A scale of 1 cm to 50 km says every centimetre on the drawing stands for 50 km on the ground.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
A scale is a rate
It behaves exactly like £3 per kilogram. Multiply to go one way, divide to go the other.
Drawing to real
4 cm on the map is 4 × 50 = 200 km on the ground.
Real to drawing
350 km on the ground is 350 ÷ 50 = 7 cm on the map.
A scale is a ratio between two lengths
A scale of 1 cm to 0.5 km says that every centimetre measured on the map stands for half a kilometre on the ground. It is a ratio, so it scales: 4 cm on the map is 2 km on the ground.
Scales written as a pure ratio
A scale of 1 : 50,000 means one unit on the map is 50,000 of the same units on the ground. Because no unit is named, the ratio works for any: 1 cm represents 50,000 cm, which is 500 m. Converting to a sensible unit is usually the first step.
Using it in both directions
Map to ground, multiply by the scale factor. Ground to map, divide. Deciding the direction first is what stops you producing a map distance of 40 km. A quick sanity check — real distances are bigger — catches an inverted calculation.
Areas on a map
At a scale of 1 : 50,000, an area on the map represents 50,000² times the ground area — because area scales by the square of the length factor. This is why small patches on a map can represent surprisingly large tracts of land.
Step 2: Try It Yourself
Set the scale and read the pairs off the table.
| Centimetres on the map | Kilometres on the ground |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
Every row is the same ratio. 1 to 5 is the same comparison as 4 to 20.
Step 3: Watch an Example
One step at a time.
Watch Ana Use a Map Scale
A map has a scale of 1 cm to 20 km. Two towns are 6.5 cm apart on it.
- Step 1
She checks which way she is going: from the map to the ground, so multiply.
Step 4: Your Turn
Practice makes it stick.
The Map
Problem 1 of 2
Scale 1 cm to 20 km. How many km is 8 cm?
The Other Way
Problem 2 of 2
Scale 1 cm to 20 km. How many cm on the map is 300 km?
Map and Ground
1 of 4
Scale 1 cm to 5 km. Real distance for 7 cm, in km?
2 of 4
Scale 1 cm to 5 km. Map length for 60 km, in cm?
3 of 4
Scale 1 cm to 250 m. Real distance for 4 cm, in metres?
4 of 4
Going from a real length to a map length, do you multiply or divide? Answer 1 for multiply, 2 for divide.
Step 5: Quick Check
Show what you know.
Question 1 of 1
Scale 1 cm to 30 km. Real distance for 5 cm, in km?
What You Learned
- A scale is a rate between drawing length and real length.
- Drawing to real multiplies; real to drawing divides.
- Estimate first so a wrong operation shows up immediately.