Metric and imperial: the conversions worth memorising

Two systems of measurement are in daily use around the world, and the boundary between them runs through kitchens, gyms, hardware stores and engineering specifications. Converting between them is arithmetic, but the arithmetic hides a distinction worth knowing: some conversion factors are exact by international agreement, and others are rounded values that will drift if you chain them.

The factors that are exact

Since the international yard and pound agreement of 1959, several imperial units are defined in terms of metric ones. These are not measurements — they are definitions, exact to as many decimal places as you care to write.

Everything else in the imperial system follows from these. An ounce is a sixteenth of a pound, so it is exactly 28.349523125 g; the 28.35 you remember is a rounding of an exact number, not a measurement.

Three shortcuts that get you within 2%

• Kilometres to miles: multiply by 0.6, or use consecutive Fibonacci numbers — 5 km ≈ 3 miles, 8 km ≈ 5 miles, 13 km ≈ 8 miles. The true factor is 0.621, so the error stays under 4%.
• Kilograms to pounds: double it and add 10%. 70 kg → 140 + 14 = 154 lb. The exact answer is 154.3 lb.
• Celsius to Fahrenheit: double it and add 30. 20 °C → 70 °F against a true 68 °F. Good enough for weather, not for cooking or fever.

Temperature is the odd one out

Every other conversion is a multiplication, because both scales start at zero. Temperature scales do not share an origin, so conversion needs an offset as well as a factor: °F = °C × 9/5 + 32, and °C = (°F − 32) × 5/9. The scales cross at −40, which is the same temperature in both — a useful anchor for checking that you applied the formula in the right direction.

For temperature differences rather than temperatures, drop the offset: a rise of 10 °C is a rise of 18 °F, not 50 °F. This distinction catches people out constantly in specifications and datasheets.

Mass, weight and volume in the kitchen

Recipes are where unit confusion is most common, because imperial recipes measure by volume (cups) and metric recipes by mass (grams) — and the conversion between them depends on the ingredient. A cup of water is 240 g; a cup of flour is about 120 g; a cup of honey is roughly 340 g. There is no universal cup-to-gram factor, and any table claiming one is quietly assuming water.

The fluid ounce compounds the problem: it measures volume, while the ounce measures mass. They coincide only for water, and only approximately.

When conversion errors get expensive

In 1999 NASA lost the Mars Climate Orbiter, a 125-million-dollar spacecraft, because one team supplied thruster impulse data in pound-force seconds while the navigation software expected newton-seconds. In 1983 an Air Canada Boeing 767 ran out of fuel at 41,000 feet after a refuelling calculation mixed pounds and kilograms; the crew landed it, without engines, on a disused runway.

Both failures were arithmetic that nobody double-checked. The practical lesson for smaller stakes is the same: write the unit next to every number, convert once rather than in a chain, and check the result is the right order of magnitude before using it.

A quick reference