A scale compares a length on a drawing or map with the real length it represents. A scale is written as a ratio 1:n, where 1 unit on the drawing stands for n units in real life. Most plans and maps are reductions, so n is large.
Reading a scale
To go from the drawing to the real world you multiply by the scale factor n. Keep both lengths in the same unit before you convert.
Key idea
For a scale 1:n,
Actual length = Drawing length × n
Drawing length = Actual length ÷ n
Working in centimetres and metres
Measure the drawing in cm, multiply by n, then convert to m or km at the end (100 cm = 1 m, 100000 cm = 1 km).
Worked example
A floor plan uses a scale of 1:50. A wall is drawn 6 cm long. Find its actual length.
Actual = 6 × 50 = 300 cm.
300 cm ÷ 100 = 3 m.
On a map with scale 1:25 000, a road measured 3 cm long is 3 × 25 000 = 75 000 cm = 750 m = 0.75 km in reality. Notice how a small distance on paper stands for a large distance on the ground when n is big.
The scale factor also lets you compare two lengths quickly: a length that is drawn twice as long is twice as long in reality, because every centimetre on the drawing represents the same n centimetres. Keeping this proportion in mind is a useful check on your answer.
Remember
- Scale 1:n → multiply the drawing length by n to get the actual length.
- A larger n means a greater reduction (a smaller drawing).
- Convert cm → m (÷100) or cm → km (÷100000) only at the end.