Length Unit Conversion: Metric, Imperial and More

The metric system: one base unit, powers of ten

Metric length is built on a single base unit, the meter, plus prefixes that scale it by powers of ten. Milli means one thousandth, centi one hundredth and kilo one thousand, so 1 km = 1,000 m, 1 m = 100 cm and 1 cm = 10 mm. Converting between metric units is just a matter of moving the decimal point, which is the main reason the system is used in science and by most of the world.

Since 1983 the meter has been defined through the speed of light: it is the distance light travels in a vacuum in 1/299,792,458 of a second. Fixing the speed of light as an exact number means a meter is the same everywhere, without relying on a physical bar kept in a vault. It also lets us compute very large distances from first principles. A light-year, the distance light travels in one Julian year of 365.25 days, works out to about 9.46 × 10^15 meters.

The most common slip in metric conversion is getting the direction wrong. When you go from a larger unit to a smaller one, the number gets bigger: 1.75 m becomes 175 cm. When you go from smaller to larger, it gets smaller: 2,500 m becomes 2.5 km. If you are unsure, write down one anchor fact such as 1 m = 100 cm and check that you are multiplying or dividing in the same direction.

• 1 km = 1,000 m
• 1 m = 100 cm = 1,000 mm
• 1 cm = 10 mm
• 1 mm = 1,000 micrometers

Inches, feet, yards and miles are defined in meters

Since the international yard and pound agreement of 1959, the customary units used in the United States and the imperial units used in the UK share the same lengths, and all of them are defined from the meter. One inch is exactly 2.54 cm. One foot is 12 inches, exactly 30.48 cm. One yard is 3 feet, exactly 91.44 cm. One mile is 1,760 yards, exactly 1,609.344 m. These are exact definitions, not rounded approximations, so a conversion done with them carries no inherent error.

The nautical mile used at sea and in aviation is a different unit altogether. It is defined as exactly 1,852 m, a value that comes from the length of one minute of latitude on the Earth. A nautical mile is about 15 percent longer than a statute mile, so when a speed or range is quoted in miles it is worth checking which kind is meant. Knots, the usual unit of speed for ships and aircraft, are nautical miles per hour.

Because these units mix base 12 and base 3, lengths are often written in two parts. A height of 5 feet 9 inches is 5 × 12 + 9 = 69 inches, and 69 × 2.54 = 175.26 cm. Going the other way, 170 cm is 170 ÷ 2.54 = 66.93 inches. Subtract 60 inches for 5 feet and you are left with about 6.9 inches, so 170 cm is roughly 5 feet 7 inches.

• 1 inch = 2.54 cm exactly
• 1 foot = 12 inches = 30.48 cm
• 1 yard = 3 feet = 91.44 cm
• 1 mile = 1,760 yards = 1,609.344 m
• 1 nautical mile = 1,852 m

Traditional Japanese units: shaku and ken

Many countries once had their own body-based units, and Japan still uses some of them in carpentry and architecture. In the traditional shakkanho system, one shaku is defined as 10/33 of a meter, about 30.30 cm. One sun is a tenth of a shaku, about 3.03 cm, and one ken is 6 shaku, about 1.818 m. Room layouts, sliding door widths and column spacing in Japanese buildings are often still planned on a grid of one ken or half a ken.

For longer distances there was the ri, equal to 36 cho, where one cho is 60 ken. That makes one ri 2,160 ken, or about 3.927 km. Old highways were marked with mounds roughly every ri. The length converter linked below covers shaku, sun and ken but not ri, so for ri the simplest approach is to multiply by 3.927 km by hand.

It is a coincidence, but a useful one, that the shaku and the foot are nearly the same length: 30.30 cm against 30.48 cm. Both grew out of human proportions and were later standardized. The gap is under 2 mm per unit, yet over 6 units it reaches about 1 cm, so the two should never be treated as interchangeable in measurements that matter.

Worked examples from everyday life

Screen sizes are measured diagonally. A 55-inch television has a diagonal of 55 × 2.54 = 139.7 cm. For a 16:9 screen, the width is the diagonal multiplied by 16 divided by the square root of (16² + 9²), which gives about 47.94 inches, or 121.8 cm. The height is about 26.96 inches, or 68.5 cm. When you are checking whether a TV fits a cabinet or a wall space, it is the width, not the diagonal, that you need.

Golf distances are usually given in yards. A 300-yard drive is 300 × 0.9144 = 274.32 m. Going the other way, 100 m is about 109.36 yards, so a yardage figure is roughly 10 percent larger than the same distance in meters. In athletics, the mile (1,609.344 m) is about 109 m longer than the metric 1,500 m race, and the marathon distance of 42.195 km is about 26.22 miles.

Aviation is another place where feet persist. A cruising altitude of 30,000 feet is 30,000 × 0.3048 = 9,144 m. In the other direction, a 10 km road race is about 6.21 miles, and a 5 km race is about 3.11 miles.

• 5 ft 9 in = 175.26 cm
• 55-inch diagonal = 139.7 cm
• 300 yards = 274.32 m
• 42.195 km = about 26.22 miles
• 30,000 ft = 9,144 m

Mental shortcuts and how much error they add

For a quick sense of scale, rounded factors are handy: a mile is about 1.6 km, a foot about 30 cm, a yard about 0.9 m and an inch about 2.5 cm. Each shortcut trades accuracy for speed, and it helps to know how much you give up.

Using 1.6 km per mile underestimates by about 0.58 percent, so over 100 miles you would be short by about 0.93 km. The foot, yard and inch shortcuts each underestimate by about 1.6 percent. That is fine for picturing a hiking route or a room, but not for anything you will cut, order or build, where small errors add up across many pieces. In those cases, use the exact definitions.

For conversions in the other direction, 1 km is about 0.62 miles (more precisely 0.6214) and 1 m is about 3.28 feet (more precisely 3.2808). A final sanity check catches most mistakes: a distance in miles should be a smaller number than the same distance in kilometers, and a length in feet should be a bigger number than the same length in meters. If your answer breaks that rule, you have probably multiplied where you should have divided.

• 1 mile is about 1.6 km (about 0.58 percent low)
• 1 foot is about 30 cm (about 1.6 percent low)
• 1 yard is about 0.9 m (about 1.6 percent low)
• 1 inch is about 2.5 cm (about 1.6 percent low)
• 1 km is about 0.62 miles; 1 m is about 3.28 feet