Unit Conversion for Students: A Reliable Method

Because 1 km = 1,000 m, the fractions (1,000 m / 1 km) and (1 km / 1,000 m) both equal 1. Multiplying by either one changes the units without changing the quantity. The only decision is which way up to write it: put the unit you want to get rid of in the denominator, so it cancels.

• Length: 3.5 km × (1,000 m / 1 km) = 3,500 m. "km" cancels; m remains.
• Mass: 150 lb × (0.45359237 kg / 1 lb) = 68.0 kg. "lb" cancels.
• Volume: 2.5 L × (1,000 mL / 1 L) = 2,500 mL.

If the units do not cancel — for example you end up with km²/m — the factor is upside down. Flip it.

Chain factors when there is no direct one, and convert each part of a compound unit separately.

Speed: 72 km/h to m/s 72 km/h × (1,000 m / 1 km) × (1 h / 3,600 s) = 72,000 m / 3,600 s = 20 m/s. Both km and h cancel.

Density: 1.2 g/cm³ to kg/m³ 1.2 g/cm³ × (1 kg / 1,000 g) × (100 cm / 1 m)³ = 1.2 × 1,000,000 ÷ 1,000 = 1,200 kg/m³.

For area and volume, the factor is raised to the same power as the unit. 1 m = 100 cm, so 1 m² = 100² cm² = 10,000 cm², and 1 m³ = 1,000,000 cm³.

2.5 m² × (100 cm / 1 m)² = 2.5 × 10,000 = 25,000 cm² — not 250 cm². Forgetting the square is the most common error in area questions.

Before rounding, ask whether the answer is the right size. Converting to a smaller unit gives a larger number (3.5 km → 3,500 m); converting to a larger unit gives a smaller number (2,500 mL → 2.5 L). If 150 lb came out as 330 kg, the factor was used the wrong way round — a kilogram is heavier than a pound, so the number of kilograms must be smaller.

• Defined factors are exact. 1 inch = 2.54 cm and 1 km = 1,000 m do not limit precision.
• The measurement sets the precision. 12.0 in has three significant figures, so 12.0 × 2.54 = 30.48 is reported as 30.5 cm.
• Round once, at the end. Rounding after each step of a multi-step conversion adds error.

Your course may have its own rounding rules; follow those where they differ.

• Writing the factor upside down (units do not cancel).
• Not squaring or cubing the factor for area or volume.
• Converting only one part of a compound unit (km/h → m/h, forgetting hours).
• Dropping units mid-calculation, which hides the errors above.
• Rounding intermediate results.
• Confusing similar symbols: m (metre, or milli-) and M (mega-).

• What the SI base units, prefixes and symbol rules are: SI units guide.
• How metric, Imperial and US customary units differ: Metric vs Imperial guide.
• To check an answer: kilometres to miles, pounds to kilograms, km/h to m/s.

Definitions used on this site are listed on the methodology page.