How do you convert cm to feet?
Short answer. Divide centimeters by 30.48 to get feet, so 180 cm is 5.906 ft. For feet and inches, divide by 2.54 to get inches and take out the twelves: 180 cm is 70.87 in, which is 5 ft 10.9 in, not 5 ft 9. In reverse, multiply feet by 30.48: 6 ft is 182.88 cm.
Both numbers in that answer are definitions. Since the 1959 international yard and pound agreement, an inch is exactly 2.54 cm, and a foot is twelve of them:
1 inch = 2.54 cm exactly 1 foot = 12 × 2.54 cm = 30.48 cm exactly 1 cm = 1 ÷ 30.48 ft = 0.032808398950131… ft
Feet to centimeters is clean. Centimeters to feet is not: as a fraction a centimeter is 25/762 of a foot, and 762 is 2 × 3 × 127, so the decimal runs forever. Every cm to feet figure you have ever seen was rounded by somebody.
Two routes, one answer
Decimal feet: divide by 30.48. Good for lumber, ceilings and anything that will be multiplied again:
240 ÷ 30.48 = 7.874015748… → 7.874 ft
Feet and inches: divide by 2.54, then by 12. Good for heights, which nobody quotes in decimal feet:
180 ÷ 2.54 = 70.866141… in
70.866 ÷ 12 = 5 remainder 10.866…
(5 × 12 = 60, and 70.866 − 60 = 10.866)
180 cm = 5 ft 10.9 in
The 5.9 trap
Divide 180 by 30.48 and the calculator says 5.906. It is very tempting to read that as five foot nine. It is not. The digits after the point are tenths of a foot, and a foot has twelve inches, not ten:
180 ÷ 30.48 = 5.905511811… ft Decimal part × 12 = 0.905511811… × 12 = 10.866… in 180 cm = 5 ft 10.9 in not 5 ft 9 in
The misreading costs this person 1.87 inches, which is 4.74 cm, and it always errs short because twelfths are bigger than tenths. 170 cm has the same problem: 5.577 ft looks like five foot five and a bit, but 0.5774 × 12 is 6.93, so it is 5 ft 6.9 in, nearly five seven. The fix is the inches route above, which never produces a decimal foot to misread. The same trap catches meters to feet, since 1.8 m and 180 cm are the same height.
Count up from five feet
For adult heights there is a tidy anchor. Five feet is exactly 152.4 cm, and every inch above it adds 2.54 cm. So subtract 152.4 and divide what is left by 2.54:
170 cm → 170 − 152.4 = 17.6 → 17.6 ÷ 2.54 = 6.929… → 5 ft 6.9 in 183 cm → 183 − 152.4 = 30.6 → 30.6 ÷ 2.54 = 12.047… → 6 ft 0.05 in
When the leftover passes 12, as it does for 183 cm, that is another foot. Six feet is 182.88 cm, so 183 cm is six foot by a whisker over a millimeter.
In your head, divide by 30. It runs high, because the true divisor is 30.48, and it runs high by the same amount every time: 30.48 ÷ 30 is 1.016, so 1.6%. Take 1.6% back off and you are close:
180 ÷ 30 = 6 6 − 1.6% of 6 = 6 − 0.096 = 5.904 ft Exact = 5.905511…
Conversion table: cm to feet and inches
| Centimeters | Feet (3 dp) | Feet and inches |
|---|---|---|
| 30.48 | 1.000 | 1 ft 0 in exact |
| 100 | 3.281 | 3 ft 3.4 in |
| 150 | 4.921 | 4 ft 11.1 in |
| 152.4 | 5.000 | 5 ft 0 in exact |
| 155 | 5.085 | 5 ft 1.0 in |
| 160 | 5.249 | 5 ft 3.0 in |
| 165 | 5.413 | 5 ft 5.0 in |
| 170 | 5.577 | 5 ft 6.9 in |
| 175 | 5.741 | 5 ft 8.9 in |
| 180 | 5.906 | 5 ft 10.9 in |
| 185 | 6.070 | 6 ft 0.8 in |
| 190 | 6.234 | 6 ft 2.8 in |
| 200 | 6.562 | 6 ft 6.7 in |
Conversion table: feet and inches to cm
This direction never needs rounding. Total inches times 2.54 always ends within two decimal places:
| Height | Inches | Centimeters (exact) |
|---|---|---|
| 4 ft 10 in | 58 | 147.32 |
| 5 ft 0 in | 60 | 152.4 |
| 5 ft 2 in | 62 | 157.48 |
| 5 ft 4 in | 64 | 162.56 |
| 5 ft 6 in | 66 | 167.64 |
| 5 ft 8 in | 68 | 172.72 |
| 5 ft 10 in | 70 | 177.8 |
| 6 ft 0 in | 72 | 182.88 |
| 6 ft 2 in | 74 | 187.96 |
| 6 ft 4 in | 76 | 193.04 |
From decimal inches to a tape measure
Tape measures do not have a 0.929 mark. They have sixteenths. Multiply the decimal part of the inches by 16 and round:
170 cm = 66.929133… in = 5 ft 6.929… in 0.929133 × 16 = 14.866… → 15/16 170 cm ≈ 5 ft 6 15/16 in off by 0.21 mm
More on turning decimals into fractions in how to convert a decimal to a fraction, and on how many places to keep in how to round decimals. The short version: round once, at the end, and never round 5.906 ft before taking out the inches.
Where binary arithmetic slips
Going from feet to centimeters should be the easy direction, since 30.48 has only two decimal places. Most of the time binary floating point agrees: 6 × 30.48 comes out as 182.88. Then you try an 11 foot ceiling:
11 × 30.48 in binary floating point = 335.28000000000003 11 × 30.48 exactly = 335.28
The stray 3 in the fourteenth decimal place is the same fault as 0.1 + 0.2 = 0.30000000000000004: 30.48 has no exact binary form, so the machine multiplies a number that is very slightly wrong. Prism stores the factor as the exact decimal it is, so 11 ft is 335.28 cm, and 0.1 + 0.2 is 0.3, with nothing left over in the sixteenth place.
Or let the unit converter hold the 30.48
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