How to read a map scale and work out real distances

A map scale tells you how distances on the map relate to distances on the ground. A ratio such as 1:25,000 means one unit on the map stands for 25,000 of the same unit in reality, so 1 cm on the map is 250 m and 4 cm is exactly 1 km. Once you know that, any measurement on the map converts with one multiplication. The map scale calculator I built converts both ways and works out unknown scales, and this guide explains the method.

Three ways to show scale

• Ratio scale (also called a representative fraction), such as 1:50,000 or 1/50,000. It has no units, so it works in centimetres, inches or anything else.
• Verbal scale, such as "one inch to one mile" or "1 cm to 250 m". Easy to picture, but tied to particular units.
• Bar scale, a ruler printed on the map marked in kilometres or miles. Measure with it directly.

Most good maps print more than one. The bar scale has a special advantage covered under common mistakes below.

Reading a ratio scale

At 1:25,000, 1 cm on the map is 25,000 cm on the ground. There are 100 cm in a metre and 1,000 m in a kilometre, so 25,000 cm is 250 m, and 4 cm is 1 km. That is why the 1 km grid squares on Ordnance Survey Explorer maps, which are 1:25,000, are 4 cm wide. On a 1:50,000 map such as the OS Landranger series, 1 cm is 500 m and 2 cm is 1 km. In the United States, the Geological Survey's standard topographic quadrangles are 1:24,000, where 1 inch is 24,000 inches, or 2,000 feet. The old British "inch to the mile" is 1:63,360, because a mile has exactly 63,360 inches. Ratios explained: how to simplify, scale, and divide an amount in a given ratio covers ratios in general.

Converting distances

To go from map to ground, multiply the map distance by the scale number, then change units. A route that measures 7.5 cm on a 1:50,000 map is 7.5 × 50,000 = 375,000 cm, which is 3.75 km. To go from ground to map, divide: 3.75 km on a 1:25,000 map is 375,000 ÷ 25,000 = 15 cm. To find an unknown scale, divide the real distance by the map distance in the same units: if two points 2 km apart are 8 cm apart on the map, the scale is 200,000 ÷ 8, or 1:25,000.

Areas scale by the square of the ratio. At 1:25,000, a 1 cm square on the map covers 250 m × 250 m = 62,500 m², or 6.25 hectares. Unit changes between metric and imperial are where most slips happen; the unit converter and Metric vs imperial: how we got two systems help there.

Large scale and small scale

The terms are the opposite of what many people expect. A large-scale map shows a small area in a lot of detail, such as a town plan at 1:10,000. A small-scale map shows a large area with little detail, such as a world map at 1:100,000,000. The names come from the size of the fraction: 1/10,000 is a much larger number than 1/100,000,000. For walking, 1:25,000 shows field boundaries and individual paths; 1:50,000 suits cycling or planning a longer trip; road atlases are smaller scale still.

Measuring a real route

Paths rarely run straight. Lay a piece of string or the edge of a sheet of paper along the route, marking each bend, then straighten it against a ruler or the bar scale. Divide long routes into legs and add them up. A straight-line distance from the distance between coordinates calculator is a useful lower bound, but the walk will be longer, and climbing adds time that distance alone does not show. The pace calculator turns the distance into a time estimate.

Common mistakes

• Resized maps. A ratio scale is only true at the original print size. Photocopy a map at 141% or zoom it on a screen and 1:25,000 no longer means 4 cm per km. A bar scale shrinks and grows with the map, so it stays correct.
• Mixing units. Measure in centimetres and you get centimetres on the ground; convert before you read off kilometres.
• Assuming every map uses the same scale. Check the margin each time, especially when switching between 1:25,000 and 1:50,000 sheets, where the same distance on paper means twice as far.