Scale: maps, drawings and enlargements
Scale is written image : real life. A scale of 1:50 000 means that 1 cm on the map is 50 000 cm, which is 500 m, in real life. From map to real life we multiply, the other way we divide. In an enlargement, such as 5:1, it is the other way round.
Watch Fox work it out on the board
Fox works one step at a time. Press play.
What scale means
scale = image : real life
- Reduction, for example 1:100: 1 cm on the drawing is 100 cm in real life.
- Enlargement, for example 5:1: 5 cm in the image is 1 cm in real life.
- Scale 1:1: the image is the same size as real life.
Both numbers have the same unit. We work in cm and change to m or km in the last step.
Map scales
| Scale | 1 cm on the map is | Used for |
|---|---|---|
| 1:10 000 | 100 m | Town maps, orienteering maps |
| 1:25 000 | 250 m | Detailed terrain maps |
| 1:50 000 | 500 m | Terrain maps for hiking |
| 1:100 000 | 1 km | Overview maps |
Area scale
The scale applies to lengths. An area changes in both length and width, so the number in the scale is used twice.
area scale = (length scale)²: 1:100 gives 1:100² = 1:10 000
On a drawing at a scale of 1:100, a room is 4 cm · 3 cm. In real life it is 4 m · 3 m = 12 m². We convert the lengths first and then work out the area.
Example
Example 1: from map to real life
On a map at a scale of 1:50 000, two lakes are 6 cm apart. How far is it in real life?
Real life is 50 000 times larger, so we multiply.
6 cm · 50 000 = 300 000 cm
There are 100 cm in a metre, so we divide by 100.
300 000 cm = 3 000 m
There are 1 000 m in a kilometre.
3 000 m = 3 km
1 cm is 500 m, and 6 · 500 m = 3 000 m = 3 km.
Example 2: from real life to map
Two houses are 2 km apart. How far apart are they on a map at a scale of 1:25 000?
We convert to cm: 2 km = 2 000 m = 200 000 cm.
2 km = 200 000 cm
The map is 25 000 times smaller, so we divide.
200 000 ÷ 25 000 = 8
The distance on the map is 8 cm.
8 cm
Back again: 8 cm · 25 000 = 200 000 cm = 2 km. That is correct.
Example 3: what is the scale of an enlargement?
A ladybird is 0.6 cm. In a picture it is 4.2 cm. We want to find the scale.
We write image : real life in the same unit, cm.
4.2 : 0.6
We divide both numbers by 0.6. The ratio does not change when both are divided by the same number.
4.2 ÷ 0.6 = 7 and 0.6 ÷ 0.6 = 1
The scale is 7:1, an enlargement of seven times.
7 : 1
7 · 0.6 cm = 4.2 cm, exactly the length in the picture.
Pitfalls
Dividing from map to real life, so that 6 cm becomes a tiny fraction of a centimetre.
Real life is larger than the map, so we multiply. From real life to map we divide.
Calculating with different units, for example 2 km ÷ 25 000.
Convert everything to cm first. Change to m or km in the last step.
Thinking that a surface at a scale of 1:100 is 100 times larger in real life.
The area grows in both length and width: 100 · 100 = 10 000 times. Convert the lengths first.
Practise on your own
0 of 4 correct1A drawing has a scale of 1:100. A wall is 7 cm on the drawing. How long is the wall in real life? Answer in metres.
2On a map at a scale of 1:50 000, a path is 4 cm long. How long is the path in real life? Answer in kilometres.
3A model car is 15 cm long. The real car is 4.5 m. What is the scale of the model?
4A picture of an ant is drawn at a scale of 8:1. In the picture the ant is 4 cm. How long is the ant in real life? Answer in millimetres.
More walkthroughs with Fox
Common questions
Which scale is larger, 1:10 000 or 1:50 000?
1:10 000 is the larger scale. It shows a smaller area in more detail.
How do I know whether the scale is an enlargement or a reduction?
If the second number is the larger, as in 1:100, it is a reduction. If the first is the larger, as in 5:1, it is an enlargement.
Why should the scale be written with 1 on one side?
Then we can see it straight away: 1:30 means 30 times larger in real life. 15:450 means the same thing but is harder to read.
Read also
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