What is a scale drawing?
A scale drawing represents a real object or space using a fixed ratio between the drawn measurements and the real measurements. A scale can be written as a statement, like "1cm represents 5m", or as a ratio, like 1:500.
Every length in a correct scale drawing shrinks (or grows) by exactly the same scale factor.
Finding real-life measurements from a drawing
Worked Example 1
A scale drawing uses the scale 1cm : 5m. A wall is drawn 4cm long. Find the real length of the wall.
1
Identify what 1cm on the drawing represents in real life: 1cm = 5m
2
Multiply the drawn length by the real-life value of 1cm: 4 × 5m = 20m
Answer20m
Both rectangles keep the same 4:3 proportions — only the size changes. The real room is drawn genuinely bigger than the scale drawing, not just labelled differently.
Finding drawn measurements from real-life dimensions
Worked Example 2
Using a scale of 1cm : 2m, how long should a wall be drawn if it is 10m long in real life?
1
Identify what 1cm on the drawing represents in real life: 1cm = 2m
2
Divide the real length by the real-life value of 1cm: 10 ÷ 2 = 5
Answer5cm
Scales written as a ratio
Scales are often written in the form 1:n, such as 1:50 or 1:200. This means 1 unit on the drawing represents n of the same unit in real life — so both sides must be converted to the same unit before applying the scale factor.
Worked Example 3
A scale model of a bridge is built at a scale of 1:50. The real bridge is 15m long. Find the length of the model, in centimetres.
1
Convert the real length into centimetres, to match the model's likely unit: 15m = 1500cm
2
Divide by the scale factor: 1500 ÷ 50 = 30
Answer30cm
Map scales
Maps work exactly the same way, but the scale factors are usually much larger, since real-world distances are huge compared to a page.
Worked Example 4
A map has a scale of 1:25,000. Two villages are 6cm apart on the map. Find the real distance between them, in kilometres.
1
Multiply the map distance by the scale factor: 6 × 25,000 = 150,000cm
2
Convert centimetres to kilometres: 150,000cm = 1,500m = 1.5km
Answer1.5km
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1A scale drawing uses a scale of 1cm : 4m. A wall is drawn 3cm long. Find the real length of the wall.Foundation
Q2A garden is drawn using a scale of 1cm : 2m. The garden is 10m long in real life. How long should it be drawn?Foundation
Q3A model car is built to a scale of 1:10. If a real car is 400cm long, how long is the model?Foundation
Q4A scale drawing has a scale of 1cm : 5m. A tree is drawn 3cm tall. Find the real height of the tree.Foundation
Q5A floor plan has a scale of 1cm : 1.5m. A room is drawn 4cm wide. Find the real width.Foundation
Higher (Grade 5–7)
Q6A scale model of a building uses a scale of 1:200. The real building is 60m tall. Find the height of the model, in centimetres.Higher
Q7A map has a scale of 1cm : 2km. Two towns are 7.5cm apart on the map. Find the real distance between them, in km.Higher
Q8A scale model of a bridge uses a scale of 1:250. The model is 18cm long. Find the length of the real bridge, in metres.Higher
Q9A room measures 9m by 6m in real life. Using a scale of 1cm : 1.5m, find the dimensions of the scale drawing.Higher
Q10A scale drawing uses the ratio 1:20. A wall on the drawing is 12cm. Find the real length of the wall, in metres.Higher
Higher — Hard (Grade 8–9)
Q11A map has a scale of 1:50,000. Two landmarks are 4.6km apart in real life. Find the distance between them on the map, in centimetres.Grade 8–9
Q12A scale model of a statue is built at a scale of 1:25. The model is 32cm tall. Find the height of the real statue, in metres.Grade 8–9
Q13A rectangular garden measures 15m by 9m. It is drawn on paper using a scale of 1:300. Find the area of the scale drawing, in cm².Grade 8–9
Q14A floor plan uses a scale of 1:50. A rectangular room is drawn as 8cm by 5cm. Find the real area of the room, in m².Grade 8–9
Q15Two cities are 3.5cm apart on a map with scale 1:1,000,000. A cyclist travels between the two cities at an average speed of 20km/h. How long does the journey take, in hours?Grade 8–9
Answers
Foundation (Q1–Q5)
Q112m
Q25cm
Q340cm
Q415m
Q56m
Higher (Q6–Q10)
Q630cm(60m = 6000cm, 6000 ÷ 200)
Q715km
Q845m(18 × 250 = 4500cm)
Q96cm by 4cm
Q102.4m(12 × 20 = 240cm)
Higher — Hard (Q11–Q15)
Q119.2cm(4.6km = 460,000cm, 460,000 ÷ 50,000)
Q128m(32 × 25 = 800cm)
Q1315cm²(1500cm ÷ 300 = 5cm, 900cm ÷ 300 = 3cm, 5 × 3)
Q1410m²(8 × 50 = 400cm = 4m, 5 × 50 = 250cm = 2.5m, 4 × 2.5)
Q151.75 hours(3.5cm × 1,000,000 = 3,500,000cm = 35km, 35 ÷ 20)
Common mistakes
Common Mistake 1
Multiplying instead of dividing (or vice versa)
Going from drawn to real means multiplying by the scale factor; going from real to drawn means dividing. Mixing these up is the most common scale drawing error.
Common Mistake 2
Forgetting to convert units before applying the scale
A scale of 1:50000 applies to matching units — always convert metres or kilometres into centimetres (or vice versa) before multiplying or dividing by the scale factor.
Common Mistake 3
Applying the scale factor only once for area questions
For area, the scale factor must be applied to both dimensions separately before multiplying them together — it cannot be applied directly to an area value.
Common Mistake 4
Losing track of the final unit
Answers often come out in centimetres from the working, but the question may ask for metres or kilometres — always check the required unit before giving the final answer.
Exam tips
💡 Exam Tip 1
Write the scale as "1 unit = ..." before starting
Translating the scale into a clear statement first (e.g. "1cm = 25,000cm") makes it much easier to decide whether to multiply or divide.
💡 Exam Tip 2
Convert to the smaller unit first
Converting metres or kilometres into centimetres before applying the scale factor usually avoids decimals appearing partway through your working.
💡 Exam Tip 3
Sense-check your answer's size
A real-life distance should almost always come out much larger than the drawn distance — if your answer is smaller, you've likely divided when you should have multiplied.
💡 Exam Tip 4
For area, square the scale factor as a shortcut
Once you're confident with the method, you can convert areas directly by squaring the scale factor (e.g. a 1:50 length scale becomes a 1:2500 area scale) — but only use this once you understand why it works.
Want to improve your grade faster?
If scale drawings are still causing problems, Alamin's diagnostic approach identifies exactly which skills are missing and builds a targeted plan to address them — with AI-powered practice between sessions.
Book an Assessment Session (£60)No upfront payment required — payment is taken after confirmation.