Compound Measures

Combining quantities to describe real situations

A compound measure combines two or more quantities, such as miles per hour or kilograms per cubic metre. Students meet basic rate ideas in KS3 and develop speed, density and pressure at GCSE and IGCSE. The topic depends on ratio and confident use of a formula

Key formulae and method

Speed = distance ÷ time. Density = mass ÷ volume. Pressure = force ÷ area. Write the formula, substitute values with consistent units, calculate, and include the compound unit. When the required quantity is different, use rearranging formulae

Worked examples

Example 1: A car travels 150 miles in 3 hours. Speed = 150 ÷ 3 = 50 mph. Example 2: An object has mass 540 g and volume 60 cm³. Density = 540 ÷ 60 = 9 g/cm³. Example 3: A force of 800 N acts over 20 m². Pressure = 800 ÷ 20 = 40 N/m².

Common mistakes and exam advice

Do not mix minutes with hours, centimetres with metres, or grams with kilograms unless the question permits those units. Students also lose marks by omitting compound units or applying the wrong operation. Estimate first to check whether the answer is sensible; the glossary explanation of estimation can help.

Practice exercises and answers

Exercise 1: Travel 210 km in 3.5 hours. Answer: speed = 210 ÷ 3.5 = 60 km/h. Exercise 2: Mass 360 g, volume 45 cm³. Answer: density = 8 g/cm³. Exercise 3: Pressure is 25 N/m² over area 12 m². Find force. Answer: force = pressure × area = 25 × 12 = 300 N.

Related learning across the website

Support compound measures through Ratio Lessons, Geometry Lessons, Algebra Lessons, percentages, fractions, decimals, percentages glossary, linear equations, standard form and Pythagoras’ Theorem

Benefits of one-to-one maths tutoring

One-to-one lessons with maths tutor Ryan Harvey can identify whether errors come from units, algebra or interpretation and provide targeted exam-style practice.

Contact and lesson enquiry

Students and parents can contact MasterMaths Tutoring for personalised measures support.