Working across metric and imperial without mistakes
Which conversions are exact and which are not, why a temperature difference converts differently from a temperature, and where units quietly go wrong.
Some conversions are exact, and it matters which
A surprising number of imperial units are defined in terms of SI ones, which makes those conversions exact rather than measured. Since 1959 the international agreement fixes:
- 1 inch = exactly 25.4 mm
- 1 foot = exactly 0.3048 m
- 1 pound = exactly 0.45359237 kg
- 1 nautical mile = exactly 1,852 m
Everything in the length andmass families follows from those four by pure arithmetic, with no measurement uncertainty anywhere. When a conversion is exact you can carry as many digits as you like and none of them are noise.
Other conversions are not definitions. Anything involving a physical constant — energies via the calorie, pressures via a column of mercury — is only as good as the value adopted for that constant, and different sources adopt slightly different ones. The thermochemical calorie is exactly 4.184 J by convention, but older texts use figures that differ in the third decimal. Where a unit has competing definitions, find out which one your source used before chasing a discrepancy.
A temperature difference is not a temperature
This is the conversion error that produces confidently wrong answers, because both halves of it look correct in isolation.
An absolute temperature carries an offset: °C = (°F − 32) × 5/9. So 212 °F is 100 °C, and 32 °F is 0 °C.
A difference carries no offset at all: ΔC = ΔF × 5/9. A rise of 180 °F is a rise of 100 °C — not 82.2 °C, which is what you get by running 180 through the absolute formula.
The reason is that an offset cancels when you subtract two readings. Going from 32 °F to 212 °F is a 180 °F change, and 0 °C to 100 °C is a 100 °C change; the ratio is 5/9 with nothing added. Anywhere a calculation takes a ΔT — heating, thermal expansion, temperature rise in aPCB trace — this is the conversion you want, and applying the absolute one instead is a silent error of about 18 degrees.
The temperature converter handles absolute readings. For a difference, multiply by 5/9 and leave the 32 alone.
Reciprocal units run backwards
Miles per gallon and litres per 100 km measure the same thing upside down. One counts distance per unit of fuel, the other fuel per unit of distance. In one, higher is better; in the other, lower is. They cannot be converted by multiplying.
L/100km = 235.215 / mpg (US)
That has a real consequence beyond the arithmetic. Because the relationship is a curve rather than a line, equal-looking improvements are not equal. Going from 15 to 20 mpg saves about 1.67 gallons per 100 miles. Going from 40 to 50 mpg — a bigger jump in headline terms — saves only 0.5 gallons over the same distance. Replacing the thirstiest vehicle in a fleet does far more than perfecting the most efficient one, and mpg makes that hard to see while L/100km makes it obvious.
The same trap appears in any reciprocal pair: fuel economy, and to a lesser extent things like pace versus speed in theconverter's neighbours.
Mass and weight, pounds and pounds-force
A kilogram is a mass. A pound is used for both a mass and a force, and which one is meant is usually left to context.
On Earth the distinction rarely bites, which is exactly why it catches people out when it does. In a physics calculation the two are genuinely different quantities: mass resists acceleration, weight is the force gravity applies to it. One kilogram-force is exactly 9.80665 N — the weight of one kilogram under standard gravity — and it is not an SI unit, though it survives because "this fixing holds 50 kgf" is immediately intuitive.
If you are converting for a shopping list, pounds are pounds. If you are converting for a calculation involving forces or accelerations, establish which you have first. The force calculatorkeeps them separate deliberately.
The megabyte problem
Data sizes have their own version of the same ambiguity, and it is the only place where an SI prefix is routinely used to mean something other than a power of ten.
A megabyte is officially 1,000,000 bytes. Amebibyte is 1,048,576 — that is 2²⁰. Operating systems have historically displayed the binary figure while labelling it MB, which is why a 1 TB drive shows as 931 GB: the manufacturer sold 10¹² bytes and the computer divided by 1024 three times without relabelling the result.
Nothing is missing and nobody is lying; the same quantity is being described two ways. Use decimal units for storage and file sizes, binary units for memory and block sizes, and where it matters say which you mean. Thedata size converter keeps both families distinct rather than pretending they are the same.
Convert at the edges, never in the middle
The habit that prevents most unit errors is structural rather than arithmetic: do the conversion once, on the way in and on the way out, and keep everything between in one system.
Every physics calculator on this site works that way. You can type feet, pounds and mph, and the physics still happens in metres, kilograms and seconds before the answer is converted back. Carrying mixed units through a formula is how you get an answer that is plausible and wrong — the number looks reasonable, so nothing prompts you to check it.
The same discipline applies by hand. Convert everything to one system first, do the whole calculation, convert the result at the end. It is slower for one sum and considerably faster than finding the mistake in a chain of them.