Map scale and distance

A real city is huge. A map of the city is small. How is the small map related to the real place? Through a scale.

What is this?

A scale tells us how much real distance is shown by every centimetre on the map. It is usually written like this:

$1 \text{ cm} = 1 \text{ km}$

This means every 1 cm we measure on the map = 1 km of real distance.

So if two towns are 5 cm apart on the map, they are 5 km apart in reality.

Different maps have different scales:

• A building plan: 1 cm = 1 m (small scale, lots of detail).
• A city map: 1 cm = 100 m or 1 cm = 500 m.
• A state map: 1 cm = 10 km.
• A country map: 1 cm = 100 km.

The smaller the scale (1 cm = bigger real distance), the more area we can show, but with less detail.

To find real distance from a map:

1. Measure the map distance with a ruler.
2. Multiply by the scale factor.

For example, if the scale is 1 cm = 5 km and the distance on the map is 8 cm, the real distance = 8 × 5 = 40 km.

To find the map distance from a real distance, do the reverse , divide by the scale factor.

Worked examples

Example 1. A map has scale 1 cm = 2 km. The distance between two villages on the map is 7 cm. Real distance?

• 7 × 2 = 14 km.

Example 2. A city map has scale 1 cm = 500 m. The hospital is 3 cm from the school on the map. Real distance?

• 3 × 500 = 1,500 m = 1 km 500 m.

Example 3. Two towns are 50 km apart in reality. On a map with scale 1 cm = 5 km, how far apart should they be drawn?

• 50 ÷ 5 = 10 cm.

Try it

1. Scale 1 cm = 4 km. Map distance 9 cm. Real distance?
2. Scale 1 cm = 100 m. Map distance 6 cm. Real distance?
3. Scale 1 cm = 1 km. Two cities are 25 km apart. Map distance?
4. Scale 1 cm = 50 m. Map distance 5 cm. Real distance in metres?
5. Two friends' houses are 2 km apart. The map shows them 8 cm apart. What is the scale?

Hands-on

Plan to map. Pick one room of your house. Choose a scale (say 1 cm = 1 m). Measure the lengths and widths in real life. Draw the room on paper using your scale.

Atlas distance. Open an atlas page of India. Read the scale at the bottom. Measure the distance between any two cities on the page. Multiply by the scale to get the real distance. Compare with online distance.