Every scale answer passes through three units: centimetres on the map, metres or centimetres on the ground, and kilometres in the answer. Write the unit beside every number and each change becomes visible.
This lesson is part of topographic scale, distance and area. The units and significant-figure checker gives extra practice.
What is the unit chain?
Write the chain as you work: map cm, then ground cm, then m, then km.
| Step | Operation | Example at 1:50 000 for 4 cm |
|---|---|---|
| Map length | Read and write with unit | 4 cm |
| Ground length in cm | Multiply by the scale number | 4 × 50 000 = 200 000 cm |
| Ground length in m | Divide by 100 | 2 000 m |
| Ground length in km | Divide by 1 000 | 2 km |
For areas, square the length factors: multiply by 1 000 000 to go from km² to m², and divide by the same to go back.
Worked example: a length and an area on an original map
An original map has a scale of 1:25 000. A causeway measures 5.2 cm. A rectangular plantation measures 3 cm by 2 cm.
Length: 5.2 cm × 25 000 = 130 000 cm. Divide by 100: 1 300 m. Divide by 1 000: 1.3 km.
Area: the sides on the ground are 3 × 25 000 = 75 000 cm = 750 m, and 2 × 25 000 = 50 000 cm = 500 m. The area is 750 m × 500 m = 375 000 m². Divide by 1 000 000: 0.375 km².
Check for sense: a plantation 750 m by 500 m is a reasonable size, slightly under half a square kilometre.
The mistake: converting the area like a length
A common slip is finding 3 cm × 2 cm = 6 cm² on the map and multiplying by 25 000, giving 150 000 cm², which is 15 m². That ignores that area scales by the square of the scale.
The right factor for area is 25 000² = 625 000 000. Then 6 cm² × 625 000 000 = 3 750 000 000 cm², which is 375 000 m². The safe method is to convert each side to ground units first, then multiply.
| Step | Wrong | Right |
|---|---|---|
| Scale factor for area | 25 000 | 25 000² |
| Result | 15 m² | 375 000 m² |
Check yourself
At 1:50 000, a lake measures 2.4 cm by 1.5 cm on the map. Find its ground area in km².
Answer
1 cm is 500 m at this scale. So the lake is 2.4 × 500 = 1 200 m by 1.5 × 500 = 750 m.
Area: 1 200 m × 750 m = 900 000 m², which is 0.9 km².
What to study next
Test all four skills in the cluster practice set. Keep a note of unit slips in the mistake log and paper-error review.
For a teacher to read your working and find the unit slip, see online one-to-one Geography tuition.