A scale of 1 cm to 50 km says every centimeter 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.
Step 2: Try It Yourself
Set the scale and read the pairs off the table.
| Centimeters on the map | Kilometers 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: In Real Life
A hiking map
A map says 1 centimeter is half a kilometer. The trail is 7 centimeters on the map: 3.5 kilometers of walking. The scale turns paper into distance.
Step 4: 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 5: 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 meters?
4 of 4
Going from a real length to a map length, do you multiply or divide?
Step 6: 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.
For the grown-up
A scale is a ratio between two lengths — A scale of 1 cm to 0.5 km says that every centimeter measured on the map stands for half a kilometer 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.
Turn the scale into a multiplier — Scale 1 cm : 50 km. On the map, two towns are 7 cm apart. 7 × 50 = 350 350 km apart. Going the other way, a real 200 km is 200 ÷ 50 = 4 cm on the map.