Map scales

Map scales can be written in ratios and tell you how many units of length on land, or sea, are equal to one unit of length on a map.

For example, if you are travelling from Manchester to Newcastle and need to know how far it is, it would be very difficult to work this out from a map if the map does not have a scale.

Example

The scale of a map is 1:50,000.

Dinesh measures the distance from his home to the local swimming pool on the map.

The distance is measured as {3}~{cm} on the map.

How many {cm}, {m} and {km} is this equivalent to in real life?

{1}~{cm} on the map represents {50,000}~{cm}. Therefore, {3}~{cm} on the map represents {150,000}~{cm}.

To convert from {cm} to {m}, divide by {100}.

150,000~cm \div 100 = 1,500~m

To convert from {m} to {km} divide by {1,000}.

1,500~m\div1,000=1.5~km

Question

The scale of a map is 1:50,000. What distance on the map will represent {5}~{km}?

First convert {5}~{km} to {cm}:

5~km=5,000~m=5,000\times100~cm=500,000~cm

We want to know what distance on the map represents {500,000}~{cm} in real life.

The map scale is {1:50,000}, so we divide by {50,000}:

500,000 \div 50,000 = 10

Therefore, {5}~{km} is equivalent to {10}~{cm} on the map.