How to Convert Units Step by Step

Every unit conversion works the same way: multiply by a fraction that equals one, arranged so the unwanted unit cancels. This is called the conversion factor method, or dimensional analysis.

Step by step

1. Write down the value and its unit.
2. Find a conversion factor that links the two units, such as 1 mile = 1.609344 kilometres.
3. Write it as a fraction with the unit you want on top.
4. Multiply. The old unit cancels, leaving the new one.

Example 1: miles to kilometres

Convert 5 miles to kilometres.

5 mi × (1.609344 km ÷ 1 mi) = 8.04672 km

The miles cancel, leaving kilometres. Rounded, 5 miles is about 8.05 km.

Example 2: pounds to kilograms

Convert 180 pounds. One pound is defined as 0.45359237 kilograms.

180 lb × 0.45359237 kg/lb = 81.65 kg

Example 3: a two-step conversion

Convert 42.195 kilometres, the marathon distance, to miles. Divide by 1.609344:

42.195 km ÷ 1.609344 km/mi = 26.22 mi

Exact factors to remember

The imperial and US customary units are defined in terms of metric ones, so these factors are exact, not approximations.

Checking your answer

Ask whether the result makes sense. A mile is longer than a kilometre, so miles to kilometres should give a bigger number, and kilometres to miles a smaller one. If it goes the wrong way, the fraction is upside down.

Common mistakes

• Multiplying when you should divide. Let the units cancel to decide.
• Mixing US and imperial gallons or pints, which are different sizes.
• Rounding a factor early, such as using 1.6 for a mile, when accuracy matters.

Use the length converter, weight converter or volume converter to check your working.

Try it yourself

1. Convert 12 inches to centimetres.
2. Convert 10 kilometres to miles.
3. Convert 2.5 kilograms to pounds.

Answers: (1) 30.48 cm; (2) 6.21 miles; (3) 5.51 pounds.