Metric to Imperial Conversion: Exact Factors and Examples

Why exact conversion factors matter

NIST's guidance on unit conversion recommends using exact conversion factors whenever they are available instead of approximate ones. It also says not to round any quantities used within the calculation, and to round only the final result. These two habits prevent most conversion errors.

Rounding early is the usual culprit. A familiar shortcut is that a mile is about 1.6 kilometers. That is fine for a rough estimate, but it adds up: a marathon is 26.2188 miles, and multiplying that by 1.6 gives 41.95 kilometers, about 0.58 percent short of the true 42.195 kilometers.

The 1959 agreement behind the inch, yard, and pound

Imperial and US customary units are defined in terms of metric ones. On 1 July 1959, Australia, Canada, New Zealand, South Africa, the United Kingdom, and the United States agreed to define the yard as exactly 0.9144 meters and the avoirdupois pound as exactly 0.45359237 kilograms.

Wikipedia notes that an inch of exactly 25.4 millimeters had already been adopted by the British Standards Institution in 1930, and that the 1959 definitions imply a foot of exactly 30.48 centimeters. Because these are definitions, not measurements, they are exact: there is no error in them, only whatever rounding you apply afterward.

Length: inches, feet, yards, and miles

NIST's conversion table lists the following length factors, and marks them as exact. You can multiply by them, or divide by them to go the other way.

• 1 inch = 2.54 centimeters = 0.0254 meters.
• 1 foot = 0.3048 meters, which is 30.48 centimeters.
• 1 yard = 0.9144 meters.
• 1 mile = 1.609344 kilometers.

Mass: ounces and pounds

The pound is defined exactly as 0.45359237 kilograms, which makes the avoirdupois ounce, one sixteenth of a pound, about 28.3495 grams. NIST's table lists the ounce as 2.834952 times 10 to the minus 2 kilograms.

• 1 pound = 0.45359237 kilograms.
• 1 kilogram = about 2.20462 pounds.
• 1 ounce (avoirdupois) = about 28.35 grams.

Volume: gallons, quarts, and fluid ounces

NIST's table gives US liquid volumes in metric terms. US customary volumes are not the same as imperial ones used in the UK, which is a classic source of confusion, so be sure which system a recipe or label uses.

• 1 US gallon = about 3.785412 liters.
• 1 US liquid quart = about 0.9463529 liters.
• 1 US fluid ounce = about 29.57353 milliliters.
• The UK imperial gallon is larger than the US gallon, at about 4.546 liters, so a gallon on a UK label is not a US gallon.

Temperature: Celsius and Fahrenheit

Temperature is different from the other conversions because the scales have different zero points. NIST's relation is degrees Celsius equals (degrees Fahrenheit minus 32) divided by 1.8. To go the other way, multiply Celsius by 1.8 and add 32.

A few reference points help you sanity-check an answer. Water freezes at 0 degrees Celsius, which is 32 degrees Fahrenheit, and boils at 100 degrees Celsius, which is 212 degrees Fahrenheit. Normal body temperature of 98.6 degrees Fahrenheit is 37 degrees Celsius. And the two scales meet at minus 40, where both read the same.

Metric to imperial quick reference

The factors above run from imperial to metric because that is how the units are defined. To convert from metric to imperial, you divide by the same factor, which is the same as multiplying by its reciprocal. These are the reciprocals you will use most, calculated from the exact values and rounded for convenience.

• 1 centimeter = about 0.3937 inches, and 1 meter = about 3.2808 feet or 1.0936 yards.
• 1 kilometer = about 0.6214 miles.
• 1 gram = about 0.03527 ounces, and 1 kilogram = about 2.2046 pounds.
• 1 liter = about 0.2642 US gallons, or about 33.81 US fluid ounces.
• 1 milliliter = about 0.03381 US fluid ounces.
• Degrees Fahrenheit = degrees Celsius multiplied by 1.8, plus 32.

How to convert step by step

The method is the same for any unit, and following it exactly avoids slips.

• Identify the starting unit and the target unit.
• Find the exact factor between them, and decide whether to multiply or divide.
• To go from the unit that appears in the factor's definition, such as inches to centimeters, multiply by the factor. To go back, divide by it.
• Keep all digits during the calculation, as NIST advises.
• Round only the final answer, to a precision that makes sense for the task.
• Check that the result is plausible: centimeters should be about two and a half times the inches, kilograms about 45 percent of the pounds.

Worked examples

These examples were calculated with the exact factors above and rounded only at the end.

• A height of 5 feet 10 inches is 70 inches, which is 177.8 centimeters.
• A 10-mile run is 16.0934 kilometers, and a 5-kilometer run is 3.1069 miles.
• A marathon of 42.195 kilometers is 26.2188 miles.
• A weight of 150 pounds is 68.0389 kilograms, and 70 kilograms is 154.3236 pounds.
• A 100-meter sprint is 328.084 feet, and a 100-yard dash is 91.4 meters.
• A speed of 100 kilometers per hour is 62.14 miles per hour, and 60 miles per hour is 96.56 kilometers per hour.
• Ten US gallons is 37.854 liters, and 250 milliliters is 8.454 US fluid ounces.
• A room at 22 degrees Celsius is 71.6 degrees Fahrenheit, and 72 degrees Fahrenheit is 22.2 degrees Celsius.

Mental shortcuts and how accurate they are

For quick estimates, a few approximations are useful as long as you know their error. For exact work, use the factors above.

• Inches to centimeters: multiply by 2.5, which is within about 2 percent of the exact 2.54.
• Kilometers to miles: multiply by 0.6, which is close to the exact 0.6214, though the error grows on long distances.
• Kilograms to pounds: multiply by 2.2, close to the exact 2.2046.
• Celsius to Fahrenheit: double it and add 30. For 22 degrees Celsius this gives 74 degrees Fahrenheit against the exact 71.6, so it is only a rough guide.

Area and fuel economy

Area and fuel economy trip people up because the factors are squares or reciprocals of the ones above. Area factors come from squaring the exact length factors, so they are exact too. Fuel economy is the odd one: miles per gallon measures distance per volume, while the metric convention, liters per 100 kilometers, measures volume per distance, so the conversion is an inverse relationship.

For US miles per gallon, divide 235.215 by the mpg figure to get liters per 100 kilometers, and divide 235.215 by liters per 100 kilometers to get mpg. Because of the inverse relationship, the same improvement in mpg saves less fuel at high efficiency than at low efficiency.

• 1 square inch = 6.4516 square centimeters, since 2.54 squared is 6.4516.
• 1 square foot = 0.09290304 square meters, and 1 square meter is about 10.7639 square feet.
• 1 acre = 4,046.8564224 square meters, so 1 hectare (10,000 square meters) is about 2.4711 acres.
• 1 square mile = about 2.589988 square kilometers.
• A 1,500 square foot home is about 139.4 square meters, and a 200 square meter apartment is about 2,152.8 square feet.
• 30 US mpg is about 7.84 liters per 100 kilometers, and 8 liters per 100 kilometers is about 29.4 US mpg.

Common conversion mistakes

Most errors fall into a few categories, and all of them are avoidable.

• Rounding the factor, such as using 1.6 for a mile, before multiplying.
• Mixing US and imperial volume units, since the gallon and pint differ between systems.
• Confusing fluid ounces, a measure of volume, with ounces, a measure of weight.
• Treating temperature as a simple multiplication and forgetting the 32-degree offset.
• Multiplying when you should divide, which gives an answer far off the plausible range.
• Confusing the metric tonne, which is 1,000 kilograms, with the US ton, which is 2,000 pounds.
• Reporting more digits than the original measurement justified.

Where to double-check

For anything important, confirm the factor against an authoritative source. NIST publishes its SP 811 Appendix B conversion tables, including the exact factors, and its page on unit conversion explains how to apply them. If you convert sensitive data or private measurements with an online tool, prefer one that runs in your browser rather than one that uploads your inputs.