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 about 0.2 percent low (70 kg is 154 lb by this shortcut, against an exact 154.32 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.

Chaining factors for speed, density, and other compound units

Many everyday quantities are ratios: miles per hour, pounds per cubic foot, liters per hundred kilometers. The safe method is to write the quantity as a fraction and convert the top and bottom separately, canceling units as you go, until only the target units remain. Nothing needs to be memorized beyond the single-unit factors already in this guide.

Speed is the simplest case. One mile is 1,609.344 m and one hour is 3,600 s, so 1 mph = 1,609.344 / 3,600 = 0.44704 m/s exactly. A car doing 60 mph is doing 60 x 1.609344 = 96.56 km/h, and 55 mph is 55 x 0.44704 = 24.59 m/s. Going the other way, 100 km/h is 100 / 1.609344 = 62.14 mph, and since there are 3.6 km/h in each m/s, a runner at 5 m/s is covering 18 km/h.

Density needs both a mass factor and a volume factor. Fresh water weighs about 62.4 pounds per cubic foot. Multiply by 0.45359237 kg per pound and divide by 0.028316846592 cubic meters per cubic foot, and you get 62.4 x 0.45359237 / 0.028316846592 = 999.6 kg/m3, which matches the familiar 1,000 kg per cubic meter. If the answer comes out wildly different from that kind of benchmark, one of the factors was probably inverted.

Pressure, power, and torque

Engineering and automotive specifications mix systems constantly. For pressure, 1 psi is 6.894757 kPa, and 1 bar is exactly 100 kPa, which is about 14.5 psi. A tire inflated to 32 psi is therefore at 32 x 6.894757 = 220.6 kPa, or 2.206 bar. A spec of 35 psi becomes 241.3 kPa. Weather pressure follows suit: standard sea-level pressure is about 29.92 inches of mercury, which is roughly 1,013 hPa.

Power has two horsepower definitions that people forget. A mechanical horsepower is 745.7 watts, and the metric horsepower, labeled PS or CV on European spec sheets, is about 735.5 watts. A 150 hp engine is 111.9 kW, while a 150 PS engine is 110.3 kW, a gap of about 1.4 percent.

Torque converts with 1 pound-foot = 1.355818 newton-meters, so 300 lb-ft is 406.7 N m. Do not confuse it with energy: a newton-meter of torque and a joule of energy share the same base units but describe different things. Likewise, pounds per square inch measures pressure, not force, so a load rating in pounds should not be converted with a pressure factor.

Fractions of an inch, lumber, and sheet goods

Workshop measurements arrive as fractions, which makes mental conversion harder. Multiply the fraction by 25.4 to get millimeters; the list at the end of this section gives the commonly used ones.

A few near-misses deserve care. A 1/2 inch wrench is 12.7 mm, a very close neighbor of a 13 mm socket, but the two are not interchangeable on a worn fastener, because 0.3 mm of slop rounds corners. Treat metric and inch fasteners as separate families rather than converting between them.

Building materials add a naming problem. A 2x4 in the US is a nominal size, and the dressed lumber measures 1.5 by 3.5 inches, or 38.1 by 88.9 mm. A sheet of plywood sold as 4 by 8 feet is 1,219.2 by 2,438.4 mm, while sheets made to metric standards are commonly 1,200 by 2,400 mm, about 19 mm narrower and 38 mm shorter. If a design assumes one and the store sells the other, convert the dimension you need, not the product name.

• 1/16 in = 1.5875 mm
• 1/8 in = 3.175 mm
• 1/4 in = 6.35 mm
• 3/8 in = 9.525 mm
• 1/2 in = 12.7 mm
• 5/8 in = 15.875 mm
• 3/4 in = 19.05 mm
• 7/8 in = 22.225 mm

Kitchen conversions and why grams beat cups

Cooking mixes volume units that look alike and are not. A US cup is about 236.6 mL, but a metric cup, used in Australia, New Zealand, and many modern recipes, is 250 mL. A US teaspoon is 4.93 mL and a metric teaspoon is 5 mL. A US tablespoon is 14.79 mL, a metric tablespoon is 15 mL in most places, and an Australian tablespoon is 20 mL. Over a single spoonful the differences are small, but 20 mL against 14.8 mL is a third larger, and recipes that call for several tablespoons of a strong ingredient can taste different.

The fluid ounce splits as well. The US fluid ounce is 29.57 mL, and the imperial fluid ounce is 28.41 mL. The imperial pint has 20 of them, so it holds 568 mL against 473 mL for the US pint of 16. A British recipe asking for a pint of milk holds about 20 percent more than a US pint. To convert a liter to US cups, divide 1,000 by 236.59 to get 4.23.

Volume is a poor stand-in for weight. A cup of flour can vary noticeably depending on whether it is scooped, spooned, or sifted, which is why many bakers prefer grams. When a recipe gives both, trust the gram figure; when it gives only volume, check which cup the author means.

Same name, different size: survey feet, nautical miles, and knots

A few specialist units share a name with an everyday one. The US survey foot was defined as 1,200/3,937 meter, or 0.3048006096 m, about two parts per million longer than the international foot of exactly 0.3048 m. The survey foot was deprecated at the end of 2022, with the international foot taking over for new work, but older land records and coordinates still use it. Over 100,000 feet the two differ by about 0.2 feet, so the choice matters for large-scale mapping and almost never for anything built on a house lot.

Navigation uses the nautical mile, defined as exactly 1,852 meters. That is 1.1508 statute miles, so it is about 15 percent longer than the mile on a road sign. A knot is one nautical mile per hour, or 0.5144 m/s. A boat doing 20 knots is moving at 37.04 km/h, which is 23.0 mph.

The fathom, used for water depth, is exactly 6 feet, or 1.8288 m. The furlong in horse racing is 660 feet, which is 201.168 m. None of these appear in the Length Converter, which covers millimeters through miles, but you can chain through meters.

Why professionals write the unit next to every number

Unit mix-ups have a long record of costing real money. In 1999 NASA's Mars Climate Orbiter was lost after one team's software reported thruster impulse in pound-force seconds while the navigation software expected newton-seconds, a factor of about 4.45. In 1983 an Air Canada Boeing 767 ran out of fuel in flight because the fuel load had been worked out in pounds when kilograms were required, leaving less than half the fuel it needed. The crew glided to a safe landing at Gimli, Manitoba.

The habits that prevent this are cheap. Write the unit beside every number in a calculation, and never leave a bare figure on a page. Convert once, at the boundary between two systems, with the full factor, and carry one system inside the work. After converting, check the direction: an answer in kilograms should be smaller than the same mass in pounds. If a result looks roughly 2.2, 2.5, or 3.3 times off, you have probably applied the wrong factor or inverted a correct one.

Body-weight figures deserve special care. A 33 pound child weighs 33 x 0.45359237 = 14.97 kg, and 11 stone 4 pounds, which is 158 pounds, is 71.67 kg. Medication doses are often set per kilogram, so a slip in the weight turns into a slip in the dose. For anything medical, have the conversion confirmed by a pharmacist or clinician.