The rule
reality = plan × scale denominator
Why it works
A scale of 1:50000 means one unit on the plan is fifty thousand of the same unit in reality. The units cancel, which is why the ratio works whether you measure in centimetres, inches or anything else.
How to do it by hand
- Multiply the plan measurement by the scale denominator
- That gives the real distance in the same units
- Divide by 100 for metres, by 100,000 for kilometres
- To go the other way, divide instead of multiplying
What is worth knowing
The squared factor for areas is what catches people out on plans and models. At 1:50000, one centimetre is half a kilometre — but one square centimetre is a quarter of a square kilometre, because both dimensions shrink. That is 2,500,000,000 times smaller in area, not 50,000. The same applies to volumes with a cubed factor, which is why a scale model weighs so much less than the ratio suggests: a 1:10 model is a thousand times lighter, not ten.