Compound units

Description

Compound units combine two or more base units to measure a derived quantity. They are written using division (per) or multiplication.

Common compound units:

• Speed: metres per second (m/s), kilometres per hour (km/h), miles per hour (mph)
• Density: grams per cubic centimetre (g/cm³), kilograms per cubic metre (kg/m³)
• Pressure: newtons per square metre (N/m²), pascals (Pa)

Key formulae: $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}, \quad \text{Density} = \frac{\text{Mass}}{\text{Volume}}, \quad \text{Pressure} = \frac{\text{Force}}{\text{Area}}$$

Converting compound units: convert each part separately. $$60\text{ km/h} = \frac{60 \times 1000}{3600}\text{ m/s} = \frac{60000}{3600} \approx 16.7\text{ m/s}$$

Unitless checking: keep units in your working — if units don't cancel correctly, the formula is wrong.

Common error: mixing up which quantity is divided by which — density is mass divided by volume (not the other way round).

Links

Changing the subject Substitution Speed, distance & time