Scale factors, scale diagrams and maps
Maps and scale drawings shrink real-world distances onto a page. The "scale" tells you how much shrinkage has happened. Understanding it lets you convert between distances on paper and distances in real life.
Scale notation
Scales are written either as a ratio (1 : 25 000) or as a statement ("1 cm represents 5 km").
A ratio of 1 : n means 1 unit on the map = n units in real life, in the same units. So 1 : 25 000 means 1 cm on the map = 25 000 cm in real life = 250 m.
Map → real-life distance
Multiply the map distance by the scale factor.
Worked example: a map has scale 1 : 50 000. Two villages are 8 cm apart on the map. How far apart are they?
- 8 × 50 000 = 400 000 cm.
- Convert to a sensible unit: 400 000 cm ÷ 100 = 4000 m = 4 km.
Real-life → map distance
Divide the real distance by the scale factor (after converting to a common unit).
Worked example: scale 1 : 25 000. A road is 3 km long. How long on the map?
- 3 km = 300 000 cm.
- 300 000 ÷ 25 000 = 12 cm.
Scale drawings (architectural plans)
A scale of 1 cm : 2 m means each cm on paper represents 2 m of real space. To convert: multiply (paper → real) or divide (real → paper).
Worked example: a kitchen plan uses scale 1 cm : 1.5 m. The kitchen is 6 m wide. Width on plan = 6 ÷ 1.5 = 4 cm.
Bearings on scale diagrams
A bearing is a 3-figure angle measured clockwise from north. To use bearings with a scale diagram, draw the line from the start point at the correct bearing, then measure the length using the scale.
Worked example: from A, walk 5 km on a bearing of 070°. On a 1 : 100 000 map (1 cm = 1 km), draw a line 5 cm long at 070° from A.
⚠Common mistakes
- Forgetting to convert units before applying the scale (mixing cm and km).
- Multiplying by 1 / scale when going map → real, instead of × scale.
- Reading scale "backwards" — 1 : 50 000 means real life is 50 000× bigger than the map.
- Bearing direction — measure from north, clockwise, three figures (e.g. 070°, not 70°).
- Squaring scale factor by accident when only converting linear distances.
➜Try this— Quick check
A map has scale 1 : 200 000. Two towns are 6.5 cm apart. How far apart are they in km? Answer: 6.5 × 200 000 = 1 300 000 cm = 13 000 m = 13 km.
AI-generated · claude-opus-4-7 · v3-deep-ratio