Conversions and Units
Converting units means changing a measurement from one unit to another, for example between metric units of length, mass, capacity, time or speed, while keeping the same underlying quantity. This topic covers metric conversions and area and volume unit conversions, and it combines with speed, density and time throughout GCSE papers.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the standard metric conversion facts, for example 1 km = 1000 m, 1 kg = 1000 g, 1 litre = 1000 ml, 1 m = 100 cm.
- To convert from a larger unit to a smaller unit, multiply by the conversion factor; to convert from a smaller unit to a larger unit, divide.
- For area conversions, square the length conversion factor, for example 1 m^2 = 100^2 = 10000 cm^2; for volume, cube it.
- For time and speed conversions, remember there are 60 minutes in an hour and 3600 seconds in an hour, and convert distance and time to consistent units before dividing.
- When comparing or ordering measurements, convert every value to the same unit first.
- Check your final answer is a sensible size for the unit you have converted into.
Worked example
A car travels at a constant speed of 54 km/h. Show that this speed is equal to 15 m/s.
- Convert 54 km to metres: 54 x 1000 = 54000 m.
- Convert 1 hour to seconds: 1 x 3600 = 3600 s.
- Divide the distance in metres by the time in seconds: 54000 / 3600.
- Work out the division: 54000 / 3600 = 15.
- State the final answer: 54 km/h is equal to 15 m/s, as required.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Convert 3.4 m^2 to cm^2.
A fish tank in the shape of a cuboid has length 50 cm, width 25 cm and height 30 cm. (a) Work out the volume of the tank in cm^3. (b) Given that 1000 cm^3 = 1 litre, work out the maximum volume of water the tank can hold, in litres.
Deepak drives a distance of 245 miles. You are given that 5 miles is approximately 8 km. The journey takes 3 hours 30 minutes. (a) Work out the distance in kilometres. (b) Work out Deepak's average speed for the journey in km/h.
Free printable worksheet
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