Feet and Inches Converter

Where 5 ft 12 in comes from

Converting 5.999 feet into feet and inches is arithmetic anyone can do, and doing it in the obvious order produces an answer that cannot exist.

The obvious order is: take the whole feet, multiply the remainder by twelve, round. Five feet, and 0.999 × 12 = 11.988, which rounds to 12. So “5 ft 12 in”.

There is no such height. Twelve inches is a foot, so the answer is six feet exactly — and the arithmetic never noticed, because by the time the rounding happened the feet had already been decided.

The fix is an order of operations rather than a special case. Convert the whole value into the smallest unit, round once there, and carry back up. Do it that way and the impossible value cannot be produced, because the carry happens after the rounding rather than before it.

Every format has a modulus

The bug is not about feet. Every compound format has a number at which the smaller unit becomes one of the larger, and every one of them is a place this can happen.

The three-part formats are worse, because a rounding can carry twice. 1 h 59 min 59.6 s rounds to 1 h 59 min 60 s, which should carry to 2 h 0 min 0 s — two carries from one rounding, and an implementation that handles one and not the other will produce “1 h 60 min 0 s” instead.

Note also that the moduli are not all 60 or all 12. Fourteen pounds to the stone is the one people most often get wrong when writing code, because it is the only one in the set that is not a familiar number from somewhere else.

One value, one sign

A negative compound value has a single sign in front of the whole thing, not one on each part, and getting this wrong quietly doubles the magnitude.

Minus five and a half feet is −5 ft 6 in. It is not “−5 ft −6 in”, which would be minus five and a half feet again if the parts were added — and it is not “−5 ft 6 in” interpreted as minus five feet plus six inches, which is minus four and a half.

The convention is that the sign belongs to the composite quantity and the parts are always non-negative. So the way to convert a negative value is to take its absolute value, do the whole carry, and put the sign back at the end — which is what the calculator above does, and why its parts are never negative.

This matters most where compound values are subtracted: a difference of −0 ft 3 in is a real and common result, and it is where an implementation that writes the sign on the wrong part becomes visibly wrong.

Decimal hours are not a clock

A related confusion, and the one that costs actual money: decimal hours and clock times share their digits and mean different amounts.

7.75 hours is 7 hours 45 minutes. Read as a clock time it looks like 7:75, which is not a time at all — and the instinct to read it as “seven and seventy-five” over-states the duration by half an hour.

The error always runs in the same direction — reading decimals as minutes over-states the time — because a hundred is more than sixty. On a timesheet that is a systematic overstatement rather than a random one, so it does not average out across a week.

Payroll systems ask for decimal hours and clocks display minutes, which puts the conversion at exactly the point where a person is copying between two systems. If a figure ends in .25, .5 or .75 it is almost certainly decimal hours; if it ends in anything above .59 it definitely is.

Spotting it on a form

The useful skill is recognising the bug in something someone else produced, because its output is always a value that cannot exist.

The test is one line: is any remainder at or above its own modulus? Twelve inches, fourteen pounds, sixteen ounces, sixty minutes, sixty seconds — each of those should have carried, and seeing one means whatever produced it rounded in the wrong order.

It shows up most often in spreadsheets, where the two parts are usually two separate formulas and the second has no way of telling the first that it rounded up. It also shows up in printed reports where a database stored a decimal and a template formatted it in two independent steps.

The calculator above will take a written pair and tell you whether it is possible, which is worth doing once on any form or report that produces these formats automatically. A single “5 ft 12 in” in a set of records is not an isolated typo — it is evidence that every value in the set was rounded the same way, and that the ones which happened not to land on a boundary are wrong by a fraction rather than visibly.

Related calculators

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More in Conversion, or browse all calculators.

Sources and methodology

The measurement guidance is where the rounding-once rule comes from; the other two are why these compound formats are still in everyday and in some cases legal use rather than being a historical curiosity.

• Guide for the Use of the International System of Units (NIST SP 811)National Institute of Standards and Technology · verified 2026-09-08 · Guidance on expressing quantities and on rounding, including that a converted value should be rounded once to the intended precision rather than at intermediate steps — which is the rule this page turns into a carry order
• National Physical LaboratoryNPL · verified 2026-09-08 · The UK national measurement institute’s guidance on units and on the imperial units still in legal use for particular purposes, including the stone for body weight
• Weights and measures: the lawUK Government · verified 2026-09-08 · Which imperial units remain lawful for trade and in what contexts in the United Kingdom, which is why compound formats such as stones and pounds and feet and inches persist alongside metric ones