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.
Try it first
One map, one scale for every road on it. The road from A to B is 2 cm on the map and really 10 km. How long is the road from B to C, really, in km?
km
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
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
Ana reads the scale before anything else. One centimeter of paper stands for 20 km of ground, and that holds everywhere on this map. The same scale could have been printed as 2 cm to 40 km and would mean the same thing — what counts is what a single centimeter is worth.
Watch Leo Measure a Trail
A trail map has a scale of 1 cm to 3 km. The trail runs from the parking lot to the lake, then on to the summit. Leo starts, and you finish.
- Step 1
Leo reads the scale first: 1 cm on the map is 3 km on the ground. The trail has two straight legs, so each leg becomes kilometers on its own.
Step 5: Your Turn
Practice makes it stick.
The Garden Fence
Problem 1 of 15
A plan of a garden uses 1 cm for every 3 m. The plan is below. Fence costs $8 for every meter. What does the fence for one long side of the real garden cost?
dollars
The Model Bridge
Problem 2 of 15
Noor builds a model of a bridge at 1 cm for every 5 m. The real bridge is 90 m long. The model deck is cut from strip wood costing $2 for every centimeter. What does the strip for the deck cost?
dollars
Map and Ground
Name the direction first. Map to ground multiplies; ground to map divides.
Problem 3 of 15
Scale 1 cm to 4 km. How far is 6 cm on the map, in km?
km
Problem 4 of 15
Scale 1 cm to 4 km. A real distance is 60 km. How long is it on the map, in cm?
cm
Problem 5 of 15
Scale 1 cm to 250 m. How far is 7 cm on the map, in meters?
meters
Problem 6 of 15
Scale 1 cm to 0.5 km. How far is 11 cm on the map, in km?
km
Problem 7 of 15
Scale 1 in to 6 ft. A wall is really 48 ft long. How long is it on the drawing, in inches?
inches
Whose Step?
One line in each piece of working is a slip. Find it, then fix it.
Problem 8 of 15
Priya used a scale of 1 cm to 6 km to find the real length of a river drawn 9 cm long. One line is a slip. Which?
Priya's real length for a 9 cm river at 1 cm to 6 km
- 1Scale 1 cm : 6 km, map 9 cm
- 29 ÷ 6
- 3= 1.5
- AnswerThe real river is 1.5 km long
Problem 9 of 15
Priya's river is 9 cm on a map with a scale of 1 cm to 6 km. How long is the real river, in km?
km
Problem 10 of 15
Dev used a scale of 1 cm to 5 km to find how long a real 45 km road is on the map. One line is a slip. Which?
Dev's map length for a real 45 km road at 1 cm to 5 km
- 1Scale 1 cm : 5 km, real 45 km
- 245 × 5
- 3= 225
- AnswerThe road is 225 cm on the map
Problem 11 of 15
Dev's road is really 45 km, on a map with a scale of 1 cm to 5 km. How long is the road on the map, in cm?
cm
Pick the Move
Choose the move before you make it.
Problem 12 of 15
A map has a scale of 1 cm to 40 km. Two cities are really 320 km apart. Which move gives the distance between them on the map?
Problem 13 of 15
A map has a scale of 1 cm to 20 km. A trail is drawn as two straight legs. Which move gives the real length of the whole trail?
Same Distance?
Decide without drawing anything. Work out what one centimeter is worth.
Problem 14 of 15
A map has a scale of 1 cm to 10 km. Select every one of these that is the same real distance as 3 cm on this map.
Problem 15 of 15
Select every scale that turns 4 cm on the map into 20 km on the ground.
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?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Two maps show the same lake. On the first, 1 cm stands for 4 km. On the second, 1 cm stands for 10 km. The lake is 15 cm long on the first map. How long is it on the second map, in cm?
cm
Stretch 2 of 2
A plan is drawn at 1 cm for every 3 m, on paper 20 cm wide. A hall has to be drawn all the way across the paper. What is the longest real hall, in meters, that still fits?
meters
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
The misconception this lesson targets is that a scale is one move rather than two. A child learns "multiply by the scale" from the first map question and then applies it in both directions, so on Dev's 1 cm to 5 km map a real 45 km becomes 225 cm of paper and nobody blinks. Two smaller slips ride alongside it: adding the scale instead of multiplying by it, carried over from scale copies, and using the scale on one leg of a journey while forgetting the rest. The cure is one habit — name the direction out loud, map to ground or ground to map, before choosing multiply or divide. The size check in the tip catches most inverted answers, though not on a map where one centimeter stands for less than a kilometer.
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.