Height Conversions: Feet and Inches to Centimeters

Why height is awkward to convert

Most length conversions involve a single unit on each side. Height is different, because in the United States and the United Kingdom a person’s height is normally written in two units at once: feet and inches, as in 5 ft 9 in or 5’9”. Almost everywhere else, and in most medical and scientific settings, the same height is a single number in centimeters, such as 175 cm.

The conversion is simple once you see that the two-unit form is really one length split into a whole number of feet and a remainder in inches. Everything below follows from two exact definitions: 1 inch = 2.54 centimeters and 1 foot = 12 inches = 30.48 centimeters. Both are exact by definition, not rounded approximations, so no accuracy is lost in the factors themselves.

From feet and inches to centimeters

There are two equivalent routes. The first turns everything into inches before converting. Multiply the feet by 12, add the extra inches, then multiply the total by 2.54. The second converts each part separately: feet × 30.48 plus inches × 2.54. Both give the same answer, so use whichever you find easier to check.

Take 5 ft 9 in. In inches, that is 5 × 12 + 9 = 69 in. Then 69 × 2.54 = 175.26 cm. Checking with the second route: 5 × 30.48 = 152.4 cm and 9 × 2.54 = 22.86 cm, and 152.4 + 22.86 = 175.26 cm. The two routes agree.

A second example: 6 ft 2 in is 6 × 12 + 2 = 74 in, and 74 × 2.54 = 187.96 cm. For everyday purposes, such as a profile or a form, rounding to the nearest whole centimeter (176 cm and 188 cm) is normally fine.

From centimeters to feet and inches

Going the other way has one extra step, because the answer has to be split back into feet and inches. First divide the centimeters by 2.54 to get total inches. Then divide by 12: the whole-number part is the feet, and the remainder is the inches.

For 170 cm: 170 ÷ 2.54 = 66.929 in. Dividing by 12 gives 5 feet with a remainder of 66.929 − 60 = 6.929 in. So 170 cm is about 5 ft 6.93 in, which most people would round to 5 ft 7 in. The same method gives 180 cm = 70.866 in = 5 ft 10.87 in, or roughly 5 ft 11 in.

Notice that the inches part is a decimal. When a form asks for a whole number of inches you have to round it, and that rounding is worth up to half an inch, or about 1.3 cm, in the result.

Reference values

These values are calculated from the exact factors above and are useful for sanity checks. Centimeter values are rounded to two decimals where needed.

• 5 ft 0 in = 60 in = 152.4 cm
• 5 ft 6 in = 66 in = 167.64 cm
• 5 ft 9 in = 69 in = 175.26 cm
• 6 ft 0 in = 72 in = 182.88 cm
• 6 ft 2 in = 74 in = 187.96 cm

In the other direction: 150 cm is 59.06 in (4 ft 11.06 in), 160 cm is 62.99 in (about 5 ft 3 in), and 190 cm is 74.80 in, which is 6 ft 2.80 in. Each extra 2.54 cm adds exactly one inch, which is a handy way to move up or down from a known value. Likewise, each extra 30.48 cm adds exactly one foot.

Common mistakes

The most frequent error is treating the part after the apostrophe as a decimal. 5’9” means five feet and nine inches, not 5.9 feet. Since 5.9 ft × 30.48 = 179.83 cm, while 5 ft 9 in is 175.26 cm, the mistake adds more than 4.5 cm. The decimal-feet equivalent of 5 ft 9 in is 5.75 ft, because 9 ÷ 12 = 0.75.

A second error is multiplying the feet by 2.54, which is the inch factor, instead of 30.48. A third is forgetting that a foot has twelve inches, not ten, which makes sums such as 5 ft 10 in plus 3 in easy to get wrong: that is 6 ft 1 in, not 5 ft 13 in.

Rounding and where precision matters

Self-reported heights are rarely accurate to better than a centimeter or so, so presenting 175.26 cm as though it were precise can be misleading. Rounding to the nearest centimeter, or to the nearest half-inch when going the other direction, keeps the result honest.

If a height is being used for something that matters, such as a medical record, a clothing specification or an engineering drawing, use the exact factors, keep extra digits until the final step and check the original document. A unit converter such as this one can do the arithmetic instantly in the Length category, with a choice of decimal places, but it cannot know whether the figure you typed was measured or estimated.