How this is worked out
Every category has a base unit, and each unit records how many base units it represents. Any conversion is then one multiplication and one division:
result = value × from.factor ÷ to.factor
That structure matters because it means there is no per-pair lookup table to get wrong. Adding a new unit is one number, and it is immediately convertible to every other unit in the category.
The factors here are exact by definition rather than rounded. Since the 1959 international yard and pound agreement, an inch is exactly 25.4 millimetres and a pound is exactly 0.45359237 kilograms. Using 2.54 and 0.4536 instead looks close enough and is not: convert metres to feet to inches and back with rounded factors and you drift. With exact ones the round trip returns the number you started with.
Temperature is the exception and gets its own code path. The scales have different zero points as well as different degree sizes, so a conversion needs an offset as well as a factor — which is why −40 is the same number in Celsius and Fahrenheit, and why no single multiplier can do the job.
A worked example
- 1 mile in kilometres
- 1.609344 (exact)
- 1 kilogram in pounds
- 2.204623
- 1 US gallon in litres
- 3.785411784 (exact)
- 1 acre in square metres
- 4,046.8564224 (exact)
- 100°C in Fahrenheit
- 212°F
- −40°C in Fahrenheit
- −40°F
- 1 TB in TiB
- 0.9095 — the missing 9%
Why your 1TB drive shows as 931GB
It is not missing space and it is not a fault. Drive manufacturers use the decimal definitions — a terabyte is 1,000,000,000,000 bytes — because those are the internationally standardised SI prefixes. Windows reports capacity in binary units, where a tebibyte is 1,099,511,627,776 bytes, but labels them "TB".
One terabyte is 0.9095 tebibytes. So a genuine 1TB drive genuinely holds 931 of the units Windows is counting, and the shortfall is entirely a labelling disagreement. macOS and most Linux distributions switched to decimal reporting years ago, which is why the same drive shows a different number on a Mac.
Both families are in the converter and labelled clearly, because knowing which one a number is in is usually the whole question.
A pint is not a pint
A US liquid pint is 473ml. An imperial pint is 568ml — twenty per cent larger. The same split runs through fluid ounces, quarts and gallons, and it is a genuine source of error in recipes, fuel economy figures and anything involving a bar.
The imperial gallon is 4.54609 litres against the US gallon's 3.785. That is a 20% difference, and it is why a UK car quoted at 50 miles per gallon is not directly comparable to a US car quoted at 50 — the American figure is worse than it looks. Both fluid ounce sizes are in the converter and labelled by system.
The US fluid ounce is 29.57ml and the imperial is 28.41ml, which is confusing in a different way: the imperial ounce is the smaller one, even though the imperial pint is bigger. That is because an imperial pint has 20 fluid ounces and a US pint has 16.
Precision, and where it stops mattering
The converter shows more significant figures for small numbers than large ones, because a fixed number of decimal places destroys one end or the other. 0.00003048 and 1,609.344 both need to read correctly, and two decimal places would render the first as 0.00.
That said, most of the precision here is not physically meaningful for what you are measuring. If you are converting a room measurement taken with a tape measure, four decimal places of a metre is nine decimal places more accuracy than the measurement had. Use the precision as a guarantee that the arithmetic did not introduce error, not as a claim about your input.
Where it genuinely matters is chained conversions — metric to imperial to metric again, or through several units in a recipe or a spreadsheet. That is exactly where rounded factors accumulate visible drift and exact ones do not.
The units that are defined by other units
Several units in this converter exist only as definitions in terms of others. A nautical mile is exactly 1,852 metres, defined that way in 1929 to approximate one minute of latitude. A knot is one nautical mile per hour, which is why it is not a round number in metres per second.
An acre is 4,840 square yards, which is 4,046.8564224 square metres exactly — an awkward figure that comes from its origin as the area one man with one ox could plough in a day. A hectare, by contrast, is simply 10,000 square metres, which is why it is easier to work with and why most of the world uses it.
None of these are approximations. Where a factor here has many decimal places it is because the exact definition has many decimal places, not because something was measured imprecisely.
Assumptions and sources
- Length and mass
- International yard and pound agreement (1959): 1 inch = 25.4 mm exactly, 1 pound = 0.45359237 kg exactly. All derived units follow.
- Volume
- US gallon = 231 cubic inches exactly (3.785411784 L). Imperial gallon = 4.54609 L exactly.
- Data
- SI decimal prefixes (kB, MB, GB, TB) and IEC binary prefixes (KiB, MiB, GiB, TiB). Both are standard; they are different units.
- Temperature
- Celsius, Fahrenheit and Kelvin converted through Celsius with the standard offsets. Kelvin has no degree symbol by convention.