Map scales and ratio

• A map scale is a ratio of the distance on a map to the actual distance on the ground.
• The scale of a map shows how much you need to enlarge the map to get the actual size. For example, a scale of 1 : 25,000 means each 1 cm on the map represents 25,000 cm. This is the same as 250 m.
• The scale 1: 25,000 on the map could also be given as 4 cm to 1 km.
• Maps are made at different scales for different purposes. Eg, a 1 : 25,000 scale map is useful for walking as it shows greater detail. However, a map with a 1 : 250,000 scale shows a greater area, but in far less detail. This would be a useful map for planning a car journey.

Map scales are often written as a ratio, eg 1 : 250,000. They can also be written using measurements, eg 2 cm to 5 km.

To understand a map scale, find the real distance represented by each unit (1 cm or 1 inch) on a map. This will differ depending on the type of scale. Some map scales use centimetres (cm) and others may use inches. This process is referred to as interpreting the scale. This is an essential skill for any map-based problem solving.

For a measurement-based scale, where more than one unit is given:

1. Divide both parts of the scale by the number of units. Eg, for a scale of 5 cm to 6 km, divide both parts of the scale by 5
2. The scale will now give the real distance represented by 1 unit on the map.

For a ratio scale:

1. Write both parts of the ratio with equal units, eg centimetres (cm).
2. Divide the greater number by 100 to convert to metres (m).
3. Divide the greater number by 1000 to convert to kilometres (km).
4. The scale will now give the real distance represented by 1 unit on the map.

1. In order to write the ratio, both measurements need to have the same units. Write both parts of the ratio with the same units (using the smaller units, usually cm).

• To convert km to metres, multiply by 1000
• To convert metres to cm, multiply by 100

2. Simplify by dividing both parts of the ratio by their highest common factor (HCF).

To find the real distance using a map scale, first measure the distance on the map. For distances that are not in a straight line (eg, a journey on a map), use a piece of string that can be measured against a ruler. For distances that are a straight line, use a ruler.

The method used then depends on the way the scale is written.

For a measurement-based scale where one or more units (cm or inch) represent a given distance, eg 2 cm to 5 km, or 1 inch to 16 miles:

1. Interpret the scale, if necessary. Find the real distance represented by each unit (cm or inch) on the map.

2. Multiply the measured distance by the distance each unit on the map represents.

For a measurement-based scale where more than one unit (cm or inch) represents 1 km (or 1 mile), eg 4 cm to 1 km, or 2 inches to 1 mile:

• Divide the measured distance by the number of units on the map (cm or inch) that represent 1 km (or 1 mile).

To find the real distance using a ratio map scale (eg 1 : 250,000), first measure the distance on the map. Use a ruler for straight lines, or for distances not in a straight line (eg, a journey on a map), use a piece of string that can be measured against a ruler.

There are two possible methods.

Either multiply by the scale to find the real distance in cm:

1. Find the real distance by multiplying the measured distance by the scale.
2. Convert the distance (in cm) to metres by dividing by 100
3. Convert the distance (in metres) to km by dividing by 1000

Or interpret the scale:

1. Interpret the scale by finding the real distance represented by each cm on the map.
2. Multiply the measured distance by the distance each unit on the map represents.

Both calculations will give the same answer.

To find the distance on the map that represents the given real distance:

1. Interpret the scale by finding the real distance represented by each cm on the map.
2. For the given real distance, divide by the distance on the map that each cm represents.

Practise map scales in this quiz. You may need a pen and paper to complete these questions.

Some drivers may prefer to use a paper map to plan their journeys and to be able to find alternative routes when there is traffic. Although many drivers use satellite navigation and travel apps, a paper map does not lose its signal or misdirect you.

Mountain rescue teams use their map skills both in training and in real life and death situations. Planning and coordinating the team and directing a rescue helicopter to the site of an incident is essential to a successful outcome. The team will use map scales to work out the distance they need to travel and how far they may need to carry an injured person to safety.