Two numbers that mean the same height
A height in feet can be written two ways, and they look so similar that people mix them up constantly. 5 feet 7 inches is how you say it. 5.5833 feet is how you calculate with it. Same person, same tape measure, completely different-looking numbers.
The reason is that inches are twelfths of a foot rather than hundredths. A decimal point expects hundredths, so the moment you write a height as 5.7 and mean five foot seven, the arithmetic has already gone wrong.
The formula
inches = (cm ÷ 2.54) mod 12
Both factors are exact. The 1959 international yard and pound agreement defined the inch as exactly 2.54 centimetres, and twelve of those make 30.48. There is no measurement here to refine and no rounding to argue about.
Worked example
170 centimetres.
170 ÷ 30.48 = 5.5774 feet
To read that out loud you take the whole 5 feet and turn the leftover into inches: 0.5774 × 12 = 6.93, so 5 feet 6.9 inches, which almost everybody would round to 5 feet 7.
Notice that 5.5774 and "5 feet 7" share a 5 and nothing else. If you had guessed that 5.5774 feet meant five foot five and a bit, you would be two inches out.
The mistake worth naming: 5 feet 11 is not 5.11
This one appears everywhere, in spreadsheets and forms and sports statistics, and it is worth doing the arithmetic once so it sticks.
Eleven inches is eleven twelfths of a foot, which is 0.9167. So 5 feet 11 inches is 5.9167 feet, not 5.11. Writing 5.11 describes a height of five feet and one and a third inches, which is nearly ten inches shorter than the person you were describing.
| Said as | Actually is | Often written as |
|---|---|---|
| 5 ft 3 in | 5.25 ft | 5.3 |
| 5 ft 6 in | 5.50 ft | 5.6 |
| 5 ft 9 in | 5.75 ft | 5.9 |
| 5 ft 11 in | 5.9167 ft | 5.11 |
The middle column is the one to use in any calculation. The right-hand column is a way of writing it down that nobody intends as a decimal but which spreadsheets happily treat as one.
Which form to use, and when
- Feet and inches for saying, reading a tape, filling in a form, telling a doctor.
- Decimal feet for anything you are going to multiply, add or average. Areas, volumes, scaling a drawing, working out a mean height.
- Centimetres if you have the choice, because they are already decimal and the problem never arises.
This calculator gives you all three at once, so you can pick the one your situation needs rather than converting twice. If you are working in metres rather than centimetres, the meters to feet converter handles that end, and the height converter covers the same ground with a few more options.