Unit Conversion - Changing Between Systems
Unit conversion is the skill of expressing the same measurement in a different unit. It is used constantly in science, cooking, engineering, travel, and everyday life. The key principle: multiply by the conversion factor when going to a smaller unit, divide when going to a larger one.
The mathematical technique behind reliable unit conversion is called dimensional analysis, formalised by the French mathematician Joseph Fourier in the early 1800s: because a conversion factor like “1,000 m per km” is really just a fraction equal to 1, you can multiply any quantity by it without changing its true value, only its units – and chaining several such fractions together lets you convert confidently between units that have no direct, memorised link at all. Pilots, pharmacists, and chemical engineers all rely on this same rigorous chain-of-fractions method every single day, because in those fields a careless conversion error is not just embarrassing, it can be genuinely dangerous.
How Conversion Factors Work
A conversion factor is a fraction equal to 1, where the numerator and denominator express the same quantity in different units. Multiplying by it changes the unit without changing the value.
Example: 1 km = 1,000 m, so (1,000 m / 1 km) = 1. 5 km × (1,000 m / 1 km) = 5,000 m.
Metric to Metric Conversions
| Conversion | Factor | Example |
|---|---|---|
| km to m | × 1,000 | 3 km = 3,000 m |
| m to cm | × 100 | 2.5 m = 250 cm |
| cm to mm | × 10 | 4.7 cm = 47 mm |
| kg to g | × 1,000 | 0.85 kg = 850 g |
| l to ml | × 1,000 | 1.25 l = 1,250 ml |
Metric to Imperial Conversions
| Metric | Imperial | Approx. factor |
|---|---|---|
| 1 cm | 0.394 inches | cm ÷ 2.54 = inches |
| 1 km | 0.621 miles | km × 0.621 = miles |
| 1 kg | 2.205 pounds | kg × 2.205 = lb |
| 1 litre | 1.76 pints (UK) | l × 1.76 = pints |
| 1 litre | 0.264 gallons (US) |
Temperature Conversion
| From | To | Formula |
|---|---|---|
| Celsius | Fahrenheit | F = (C × 9/5) + 32 |
| Fahrenheit | Celsius | C = (F − 32) × 5/9 |
| Celsius | Kelvin | K = C + 273.15 |
Worked Examples
7.5 × 0.621 = 4.658 miles.
65 × 2.205 = 143.3 lb.
F = (20 × 9/5) + 32 = 36 + 32 = 68 °F.
2 × 240 = 480 ml. 480 ÷ 1,000 = 0.48 l.
Key Takeaways
- A conversion factor is a fraction equal to 1 that changes the unit of a quantity.
- In metric: conversions are always powers of 10 – multiply or divide.
- Keep track of units at every step to avoid errors (dimensional analysis).
- Approximate conversions are fine for everyday use; exact ones are needed in science.
Practice: Metric ↔ Imperial
You Have Completed the Measurement Section!
Well done – you have worked through all 12 topics in the Measurement section on MathsFamily. Return to the Resources page to continue your mathematics journey.