind the conversions
Each unit is stored as the number of SI base units it represents. Converting from one unit to another is therefore a multiplication followed by a division, with no chain of intermediate approximations.
Results are shown to eight significant figures rather than to a fixed number of decimal places, because the sensible precision differs enormously across a single quantity: one millimetre is 0.00000062 miles, and a fixed two-decimal display would render it as zero.
Common mistakes
- Mixing US and imperial gallons, pints or fluid ounces. They share names and differ by roughly a fifth.
- Converting an area or a volume with a linear factor. Area factors are the square of the linear factor and volume factors the cube: 1 square foot is 0.09290304 square metres, not 0.3048.
- Rounding the factor before the multiplication rather than rounding the result afterwards.
- Treating the tonne, the short ton and the long ton as one unit. This converter uses the metric tonne of 1,000 kg.
- Assuming a stone is a US unit. It is 14 pounds and is used for body weight chiefly in the UK and Ireland.
자주 묻는 질문
How many millimetres are in an inch?
Exactly 25.4. This is a definition rather than a measurement: the international yard and pound agreement of 1959 fixed the yard at exactly 0.9144 metres, which makes the inch exactly 25.4 millimetres and the foot exactly 0.3048 metres.
Is a US gallon the same as an imperial gallon?
No. A US liquid gallon is 3.785411784 litres and an imperial gallon is 4.54609 litres, so an imperial gallon is about 20% larger. US and imperial pints and fluid ounces differ in the same way, which is why a recipe or a fuel-economy figure has to state which system it uses.
Why are some conversion factors exact and others not?
A factor is exact when the units are defined in terms of one another. The inch, pound, mile and US gallon are all defined against SI units, so their factors are exact. Factors that rest on a measured physical constant, or on a unit whose definition has changed over time, are not.
How do I convert square feet to square metres?
Multiply by 0.09290304, which is 0.3048 squared. Squaring the linear factor is the step people miss: using 0.3048 directly understates the area by a factor of about 3.3.
What is the difference between mass and weight?
Mass is the amount of matter in an object and does not change with location; weight is the force gravity exerts on that mass and does. The kilogram, gram, pound, ounce and stone in this converter are units of mass, even though everyday English calls the reading on a scale a weight.
참고 자료
- National Institute of Standards and Technology. Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 edition, Appendix B — Conversion Factors. Factors printed in boldface are exact.
- National Institute of Standards and Technology. Refinement of Values for the Yard and Pound (1959) — the international yard and pound agreement defining 1 yd = 0.9144 m and 1 lb = 0.45359237 kg exactly.
- Bureau International des Poids et Mesures. The International System of Units (SI), 9th edition, 2019. bipm.org.
- National Institute of Standards and Technology. NIST Handbook 44 — Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices.