How to convert between metric and imperial units

Defined units, not measured ones

It surprises many people that the inch, the foot, and the pound are defined in terms of metric units. Nobody measures a foot and reports how many meters it is; the foot is defined to be exactly 0.3048 meters. That is why a good converter can be exact, and why disagreement between two tools is almost always a rounding difference.

The NIST Guide for the Use of the International System of Units (SP 811) lists these as exact factors, and the arithmetic below follows from them:

• 1 inch = 2.54 cm = 25.4 mm exactly (NIST marks the inch factor as exact).
• 1 foot = 0.3048 m exactly, and 1 yard = 0.9144 m exactly.
• 1 mile = 5,280 feet, which works out to exactly 1,609.344 m, or 1.609344 km.
• 1 pound (avoirdupois) = 0.45359237 kg exactly. NIST's table prints this as 4.535 924 E-01 and a footnote gives the exact value 4.535 923 7 E-01.
• 1 ounce (avoirdupois) = 1/16 pound = 28.349523125 g, and 1 stone = 14 pounds = 6.35029318 kg.

The basic rule: multiply one way, divide the other

A conversion factor is a ratio between two units. To go from imperial to metric, multiply by the factor. To go back, divide by it. Before you press anything, do a size check: a meter is longer than a foot, so a number in meters should be smaller than the same length in feet. A kilogram is heavier than a pound, so a number in kilograms should be smaller than the number in pounds.

Worked examples, calculated from the exact factors:

• 6 feet x 0.3048 = 1.8288 m.
• 70 inches x 2.54 = 177.8 cm. A height of 5 ft 10 in is 70 inches, not 5.10 feet.
• 150 pounds x 0.45359237 = 68.04 kg (68.0389 to four decimals).
• 70 kilograms / 0.45359237 = 154.32 pounds.
• 50 miles x 1.609344 = 80.4672 km.
• 10 kilometers / 1.609344 = 6.2137 miles, so a 5K is 3.107 miles.
• 1 meter / 0.3048 = 3.28084 feet, and 1 kilogram / 0.45359237 = 2.204623 pounds.

Squared and cubed factors

Area and volume are where most conversion mistakes happen, because the factor must be squared or cubed. One foot is 0.3048 m, so one square foot is 0.3048 x 0.3048 = 0.09290304 m2, and one cubic foot is 0.3048 x 0.3048 x 0.3048 = 0.028316846592 m3, which is 28.316846592 liters. In centimeters, 1 square inch = 2.54 x 2.54 = 6.4516 cm2, and 1 cubic inch = 2.54^3 = 16.387064 cm3. NIST lists the square inch as exactly 6.4516 E-04 m2.

Worked example: a room measures 12 ft by 10 ft. The area is 120 sq ft. In metric that is 120 x 0.09290304 = 11.148 m2. A common wrong approach multiplies 120 by 0.3048 and gets 36.58, which is more than three times too large. Converting each side first confirms the right answer: 12 ft = 3.6576 m and 10 ft = 3.048 m, and 3.6576 x 3.048 = 11.148 m2.

The reverse direction uses the inverse: 1 m2 = 1 / 0.09290304 = 10.7639 sq ft, so a 100 m2 apartment is about 1,076 sq ft. For land, 1 acre = 43,560 sq ft = 4,046.8564224 m2 = 0.40468564 hectares. For volume, 1 m3 = 35.3147 cu ft, and one liter is a thousandth of a cubic meter.

The Area Converter and Volume Converter apply these squared and cubed factors for you, so you never have to remember which exponent to use.

Gallons, pints, and the US versus imperial split

The US gallon is defined as 231 cubic inches. With 1 inch = 2.54 cm, that is 231 x 16.387064 cm3 = 3,785.411784 cm3, or 3.785411784 L. NIST lists it rounded as 3.785 412 L. The imperial (UK and Canadian) gallon is larger, at 4.546 09 L in the same NIST table. The ratio is 4.54609 / 3.785412 = 1.201, so an imperial gallon is about 20.1 percent bigger.

That gap carries through to everything built on the gallon. 30 miles per US gallon is 30 x 1.20095 = 36.03 miles per imperial gallon for the identical car on identical roads. This is why UK fuel-economy figures look better than US ones. The Volume Converter uses US customary units throughout: 16 cups per gallon, 128 fluid ounces per gallon. One US cup is about 236.59 mL and one US pint is about 473.18 mL (NIST: 2.365 882 E+02 mL and 4.731 765 E-01 L), so if a recipe or product label is British, do not assume its pint or fluid ounce matches the US one.

Fuel economy has its own metric conversion because it is a ratio of distance to volume. NIST's guide says to divide 235.215 by the miles-per-US-gallon value to get liters per 100 km. So 30 mpg is 235.215 / 30 = 7.84 L/100 km, and NIST's own example, 24 mpg, comes out at 9.8 L/100 km.

Tons, tonnes, and ounces

Three different units are called a ton. The US short ton is 2,000 pounds, which is 907.18474 kg. The long ton used historically in the UK is 2,240 pounds, or 1,016.0469 kg. The metric tonne, called a metric ton in the US, is exactly 1,000 kg, or 2,204.62 pounds. The metric ton is about 10.2 percent heavier than the short ton, so "a ton of gravel" can mean quite different quantities depending on the supplier. The Weight Converter offers US (short) tons and metric tons, and does not include the long ton.

The ounce is also split. Mass uses the avoirdupois ounce, 28.35 g. Troy ounces, used for precious metals, are heavier at 31.10348 g (NIST: 3.110 348 E-02 kg). And a fluid ounce measures volume, not weight: a US fluid ounce is about 29.57 mL. A pint of water is roughly a pound by weight, but that is a property of water and does not make a fluid ounce and an ounce the same thing.

In everyday speech, weight and mass are used interchangeably, and that is fine for conversions on Earth.

Mental-math shortcuts and how wrong they are

Shortcuts are useful for quick estimates, as long as you know the size of their error. Each of these was checked against the exact factor:

• Inches to centimeters: multiply by 2.5. It runs 1.6 percent low (10 inches is 25 cm, exact is 25.4 cm).
• Miles to kilometers: multiply by 1.6. It runs 0.6 percent low (50 miles is 80 km, exact is 80.47 km).
• Kilometers to miles: multiply by 0.6. This is 3.4 percent low, so 0.62 is better (100 km is 62.1 miles, not 60).
• Kilograms to pounds: double it and add 10 percent, which is the same as multiplying by 2.2. It runs 0.2 percent high (70 kg is 154 lb).
• Meters to feet: multiply by 3.28, which is within 0.03 percent.
• Feet to meters: multiply by 0.3, which runs 1.6 percent low (100 ft is 30 m, exact is 30.48 m).
• Liters to US gallons: divide by 4. It runs about 5 percent low (40 L is 10 gal by this rule, exact is 10.57 gal).

Common mistakes and rounding

The same errors turn up again and again. People forget to square or cube the factor for area and volume. They use a US gallon for an imperial one, or the reverse. They mix up short tons and tonnes. They treat 5 ft 10 in as 5.10 feet instead of 5.83 feet. And they round too early, converting a rounded intermediate value and then rounding again, so errors stack up. Convert once with the full factor and round at the end.

Temperature is the exception to everything above. Celsius and Fahrenheit do not share a zero point, so converting needs a multiplication and an offset, not a single factor. Use the Temperature Converter for that, and see the dedicated temperature guide for the formulas.

A note on the tools themselves: the Length Converter works through meters using the exact length factors above. For mass and volume, EveryFix uses rounded constants, 0.453592 kg per pound and 3.78541 L per US gallon, which differ from the exact definitions by less than one part in a million. For 200 pounds that is 90.7184 kg against the exact 90.718474 kg, so the difference only appears after the fourth decimal place. That is far below any practical need, but it is the reason your result might differ from a calculation done with all the digits.