How to use a map scale

A scale like 1 : 20 tells you that 1 cm on the paper is 20 cm in reality. So to get from a length you measure on the map to the real length, you multiply by the number on the right. That's the whole method. The only thing that trips people up is the direction.

When do I use this?

Whenever a map or a drawing comes with a scale and you need a real-world length, or you know a real length and need to know how big it should be on the drawing. What a scale is, and why the drawing is always written first, is in scale and scale drawings.

The procedure

1. Read the scale. The drawing is on the left and reality on the right: 1 : 20 means 1 on the paper is 20 in reality.
2. Measure the length on the paper.
3. Multiply by the number on the right. The unit is whatever the question says, and it's the same unit on both sides.

A classic example of a question could be that we're given the scale 1 : 20. How much is 4 centimetres on the paper in reality? Here 1 cm on the paper corresponds to 20 cm in reality, so we can multiply 20 by 4 to find what it corresponds to in reality:

$$20 \times 4 = 80\,\text{cm}$$

So 4 centimetres on the paper corresponds to 80 cm in reality with a scale of 1 : 20.

Worked examples

Example 1: a scale of 1 : 20

This is the one above. 4 cm on the paper, multiply by 20:

$$20 \times 4 = 80\,\text{cm}$$

Example 2: a map at 1 : 10000

A map has the scale 1 : 10000, in cm. That means 1 cm on the paper is 10000 cm in reality. Two places are 3 cm apart on the map. Then in reality they are

$$10000 \times 3 = 30000\,\text{cm}$$

apart. Same move, just a bigger number on the right of the scale.

Example 3: going back the other way

The scale works in both directions. If 1 cm on the paper is 20 cm in reality, then 20 cm in reality is 1 cm on the paper. So to go from a real length to the drawing, we divide instead. With a scale of 1 : 20, a wall that is 100 cm long in reality should be drawn as

$$100 \div 20 = 5\,\text{cm}$$

We can check this is right, because we know that 5 cm on the paper is $20 \times 5 = 100$ cm in reality, which is where we started.

Common mistakes

• "I multiply when I should divide, or the other way round." Paper to reality: multiply by the number on the right. Reality to paper: divide by it. The drawing is always the left side of the scale, so if your answer is supposed to be on the paper, it should come out smaller.
• "I change the unit halfway through." The scale doesn't have a unit of its own. The question decides the unit, and it's the same on both sides. 1 : 20 in cm means 1 cm is 20 cm.

Related

What a scale is, including scales that make things bigger like 50000 : 1, is in scale and scale drawings. The same "how many times longer" idea between two shapes is in similar triangles.