What are map scales?
A map cannot be the same size as the area it represents. It needs to be scaled down to fit on a page or a screen.
Map scales can be written in two ways, a simple scale with units or a ratio scale.
Simple scales
A map scale is given as 1 cm = 2 km.
This means that every cm on the map represents 2 km in real life.
Example
The distance between two towns on a map is 8 cm.
To calculate the actual distance between the two towns we use the scale:
\(1~cm = 2~km\)
\(8~cm = 2 \times 8~km\)
\(8~cm = 16~km\)
Question
A theme park map has a scale of 1 cm = 250 m.
The distance on the map between the rollercoaster and the waterslide is 6 cm.
What is the actual distance between the rollercoaster and the waterslide?
Answer
The scale is:
\(1~cm = 250~m\)
\(6~cm = 6 \times 250~m = 1500~m\)
The actual distance is 1500 m = 1.5 km.
Ratio scales
Ratio scales on maps are usually given as 1: n
For example, 1:10000 or 1:25000
1:10000 means 1 cm on the map represents 10000 cm in real life.
Similarly, 1: 25000 means 1 cm on the map represents 25000 cm in real life.
Key point
A ratio has no units.
Actual distances can be calculated from a map using a ratio scale 1:n.
To do this follow these 3 steps:
Measure the required distance on the map in cm.
Multiply this length by the n number in the ratio, this will give the actual distance in cm.
Divide the actual distance by 100 to convert from cm into metres and then divide by 1000 to convert from metres into km.
Example
The distance between Bangor and Groomsport on a map is 12 cm.
The scale on the map is 1:50000.
The distance on the map is 12 cm.
The actual distance in cm is \(12 \times 50000 = 600000~cm\).
Convert 600000 cm into metres and then kilometres.
So, to recap:
\(1: 50000\)
\(12: 12 \times 50 000 = 600000~cm\)
\( = 600000~cm/100 = 6000~m\)
\( = 6000m/1000 = 6km\)
The actual distance from Bangor to Groomsport is 6 km.
Question
The distance on a map from Tower Bridge to the London Eye is 10 cm.
If the map has a scale of 1:25000, find the actual distance in Kilometres?
Answer
The scale is 1:25000.
The map distance is 10 cm.
1:25000
\(10: 25000 \times 10 = 250000~cm\)
The actual distance is 250000 cm.
\(250000~cm = 2500~m = 2.5~km\)
The actual distance from Tower Bridge to the London Eye is 2.5 km.
Test section
Question 1
A map has a scale of \(1~cm = 5~km\).
On the map, the distance between two villages is \(3~cm\).
What is the actual distance between the two villages?
Answer
\(15~km\)
Question 2
A map has a scale of \(1~cm ~=~10~kilometres\).
The distance between two cities on the map is \(4.8~cm\).
What is the actual distance between the cities?
Answer
\(48~km\)
Question 3
The distance on a road map between Belfast and Dublin is \(16~cm\).
The map has a scale \(1:1000000\).
What is the actual distance between the two cities?
Answer
\(160~km\)
Question 4
A tourist map uses the scale \(1:50000\).
The distance between two seaside resorts on the map is \(12~cm\).
What is the actual distance between the two resorts?
Answer
\(6~km\)
More on Ratio and proportion
Find out more by working through a topic
- count1 of 3
- count2 of 3
