The unit conversions people get wrong, and why
The three big ones: applying a linear factor to an area or volume, treating feet-and-inches or stone-and-pounds as decimals, and converting a temperature difference as though it were a temperature. Each is a systematic error, not a rounding one.
Updated 2026-08-22
Area and volume do not use the linear factor
A foot is 0.3048 metres. A square foot is not 0.3048 square metres — it is 0.0929, because both dimensions shrink. A cubic foot is 0.0283 cubic metres, because all three do. The factors are the linear one squared and cubed, and using the linear factor understates area by a factor of more than three and volume by more than thirty.
This is the single most expensive conversion error in ordinary life, because it appears in property listings, flooring quotes, paint coverage, shipping volumes and concrete orders. A thousand-square-foot apartment is 92.9 square metres; divide by 3.28 instead and you get 305, which would be a mansion. The error is large enough that it is usually caught — but the smaller version, converting a floor area for a quote, is not, and it is why an order arrives at a third of what was needed.
The rule is simple once stated: count the dimensions. Length uses the factor, area uses the factor squared, volume uses it cubed. Anything measured in units with a superscript needs the corresponding power.
Feet and inches are not decimals
Five foot nine is 5.75 feet, not 5.9. Twelve inches to the foot means the fractional part of a decimal foot is twelfths, not tenths, and treating one as the other is an error of about four and a half centimetres — the gap between two visibly different heights.
The same shape of mistake appears with stone and pounds, where fourteen pounds to the stone means eleven and a half stone is 11 st 7 lb rather than 11 st 5 lb. And with time, where 2.5 hours is two hours thirty minutes but 2.5 on a digital clock is nothing at all, which is why timesheets that record 8.45 for eight forty-five overpay by a small amount every single day.
The safe habit is to convert the sub-unit separately and add. Nine inches is 22.86 centimetres; five feet is 152.4; the total is 175.26. That takes one extra step and removes an entire class of error.
A difference is not a value
If the temperature rises by 10 °C, it has risen by 18 °F, not by 50. The 32 in the Fahrenheit formula is an offset between where the two scales place zero, and an offset applies to points on a scale rather than to the gaps between them. Converting an interval with the full formula is wrong every time.
The same distinction matters for anything with a non-zero origin. Altitude above sea level converts differently from a height difference only if the reference points differ. Dates and durations behave this way too: a duration of one month is not a fixed number of days, which is why adding a month to 31 January produces different answers in different libraries.
The test to apply is whether the quantity has a meaningful zero. Length, mass and time intervals do — zero means none. Celsius and Fahrenheit do not; their zeros are arbitrary points chosen for historical reasons, which is why kelvin exists for any physics where ratios matter.
The same word, different units
An ounce is at least three things. The avoirdupois ounce of 28.35 grams is used for food and post. The troy ounce of 31.1 grams is used for precious metals, and there are twelve to the troy pound rather than sixteen — which is why a pound of gold weighs less than a pound of flour. The fluid ounce is not a weight at all, and comes in a US version of 29.57 millilitres and an imperial one of 28.41, four percent apart.
A gallon is two units twenty percent apart, which is why fuel economy figures cannot be compared between the US and the UK without conversion — 30 mpg means noticeably different things in each. A ton is three: the short ton of 2,000 pounds, the long ton of 2,240, and the tonne of 1,000 kilograms, all close enough to be confused and far enough apart to matter on a freight invoice.
A billion used to be two numbers, and in some languages still is. A mile is one thing on land and another at sea, 15 percent longer. Even the calorie is two, differing by a factor of a thousand — food labels use the kilocalorie and write it with a capital C, which is why nutritional advice and physics textbooks appear to disagree by three orders of magnitude.
How to not get caught
Carry the units through the calculation rather than converting at the end. If the units on both sides do not match, the working is wrong regardless of what the arithmetic says. This is the habit that engineering courses drill for a reason: it catches the dimensional errors automatically, because square metres cannot equal metres no matter how the numbers were multiplied.
Sanity-check the magnitude before trusting the digits. A person is not four metres tall, a room is not eight square metres if it holds a sofa, a parcel is not 40 kilograms if you can lift it easily. Most conversion errors are off by a factor of ten, three or two — large enough that a moment of estimation catches them.
And write the unit down every time. A number without a unit is the root cause of most of these failures: the Mars Climate Orbiter was lost in 1999 because one team supplied thrust in pound-force seconds and the other expected newton-seconds, and nothing in the interface said which. That is the same error as a timesheet reading 8.45, differing only in the size of the bill.