15.4 Scale Drawings and Maps

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: using scales written in words, ratio scales and bar scales to find real and drawn lengths. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Use a scale such as 1 cm represents 5 m to change between drawn and real lengths
• Use ratio scales such as 1 : 50 000 on maps
• Read and use a bar scale
• Make and use accurate scale drawings

Key words

• Scale: Tells you how a length on a drawing or map compares with the real length.
• Scale drawing: An accurate drawing where every length is the real length divided by the same number.
• Ratio scale: A scale written as 1 : n. 1 unit on the map is n of the same units in real life.
• Bar scale: A marked line on a map showing what real distance each length represents.

Scales written in words

A scale such as 1 cm represents 5 m means every centimetre on the drawing stands for 5 metres in real life.

• drawing length to real length; Do this multiply by the scale
• real length to drawing length; Do this divide by the scale

Worked example: 1 cm represents 5 m

(a) A wall is 7.4 cm long on the drawing. Real length = 7.4 × 5 = 37 m.
(b) A path is 22 m long. Drawing length = 22 ÷ 5 = 4.4 cm.

Answer: (a) 37 m (b) 4.4 cm

Ratio scales on maps

A map scale of 1 : 25 000 means 1 cm on the map is 25 000 cm in real life. Change the answer to sensible units at the end.

Key fact: 100 cm = 1 m and 1000 m = 1 km, so 100 000 cm = 1 km.

Worked example: map scale 1 : 25 000

(a) Two churches are 6.2 cm apart on the map. 6.2 × 25 000 = 155 000 cm = 1550 m = 1.55 km.
(b) A footpath is 2 km long. 2 km = 200 000 cm. 200 000 ÷ 25 000 = 8 cm.

Answer: (a) 1.55 km (b) 8 cm

Worked example: writing a scale as a ratio

1 cm represents 3 km. Change 3 km to centimetres: 3 × 100 000 = 300 000 cm.

Answer: 1 : 300 000

Bar scales

A bar scale lets you measure a distance on the map with a ruler (or a strip of paper) and read it straight off. It still works if the map is printed bigger or smaller.

Worked example: using the bar scale

On the printed map, Elmford and Kirkby are 6.4 cm apart in a straight line.
The bar scale shows 1 cm represents 1 km, so the distance is 6.4 × 1 = 6.4 km.
The winding road is longer than the straight-line distance.

Answer: about 6.4 km in a straight line

Making a scale drawing

Change every real length to a drawing length using the same scale, then draw accurately with a ruler. You can then measure the drawing to find other real lengths.

Worked example: a bedroom 6 m by 4.5 m at 1 : 50

6 m = 600 cm and 600 ÷ 50 = 12 cm. 4.5 m = 450 cm and 450 ÷ 50 = 9 cm.
Draw a 12 cm by 9 cm rectangle. The diagonal measures 15 cm on the drawing.
Real diagonal = 15 × 50 = 750 cm.

Answer: drawing 12 cm by 9 cm; real diagonal 7.5 m

Common mistakes

• Forgetting to change units: 1 : 50 000 gives centimetres, so 4 cm on the map is 200 000 cm = 2 km, not 200 000 km.
• Multiplying when you should divide. Real lengths are bigger than drawn lengths, so check your answer makes sense.
• Measuring from the end of the ruler instead of from 0.
• Using a different scale for each side of a scale drawing.

Revision questions

Try these, then check your answers below each one.

Question 1. A scale drawing uses 1 cm to represent 5 m. A wall is 7.2 cm long on the drawing. How long is the real wall in metres?

Answer: 36 m

Working: 7.2 × 5 = 36 m.

Question 2. A map has scale 1 : 25 000. Two points are 8 cm apart on the map. How far apart are they in real life, in km?

Answer: 2 km

Working: 8 × 25 000 = 200 000 cm = 2 km.

Question 3. A map uses the scale 1 cm represents 4 km. Write this as a ratio. (Choose from: 1 : 400 000, 1 : 4000, 1 : 40 000, 1 : 4.)

Answer: 1 : 400 000

Working: 4 km = 4 × 100 000 = 400 000 cm, so the scale is 1 : 400 000.

Related lessons

• Previous lesson: 15.3 Accurate Drawings 1
• Next lesson: 15.5 Accurate Drawings 2
• In this chapter: 15.1 3D Solids
• In this chapter: 15.2 Plans and Elevations
• In this chapter: 15.6 Constructions

Continue in the full course

This lesson is section 15.4 (EGCMF1504) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.