Unit conversion mistakes that cost real money

In 1999 NASA lost the Mars Climate Orbiter during orbital insertion. The ground software supplied by the contractor reported thruster impulse in pound-force seconds; the navigation software at JPL consumed those numbers as newton-seconds. One pound-force second is about 4.45 newton-seconds, so every trajectory correction was under-counted by a factor of four and a half. The accumulated error put the spacecraft roughly 170 km lower than intended at arrival, inside the atmosphere rather than above it. The failure review's finding was not that someone did bad arithmetic; it was that neither interface declared its units.

Air Canada Flight 143, a Boeing 767, ran out of fuel mid-flight over Manitoba in 1983. Canada was mid-way through metrication and the aircraft was one of the airline's first to use kilograms; the fuelling calculation used the pounds-per-litre figure the crew and ground staff were used to. A pound is 0.454 kg, so the aircraft was loaded with well under half the fuel it needed. Both engines flamed out and the crew glided it to a former air force runway at Gimli. Nobody was killed, which is the only reason it is remembered as a piece of airmanship rather than a disaster.

°F = °C × 9/5 + 32 converts a temperature. It does not convert a temperature *change*. If a process warms by 10 °C, that is a change of 18 °F, not 50 °F. The offset belongs to the zero point of the scale, and a difference has no zero point. This one produces no crash and no obviously silly number, just a plausible-looking value that is simply wrong, which is exactly why it survives code review. Kelvin and Celsius share a degree size, so ΔK and Δ°C are interchangeable; Fahrenheit and Rankine likewise.

There are 2.54 cm in an inch, but there are 2.54² = 6.4516 cm² in a square inch and 2.54³ = 16.387 cm³ in a cubic inch. Doubling every linear dimension of a room quadruples its floor area and octuples its volume. This shows up whenever someone converts a length factor and then applies it to paint coverage, soil, concrete, or freight volume. The check is dimensional: if the unit has an exponent, the conversion factor carries the same exponent.

An imperial gallon is 4.546 L and a US gallon is 3.785 L, so 30 mpg quoted in the UK is about 36 mpg quoted in the US for the same car, or rather the same car achieves a different number depending on which gallon you divide by. Fuel economy comparisons between US and UK sources are meaningless without qualification. Litres per 100 km avoids the problem entirely, and also has the useful property of being linear in fuel consumed, which mpg is not.