Scales are used on maps in the same way that they are used in plans.
A scale of 1 : 50 000 is used on many Ordnance Survey maps.
This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km).
Converting measurements on a map
We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.
(a) Imagine we have measured a distance as 3 cm on this map, and we want to find out how far this is in real life.
To work out the distance in real life, we need to multiply this length by 50000.
This gives 3 cm × 50000 = 150000 cm which is 1500 m or 1.5 km.
Alternatively, we could have just remembered that each 1 cm on the map is 0.5 km in real life.
Hence, 3 cm on the map must be 3 × 0.5 km = 1.5 km in real life.
(b) Now imagine we want to walk 4.5 km in real life, and we need to find out how far this is on the map.
To work out the distance on the map, we need to divide this length by 50000.
4.5 km = 4500 m = 450000 cm. Dividing 450000 cm by 50000 gives a distance on the map of 9 cm.
Alternatively, we could have just remembered that each 0.5 km in real life is 1 cm on the map.
If we divide 4.5 km by 0.5 km we get 9, so the distance on the map must be 9 cm.
working out what 1 cm on the map is equivalent to as a real life distance. 
Example
A map has a scale of 1:25000.
This means that 1 cm on the map is 25000 cm in real life, which is 250 m or 0.25 km.
It is also useful to note that if 1 cm is 0.25 km, then 4 cm will represent 1 km in real life.
4 cm on the map represents 1 km in real life 
(a) The distance between two points on this map is 10 cm. What is the distance in real life?
Each 1 cm is worth 0.25 km, so the distance in real life is 10 × 0.25 km = 2.5 km.
(a) The distance between two points in real life is 7 km. What is the equivalent distance on this map?
Each 1 km is equivalent to 4 cm on the map, so the distance on the map will be 4cm × 7 = 28 cm.
Work out the answers to the questions on the right, then click to see whether you are correct.
