Map scale

One centimetre on the map, half a kilometre under your feet

At the bottom of every map is a quiet label: 1 : 50 000. That is not a maths decoration. It is a ratio that says: one part on the map = 50 000 of the same parts in reality.

So 1 cm on the map is 50 000 cm in reality. And because 50 000 cm = 500 m, it holds: 1 cm on the map = half a kilometre in the field.

The whole magic of maps is in this conversion. You measure a route on paper with a ruler, multiply by the scale and you know how much you will walk.

Remember converting centimetres to kilometres as crossing out zeros: a kilometre has 100 000 cm, so cross out five zeros from the scale number and you have kilometres. Scale 1 : 50 000 → 0.5 km. Scale 1 : 100 000 → 1 km per centimetre.

Today you will learn to read a scale both ways: from the map to reality and from reality to the map.

Tereza and Adam plan a Saturday trip above the dam. The walking map has a scale 1 : 50 000. Adam measures the route with string along the path: 14 cm. “So we are there in a moment,” he waves. Tereza counts: 1 cm is half a kilometre, so 14 × 0.5 = 7 km. “Seven kilometres there and seven back. That is a whole afternoon, not a moment.” Adam looks at the snack in his backpack and packs a second one. The string does not lie — you just have to know how to read it.

Scale both ways

A scale 1 : M means: reality is M times bigger than the map. Both numbers are in the same unit — so 1 cm on the map = M cm in reality.

From the map to reality (the most common direction):

Step 1: measure the distance on the map in cm. Step 2: multiply by the scale number → reality in cm. Step 3: convert to km (cross out five zeros, so divide by 100 000).

Example: 6 cm on a map 1 : 25 000. Reality: 6 × 25 000 = 150 000 cm = 1.5 km.

From reality to the map (you draw a plan):

Step 1: convert reality to cm. Step 2: divide by the scale number.

Example: 3 km on a map 1 : 100 000. Three kilometres = 300 000 cm. Divided by 100 000 → 3 cm.

Which scale is more detailed? The one with the smaller number. A map 1 : 10 000 shows every path (1 cm = 100 m), a map 1 : 500 000 a whole region (1 cm = 5 km). Walking maps often have 1 : 50 000, town plans 1 : 10 000.

Scale also works for models and flat plans — the ratio of shrinking is still the same tool.

A route of 9 cm on a map 1 : 50 000. How many kilometres?

Step 1: measured 9 cm.

Step 2: reality in cm: 9 × 50 000 = 450 000 cm.

Step 3: to kilometres — I cross out five zeros: 450 000 cm = 4.5 km.

Result: 4.5 km. A faster path with the conversion on the edge: 1 cm = 0.5 km, so 9 × 0.5 = 4.5 km. Both paths must give the same — if they do not, a zero got lost when crossing out.

学校 is 2.4 km from home. How many cm will that be on a plan 1 : 20 000?

The opposite direction — from reality to the map.

Step 1: convert to centimetres: 2.4 km = 240 000 cm.

Step 2: I divide by the scale: 240 000 : 20 000 = 12.

Result: 12 cm on the plan. Check the other way: 12 × 20 000 = 240 000 cm = 2.4 km. That checks out. A hint: on the map a smaller number always comes out than in reality — the map shrinks. If more comes out, the direction of the calculation is backwards.

What scale does a map have if 4 cm match 6 km?

Step 1: both distances into the same unit: 6 km = 600 000 cm.

Step 2: the scale is the ratio map : reality = 4 : 600 000.

Step 3: I simplify by four so there is a one on the left: 1 : 150 000.

Result: scale 1 : 150 000. Check: 1 cm = 150 000 cm = 1.5 km, so 4 cm = 6 km. That checks out. A scale is always written with a one on the left — that is why you simplify by the first number.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.

Convert centimetres on the map to real kilometres. Write only the number in km, decimal with a point.

Practise the questions

On paper: planning a trip

For each question write the conversion “1 cm = … km” before you start calculating.

1. Map 1 : 25 000: the route measures 11 cm. How many kilometres will you walk? And how many cm on a map 1 : 100 000 does a route of 11 km measure?

2. A bike trip of 18 km you want to mark on a map 1 : 75 000. How many cm will the route measure?

3. On a flat plan 1 : 100 a room is 4.2 cm long. How long is it for real? (The same rule, just a smaller number.)

4. Decide and explain: which map is more detailed, 1 : 10 000 or 1 : 200 000? On which would you draw the school pitch?

Now you 💪

1. I read a scale as a ratio: 1 cm on the map = the scale number in cm in reality.
2. I convert cm to km by crossing out five zeros and back.
3. I can go both ways: from the map to the field and from the field to the map.

What to take from this lesson

• Scale 1 : M = reality is M times bigger, both in cm.
• Out from the map: times the scale. Onto the map: divided by the scale.
• A kilometre = 100 000 cm. Cross out five zeros.
• A smaller scale number = a more detailed map.
• Write the conversion 1 cm = … km on the edge before you measure.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款