Map Scale (RF)
Representative fraction linking map distance to real-world distance.
Formula
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Example
1 cm = 500 m: RF = 1/50000
How it works
The representative fraction (RF) tells you how a distance on a map compares with the same distance on the ground, using the same units for both. It works because a map is a scaled-down version of reality: if 1 unit on the map corresponds to many of those same units on the ground, the ratio gives the scale directly. An RF of 1/10000 means 1 cm on the map represents 10,000 cm on the ground.
When to use it
Use this formula when converting between map measurements and real-world distances, especially in surveying, cartography, and route planning. It is also useful when you need to compare or choose maps with different scales.
Worked example, step by step
A map shows a road length of 3 cm, and the actual ground distance is 1.5 km. Convert the ground distance to the same unit as the map: 1.5 km = 150,000 cm Use RF = d_map / d_ground RF = 3 / 150,000 RF = 1 / 50,000 Final answer: the map scale is 1:50,000
Common mistakes to avoid
- mixing units, such as cm on the map with km on the ground, without converting first
- writing the ratio backwards as ground distance over map distance
- forgetting that RF has no units because both distances must be in the same unit
Did You Know?
On a 1:50,000 map, one centimetre stands for half a kilometre on the ground.
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