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Pioneers Maths

Maths · Ratio & Proportion

Scale (maps & drawings)

Use scale factors on maps and technical drawings.

Not startedCAMBRIDGE · 8CBSE · VIIIIB · MYP-2

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What is a scale?

A scale shows how distances on a map or drawing compare to real life. For example, 1 cm on paper might represent 100 cm (or 1 metre) in reality. This ratio helps us shrink large objects or places to fit on paper.

Reading a scale

Scales are written as ratios like 1:50 or 1:1000. The first number shows the map distance. The second shows the real distance. A scale of 1:200 means 1 cm on the map equals 200 cm in real life.

Finding real distances

To find a real distance, multiply the map distance by the scale factor. If the map distance is 3 cm and the scale is 1:500, the real distance is 3 × 500 = 1500 cm.

Finding map distances

To find a map distance, divide the real distance by the scale factor. If a room is 800 cm long and the scale is 1:100, the map length is 800 ÷ 100 = 8 cm.

Converting units

Often you need to convert units at the end. Remember: 100 cm = 1 m and 1000 m = 1 km. A result of 150000 cm can be written as 1500 m or 1.5 km.

Worked examples

  1. 1. A map has a scale of 1:20000. Two towns are 5 cm apart on the map. What is the real distance in metres?

    1. The scale is 1:20000, so 1 cm on the map equals 20000 cm in real life.
    2. Map distance = 5 cm, so real distance = 5 × 20000 = 100000 cm.
    3. Convert to metres: 100000 cm ÷ 100 = 1000 m.

  2. 2. A garden is 12 m long. On a drawing with scale 1:50, how long should it be in cm?

    1. Real length = 12 m = 1200 cm.
    2. Scale is 1:50, so divide the real distance by 50.
    3. Drawing length = 1200 ÷ 50 = 24 cm.

  3. 3. A floor plan uses a scale of 1:100. A wall is drawn as 7.5 cm. What is the actual length in metres?

    1. Scale 1:100 means multiply the drawing measurement by 100.
    2. Actual length = 7.5 × 100 = 750 cm.
    3. Convert to metres: 750 ÷ 100 = 7.5 m.

Try it yourself

A map scale is 1:5000. A path measures 8 cm on the map. What is the real distance in metres?

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