Compound measures

Speed, density, pressure and flow rate all combine two other measures. Explore the formula triangle for each, rearrange it to find any of the three quantities, then practise mixed questions.

Curriculum rangeYears 8-11

Distance150 km

Time3 h

\text{Speed} = \dfrac{\text{distance}}{\text{time}} = \dfrac{150}{3} = 50 \text{ km/h}

Learning notes

Compound measures essentials

Keep these rules beside you while you explore and practise.

1Speed, distance and time

\text{speed} = \dfrac{\text{distance}}{\text{time}}

Rearranged: $d=st$ , and $t=\dfrac{d}{s}$ .

2Density, mass and volume

\rho = \dfrac{m}{V}

1 g/cm³ is the same as 1 kg/litre, and equals 1,000 kg/m³.

3Pressure, force and area

P = \dfrac{F}{A}

Pressure is measured in pascals (Pa), where $1\,\mathrm{Pa}=1\,\mathrm{N}/\mathrm{m}^2$ . The same force spread over a bigger area gives a smaller pressure.

4Flow rate

\text{rate} = \dfrac{\text{volume}}{\text{time}}

Rates of flow (litres/minute, litres/second) and other unit rates (people/hour, cost per item) use the same volume-over-time structure as speed -- just with a different pair of quantities.

5Reading the formula triangle

Cover the quantity you want to find. If the two remaining letters are side by side, multiply them; if one sits above the other, divide top by bottom.

💡Always check the units match before combining two measures -- convert km/h to m/s, or litres to m³, before you calculate.