Architecture: Floor plans and blueprints are drawn at scales such as 1:100 so that a 5 m room appears as 5 cm on paper — accurate enough to plan construction.
Cartography: Maps show real distances at a reduced scale — Ordnance Survey Landranger maps use 1:50 000, so 1 cm represents 500 m of real terrain.
Engineering: Technical drawings of components use scale to convey exact measurements compactly, allowing manufacturers to produce parts to precise dimensions.
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Scale 1:n means 1 unit on the drawing = n units in real life
A scale drawing is a smaller (or sometimes larger) version of a real object. Every measurement on the drawing is in the same ratio to the real measurement. The scale tells you this ratio. For example, scale 1:50 means every 1 cm on the drawing represents 50 cm in real life.
Example 1 — A drawing uses scale 1:50. A wall measures 6 cm on the drawing. How long is the real wall?
Step 1
Identify the scale factor: scale is 1:50, so multiply drawing by 50.
Step 2
Real length = drawing × scale = \(6 \times 50 = 300\) cm
Step 3
Convert to metres: \(300 \div 100 = \mathbf{3 \text{ m}}\)
Example 2 — A map uses scale 1:100. The kitchen on the plan is 4 cm long. What is the real length?
Step 1
Scale is 1:100 → multiply by 100.
Step 2
Real length = \(4 \times 100 = 400\) cm
Step 3
Convert: \(400 \div 100 = \mathbf{4 \text{ m}}\)
Key rule: Scale 1:n → multiply the drawing measurement by n to get the real measurement.
Units: If the scale is 1:50 and the drawing is in cm, the real measurement is also in cm (just 50× bigger). Then convert: 300 cm = 3 m. Always work in the same units on both sides.
✓ Quick Check 1 — Understanding Scale
Question 1 of 10
Converting Between Drawing and Real Measurements
Drawing → Real: × scale number | Real → Drawing: ÷ scale number
The relationship between drawing and real measurements works in both directions. To go from drawing to real, multiply. To go from real to drawing, divide. Always use the same units on both sides before calculating.
Example 1 — A real room is 5 m wide. Scale is 1:50. How wide is it on the drawing?
Step 1
Convert to the same units as the drawing: \(5 \text{ m} = 500 \text{ cm}\)
Example 2 — A drawing shows a garden 8 cm × 6 cm. Scale 1:200. Find real dimensions.
Step 1
Real length = \(8 \times 200 = 1600\) cm \(= \mathbf{16 \text{ m}}\)
Step 2
Real width = \(6 \times 200 = 1200\) cm \(= \mathbf{12 \text{ m}}\)
Step 3
Real garden: \(16 \text{ m} \times 12 \text{ m}\)
Common mistake: Forgetting to convert units. If real = 3 m and scale is 1:50, you must convert to cm first: \(300 \text{ cm} \div 50 = 6 \text{ cm}\). Using 3 ÷ 50 gives 0.06 cm — far too small!
✓ Quick Check 2 — Converting Between Drawing and Real Measurements
Question 1 of 10
Maps and Map Scales
Example 1 — A map has scale 1:50000. Two points are 4.5 cm apart on the map. What is the real distance in km?
Step 1
Real distance = \(4.5 \times 50000 = 225\,000\) cm
Step 2
Convert: \(225\,000 \div 100 = 2250\) m
Step 3
\(2250 \div 1000 = \mathbf{2.25 \text{ km}}\)
Map scales: 1:50000 means 1 cm on map = 50000 cm = 500 m = 0.5 km in real life. This is the scale used on Ordnance Survey Landranger maps of the UK.
Always check your units and convert carefully. \(1 \text{ km} = 1000 \text{ m} = 100\,000 \text{ cm}\). Never mix units mid-calculation — convert everything to cm first, then convert back at the end.
Producing your own scale drawing (choosing a scale, converting, drawing accurately) gets its own full lesson — see Lesson 15.3 — Creating Scale Drawings.
✓ Quick Check 3 — Maps and Map Scales
Question 1 of 10
Practice: Scale Drawing Conversions
Work out each missing value, type your answer (numbers only, e.g. 200 for 200 cm or 1 for 1 km), then click Check All.
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Question
Answer
Result
1
Scale 1:50, drawing 4 cm → real (cm)?
2
Scale 1:100, drawing 3.5 cm → real (cm)?
3
Scale 1:50, real 300 cm → drawing (cm)?
4
Scale 1:200, real 10 m → drawing (cm)?
5
Scale 1:50000, map 2 cm → real (km)?
6
Scale 1:100, drawing 7.5 cm → real (cm)?
7
Scale 1:50, real 5 m → drawing (cm)?
8
Scale 1:25, drawing 8 cm → real (cm)?
9
Scale 1:20, drawing 6 cm → real (cm)?
10
Scale 1:100000, map 3 cm → real (km)?
⚠ Things to Watch Out For
Confusing drawing measurement with real measurement: Scale 1:50 means 1 cm on the drawing = 50 cm in reality. Drawing measurement is always smaller than real measurement (for scale factors > 1).
Multiplying instead of dividing (and vice versa): Drawing → Real: MULTIPLY by the scale factor. Real → Drawing: DIVIDE by the scale factor.
Scale 1:25000 on maps: 1 cm on the map = 25,000 cm = 250 m = 0.25 km in reality. Always convert the real measurement to useful units (metres or km) after calculating.
Units mismatch: If scale is 1:100 and real length is in metres, convert to cm first: 3 m = 300 cm. Then 300 ÷ 100 = 3 cm on drawing.
Not converting the answer: After calculating, convert to appropriate units. "3m drawing measurement" doesn't make sense — convert to cm: 3 cm drawing.