Convert cm to ft

Centimetres are the everyday metric length — body measurements, paper, furniture — and they are the one metric unit that has no direct customary counterpart, which is why so much converting happens through them.

A foot is twelve inches, and it is the unit heights and room sizes are quoted in across the United States. Aviation quotes altitude in feet almost everywhere, including in countries that are metric for everything else; China is the exception, where controllers clear aircraft in metres.

The factor is 0.032808, and almost nobody carries that around. Rounded to 0.033 it is off by 0.58 % — which stays invisible on small numbers and turns into a whole unit somewhere around 1,000 cm.

That is the number worth knowing before you round: not the error itself, but where it stops being ignorable. Below that point the shorter factor is the sensible one; above it, use the field above, which never rounds until it prints.

The foot has been defined in metric terms since the international yard and pound agreement of 1959, and in this page's units that comes out at 30.48 cm to one. The definition is exact by stipulation — it was not measured, and it cannot be refined by measuring it better. The decimal above is the whole of it, with nothing rounded away at the end.

Before that agreement the US and the British versions differed slightly, and old survey figures still carry the older definition. For anything outside land surveying the difference is far below the precision anybody is working to.

A height in feet is spoken as two numbers, and the field above gives one. Dividing 178 by 30.48 produces 5.84 feet, which is arithmetically correct and has never been said aloud by anybody describing a person. The form everybody uses is five foot ten, and reaching it means treating the whole number and the remainder as two separate things.

Keep the five and multiply the 0.84 by twelve: 10.1, so ten inches. The reason this cannot be skipped is that the remainder is a fraction of twelve, not of ten, so the digits after the point carry no information you can read directly. 0.5 means six inches, 0.25 means three, 0.75 means nine, and nothing else in the range maps onto anything you would guess.

This is the error the decimal invites, and it is worth naming before anything else. 5.5 feet means five and a half feet, which is five foot six and 167.64 cm. Five foot five is 5.4167 feet and 165.1 cm. Read one as the other and you are out by an inch — a difference that matters on a licence application, a medical record or a height requirement.

The same trap runs through the whole range because two different notations are competing for the same shape. 6.8 feet is six foot ten, not six foot eight; six foot eight is 6.667 feet. Where a system will only accept one number, write the decimal and label it as feet; where it accepts two, write the whole feet and the whole inches and never mix the two conventions in a single field.

The United States quotes every personal height in feet and inches, and so does the United Kingdom in conversation, in the same way it keeps stone for body weight. Canada is the interesting middle case: official records and medical charts are metric, and a person asked how tall they are answers in feet. Ireland behaves the same way. Almost everywhere else the answer is a whole number of centimetres and there is no second unit involved.

This is why the conversion is asked for so often in one direction. Metric countries produce heights that have to be restated for an American reader, form or requirement, while the reverse question is usually somebody decoding a figure rather than filling one in. Statistical publications go the other way for a reason of their own: national average heights are always quoted in centimetres, because a single number can be averaged and a pair of them cannot.

Most American forms that ask for height provide two fields, one labelled ft and one labelled in, or a pair of dropdowns. Neither will take 5.84, and a field that silently accepts it will store a height of five feet and eighty-four inches or reject the record later. Convert to the two whole numbers before you start typing rather than trying to make one field carry both.

A few systems ask for total inches instead, which is the safest form to hold in reserve: 178 cm is 70.1 inches, so five foot ten is 70. Medical and aviation forms sometimes want that figure directly. If a form gives one box and does not say which unit it means, the units word next to it is the only reliable guide — a bare number in a height field is read as inches in the United States and as centimetres nearly everywhere else.

The useful anchors are the whole and half feet, because they are the figures other people quote at you. Five foot is 152.4 cm, five foot six is 167.64, five foot ten is 177.8, six foot is 182.88 and six foot four is 193.04. Each inch adds 2.54 cm, so the steps between them are even and easy to walk up or down from whichever anchor is nearest.

Two of those are worth remembering exactly. Six foot is 182.88 cm and not 183, so somebody measured at 183 is fractionally over rather than exactly on the mark, which is the sort of distinction a height requirement is written to catch. And five foot ten is 177.8, which means 178 cm — a common, almost default figure in metric countries — is the first centimetre above it rather than a comfortable middle.

The conversion is exact and the input usually is not. A height measured with shoes on, on carpet, or with the chin lifted, will be one to three centimetres out, which is up to an inch — more than the entire precision the feet-and-inches answer claims. Measure barefoot against a hard wall on a hard floor, with the head level rather than tilted back, and mark the wall with something rigid held flat on the crown.

There is also a real daily variation. The spine compresses under its own load through the day, so a person measures slightly taller in the morning than in the evening, by something around a centimetre. That is close to half an inch, which is enough to move a borderline height across a whole inch step. If a figure has to match one recorded elsewhere, match the time of day as well.

The reason the metric side feels simpler is not the factor, it is that a height in centimetres is a single number. You can sort it, average it, subtract one from another and plot it without thinking. Feet and inches is a mixed-radix pair, and every one of those operations needs converting first — the difference between five foot eleven and six foot two is not three of anything until you turn both into inches.

That is worth knowing when you are comparing rather than reporting. If you are checking whether one person is taller than another, or how far a height falls below a requirement, convert both sides to centimetres or to total inches, do the arithmetic there, and convert the result back at the end. Doing it directly in feet and inches means borrowing twelve rather than ten, which is exactly the kind of arithmetic people get wrong in their heads.