Use map scales and scale drawings to convert between real distances and lengths on the page. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A scale of 1:200 means 1 cm on the drawing is 200 cm in real life (or 2 m). Multiply by the scale to go from drawing to real; divide to go the other way. Keep the units consistent before you multiply — convert 2 m to 200 cm, or convert the scale into cm-to-m, but not a jumble of both.
Bearings and scale drawings often travel together: measure the drawing with a ruler, then convert. Map scales such as 1:50000 are the same skill with bigger numbers. Write the units of the real length in the answer.
Scale 1:n means 1 cm on the map is n cm in real life. Convert the real length into the unit the question wants (m or km) after multiplying. Bearings and map distances in later topics use this same multiplication.
Objectives
1:50 means multiply the drawing length by 50 to get the real length.
1:50 with both lengths in centimetres is real cm = drawing cm × 50.
1 cm to 2 km means the scale factor is not 2. It is 2 km per cm.
Key points
Read a scale like 1 : 25,000 or 1 cm : 4 m.
Convert a map or drawing length into a real distance.
Convert a real distance into the length to draw.
Change units (cm to m to km) after scaling.
Worked examples
Example 1
A plan uses the scale 1:50. A path is 2 cm on the plan. How many centimetres is the real path?
2 marks
Real length = plan length × 50.
2 × 50 = 100.
The real path is 100 cm.
Answer: 100 cm
Common slips
Slip: Real length = plan length ÷ 50. To go from the plan to real life, multiply by the scale.
Slip: 2 ÷ 50 = 0.04. Dividing makes the real length smaller than the plan.
Slip: The real path is 0.04 cm. The real path must be longer than its length on the plan.
Example 2
The scale is 1:50. A wall is 100 cm in real life. How many centimetres long is it on the drawing?
2 marks
Drawing length = real length ÷ 50.
100 ÷ 50 = 2.
The wall is 2 cm long on the drawing.
Answer: 2 cm
Common slips
Slip: Drawing length = real length × 50. To go from real life to the drawing, divide by the scale.
Slip: 100 × 50 = 5000. Multiplying makes the drawing bigger than the real wall.
Slip: The wall is 5000 cm long on the drawing. The drawing must be smaller than the real wall.
Example 3
A plan uses the scale 1:50. A wall is 4 cm long on the plan. How long is the real wall, in metres?
3 marks
Real length = 4 × 50 = 200 cm.
There are 100 cm in 1 m, so 200 ÷ 100 = 2.
The real wall is 2 m long.
Answer: 2 m
Common slips
Slip: Real length = 4 ÷ 50 = 0.08 cm. To go from the plan to real life, multiply by the scale.
Slip: There are 10 cm in 1 m, so 200 ÷ 10 = 20. There are 100 cm in 1 m, not 10.
Slip: The real wall is 20 m long. The answer is 10 times too big.
Questions and answers
GCSE Maths scale drawings questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A plan uses the scale 1:50. A path is 3 cm on the plan. How many centimetres is the real path?
Show answer
Answer: 150 cm
Real length = plan length × 50.
3 × 50 = 150.
M1 — Real length = plan length × 50.
A1 — Answer 150 cm
Question 2 Easy2 marks
The scale is 1:50. A wall is 150 cm in real life. How many centimetres long is it on the drawing?
Show answer
Answer: 3 cm
Drawing length = real length ÷ 50.
150 ÷ 50 = 3.
M1 — Drawing length = real length ÷ 50.
A1 — Answer 3 cm
Question 3 Medium2 marks
The scale is 1:50. A wall is 200 cm in real life. How many centimetres long is it on the drawing?
Show answer
Answer: 4 cm
Drawing length = real length ÷ 50.
200 ÷ 50 = 4.
M1 — Drawing length = real length ÷ 50.
A1 — Answer 4 cm
Question 4 Medium2 marks
A plan uses the scale 1:50. A wall is 8 cm long on the plan. How long is the real wall, in metres?
Show answer
Answer: 4 m
Real length = 8 × 50 = 400 cm.
There are 100 cm in 1 m, so 400 ÷ 100 = 4.
M1 — Real length = 8 × 50 = 400 cm.
A1 — Answer 4 m
Question 5 Hard2 marks
A plan uses the scale 1:50. A wall is 10 cm long on the plan. How long is the real wall, in metres?
Show answer
Answer: 5 m
Real length = 10 × 50 = 500 cm.
There are 100 cm in 1 m, so 500 ÷ 100 = 5.
M1 — Real length = 10 × 50 = 500 cm.
A1 — Answer 5 m
Question 6 Hard2 marks
A plan uses the scale 1:50. A path is 6 cm on the plan. How many centimetres is the real path?
Show answer
Answer: 300 cm
Real length = plan length × 50.
6 × 50 = 300.
M1 — Real length = plan length × 50.
A1 — Answer 300 cm
Question 7 Exam-style3 marks
A plan uses the scale 1:50. A path is 7 cm on the plan. How many centimetres is the real path?
Show answer
Answer: 350 cm
Real length = plan length × 50.
7 × 50 = 350.
The real path is 350 cm.
M1 — Real length = plan length × 50.
M1 — 7 × 50 = 350.
A1 — Answer 350 cm
Common mistakes
Most lost marks on this topic are one slip.
Dividing the drawing length by the scale.
Multiply to go from the drawing to real life.
Mixing cm on the drawing with m in the answer without converting.
Finish in the unit the question asks for.
Multiplying a real length by the scale to get the drawing.
That makes the drawing larger. Divide instead.
Spot the slip
On a scale of 1:100, 1 cm on the drawing is
100 cm in real life
1 cm in real life
10 cm in real life
Show the slip
100 cm in real life The second number is the real length for one drawing unit.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the multiplication line (6×50,000) before converting units — both lines carry marks.
Remember 100,000 cm in 1 km — it turns most map questions into one division.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.