Exact vs Rounded Conversion Factors
Some conversion factors are exact by definition. Most of the ones you see quoted aren't. Knowing which is which tells you how many digits of your answer actually mean anything.
Why the distinction matters
If you convert 12 inches to centimeters, the answer is 30.48 cm and every digit is real, because the inch is defined as exactly 2.54 centimeters. If you convert 12 kilograms to pounds, a calculator will happily show 26.455471462. Almost none of those digits mean anything, because the factor itself is a rounded value and your input probably wasn't measured to eleven digits either.
Reporting a converted figure to more precision than the original measurement had is the most common way conversion output becomes misleading. It looks more authoritative and is less trustworthy.
What makes a factor exact
An exact factor comes from a definition rather than a measurement. In 1959 the international yard and pound agreement fixed the inch at exactly 2.54 centimeters and the pound at exactly 0.45359237 kilograms. Those aren't measured approximations that might be refined later; they are the definitions themselves.
NIST marks exact factors in boldface in its conversion tables, and rounds everything else to the digits shown. This site follows the same convention: every converter states whether the factor it uses is exact or rounded.
Why the reverse factor usually isn't exact
Here is the part that surprises people. One pound is exactly 0.45359237 kilograms. But one kilogram is 1 divided by 0.45359237 pounds, which is 2.204622621848... continuing without terminating. The forward factor is exact and the reverse factor isn't, even though they describe the same relationship.
1 kg = 2.2046226… lb (rounded, doesn't terminate)
The same asymmetry applies to inches and centimeters, gallons and liters, and most other pairs. Whichever direction the definition was written in is the exact one.
Which is which
| Relationship | Value | Exact? |
|---|---|---|
| 1 inch to centimeters | 2.54 cm | Exact by definition |
| 1 foot to meters | 0.3048 m | Exact by definition |
| 1 pound to kilograms | 0.45359237 kg | Exact by definition |
| 1 ounce (avoirdupois) to grams | 28.349523125 g | Exact by definition |
| 1 US gallon to liters | 3.785411784 L | Exact by definition |
| 1 US cup to milliliters | 236.5882365 mL | Exact by definition |
| Celsius to Fahrenheit | F = C x 9/5 + 32 | Exact by definition |
| 1 kilogram to pounds | 2.2046226 lb | Rounded reciprocal |
| 1 newton-meter to foot-pounds | 0.7375621 ft-lb | Rounded |
| 1 kilopascal to psi | 0.1450377 psi | Rounded |
| 1 kilometer to miles | 0.62137119 mi | Rounded |
Significant figures calculator
Enter a number and a digit count between 1 and 15.
How many digits to keep
A practical rule: your converted answer should carry no more significant figures than the least precise number that went into it. If a recipe says 180 °C, that is three significant figures at most and arguably two, so 356 °F is right and 356.0 isn't.
Where a limit is involved, rounding direction matters as well as digit count. NIST's guidance notes that when converting a value that represents a maximum or minimum, such as a safety clearance, the converted value must be rounded in the direction that doesn't violate the original limit.
Common questions
What makes a conversion factor exact?
It comes from a definition rather than a measurement. The inch is defined as exactly 2.54 centimeters and the pound as exactly 0.45359237 kilograms, so those factors are exact at any precision.
Why is the reverse of an exact factor usually not exact?
Because dividing one by an exact decimal rarely terminates. One pound is exactly 0.45359237 kilograms, but one kilogram is 2.204622621848 and continuing pounds, so the reverse figure has to be rounded.
How many significant figures should I keep?
No more than the least precise number that went into the calculation. If a recipe says 180 degrees Celsius, that is three significant figures, so 356 Fahrenheit is right and 356.0 isn't.
Does rounding direction ever matter?
Yes. When a value represents a maximum or minimum, such as a safety clearance, NIST guidance is to round the converted value in the direction that doesn't violate the original limit.
Related guides
Sources
- NIST Guide to the SI, Appendix B: Conversion Factors. National Institute of Standards and Technology. Source for every factor in the table above, for the boldface-means-exact convention, and for the guidance on rounding converted values and limits.