Scale drawings
A scale drawing shows a real object or place with accurate proportions, but made larger or smaller. In this worksheet, you will practise calculating real lengths and drawing lengths using both written scales (such as “1 cm represents 5 km”) and ratio scales (such as “1 : 5000”). Jump to the questions
Practise now
Worksheet preview and key skills
Worksheet preview
Calculate real and drawing lengths from various scales.
Questions start with simple written scales and progress to using ratio scales, model scale contexts, and visual grid diagrams.
What you’ll practise
- using a written scale
- finding real lengths
- finding drawing lengths
- using ratio scales and converting units
Use the interactive worksheet below, or read the Topic guide for the method and worked example.
Topic guide
What is a scale drawing?
A scale drawing is a smaller or larger version of an object or place. Everything is kept in the same proportion so that the drawing is an accurate representation.
Using a written scale
A written scale tells you exactly what a measurement on the drawing represents in real life. For example, “1 cm represents 5 km”.
Finding the real length
To find the real length from a drawing length, multiply by the scale amount. If 1 cm represents 5 km, and the drawing length is 3 cm:
3 × 5 = 15 km
Finding the drawing length
To find the drawing length from a real length, divide by the scale amount. If 1 cm represents 5 km, and the real distance is 40 km:
40 ÷ 5 = 8 cm
Using a ratio scale
A ratio scale, such as 1 : 5000, has no units written in it. This means that 1 unit on the drawing represents 5000 of the same units in real life.
For example, 1 cm on the drawing represents 5000 cm in real life.
You can then convert the real-life measurement into more sensible units, like metres or kilometres. Since 100 cm = 1 m:
5000 cm = 50 m
Worked example
Question: A map uses the scale 1 cm represents 4 km. Two places are 6 cm apart on the map. Find the real distance.
Method: Multiply the drawing length by the scale amount.
6 × 4 = 24 km
Common mistakes
- Multiplying when the question requires division (e.g. going from real length to drawing length).
- Forgetting to convert centimetres into metres or kilometres when using a ratio scale.
- Treating a ratio like 1 : 5000 as though it means 1 cm represents 5000 m. Remember, ratio scales initially use the same unit on both sides!
- Measuring a diagram with a physical ruler when the relevant length is already stated in the question or can be counted on a grid.
Quick recap
Drawing to real: multiply. Real to drawing: divide. Ratio scales: both sides start with the same units.