Unit conversion is multiplication by a constant. What makes it error-prone is that several unit names refer to more than one quantity — gallons, tons, ounces and calories all have multiple definitions in active use, and mixing them up has caused genuinely expensive accidents.
Units with more than one meaning
| Unit | Definitions in use |
|---|---|
| Gallon | US 3.785 L · Imperial 4.546 L — a 20% difference |
| Ton | Metric 1,000 kg · Short 907 kg · Long 1,016 kg |
| Ounce | Weight 28.35 g · US fluid 29.57 mL · Imperial fluid 28.41 mL |
| Calorie | Small calorie 4.184 J · Food Calorie 1,000 of those |
| Mile | Statute 1.609 km · Nautical 1.852 km |
| Pint | US 473 mL · Imperial 568 mL |
Always state which definition you mean in anything technical. 'A ton of material' is ambiguous by up to 12%.
Conversions worth memorising
| From | To | Multiply by |
|---|---|---|
| Inches | Centimetres | 2.54 (exact) |
| Miles | Kilometres | 1.609 |
| Pounds | Kilograms | 0.4536 |
| US gallons | Litres | 3.785 |
| Square feet | Square metres | 0.0929 |
| °F to °C | — | (°F − 32) × 5/9 |
Temperature is the exception to 'multiply by a constant', because the scales have different zero points. Fahrenheit and Celsius need the offset applied before the ratio; Kelvin and Celsius differ only by an offset of 273.15.
Squares and cubes
Area and volume scale as powers of the linear factor. One metre is 3.28 feet, but one square metre is 3.28² = 10.76 square feet, and one cubic metre is 3.28³ = 35.3 cubic feet.
Forgetting to square or cube the factor is the most common conversion error in construction and materials estimating, and it produces answers wrong by a factor of three or more — large enough to be caught, but only if someone checks.
When unit errors get expensive
The Mars Climate Orbiter was lost in 1999 because one team supplied thrust data in pound-force seconds while the receiving software expected newton-seconds. In 1983, an Air Canada aircraft ran out of fuel mid-flight after a conversion error between pounds and kilograms during the country's transition to metric. Both involved competent people and no arithmetic mistake — only a mismatch of units.
The lesson that survives from both: carry units through every calculation explicitly rather than tracking bare numbers, and state units on every interface between systems or teams.
Significant figures
Converting does not add precision. A measurement of '5 feet' converted to 1.524 metres implies millimetre accuracy that the original never had — it should be reported as roughly 1.5 metres. Carry full precision through intermediate steps, then round the final answer to match the precision of the least precise input.