Map Scale and Measuring Distances

Map scale is the ratio between a distance on a map and the corresponding distance on the ground, shown as a ratio (1:50,000), a statement (1 cm represents 5 km) or a bar scale, and it is used to measure real distances from a map. In brief: a ratio of 1:50,000 means that 1 unit on the map equals 50,000 of the same units on the ground, so 1 cm is 500 m. A large-scale map (such as 1:10,000) shows a small area in great detail, while a small-scale map (such as 1:10,000,000) shows a large area with little detail. To measure a distance, measure it on the map and multiply by the scale factor, using a string for curved routes.

Without a scale, a map cannot be used to find how far one place is from another. This guide explains the three ways of showing scale, large and small scales, how to measure straight and curved distances, compares the scales in a table, works through numerical examples, outlines the history of scale in maps and corrects common mistakes.

What is map scale?

There are three common ways to show scale:

• Ratio (representative fraction): 1:50,000. It has no units, so it works with any unit of length, provided both sides use the same unit.
• Written (verbal) scale: “1 centimeter represents 5 kilometers”. It is easy to read, but it becomes wrong if the map is enlarged or reduced.
• Graphic (bar) scale: a line marked with real distances. It stays correct when the map is photocopied, enlarged or shrunk, because the bar changes in the same proportion.

To convert between them, remember that 1 km = 100,000 cm. So 1 cm to 5 km means 1:500,000, since 5 km = 500,000 cm. On a flat map of a small area the scale is the same everywhere; on a map of a large area, projection distortion makes the scale vary from place to place.

What are large-scale and small-scale maps?

The names refer to the size of the fraction. 1/10,000 is larger than 1/1,000,000, so 1:10,000 is the larger scale. A large-scale map (for example 1:1,000 to 1:50,000) shows a small area with much detail, such as streets, buildings and footpaths, and is used for town plans and walking maps. A small-scale map (for example 1:1,000,000 and smaller) shows a large area, such as a country or the world, with few details, and is used in atlases. If the scale is halved from 1:50,000 to 1:100,000, a given area on the ground takes only one quarter of the area on the map, because areas scale with the square of the length ratio.

How do you measure distance on a map?

For a straight-line distance, measure between the two points with a ruler, in centimeters or millimeters, and multiply by the scale: ground distance = map distance × scale factor. For a curved route (a road or river), lay a piece of string along the route, mark the ends, straighten it and measure the length against the ruler or bar scale. Alternatively, divide the route into short straight sections and add them. Another method is to mark the distance on the edge of a piece of paper and compare it with the bar scale. Remember that the map shows the horizontal distance, not the distance along slopes, so the true path over hills is slightly longer than the map suggests.

Map scales compared

Worked example: converting and measuring

1. Ground distance from ratio. On a 1:50,000 map two villages are 4.5 cm apart. The ground distance is 4.5 × 50,000 = 225,000 cm = 2,250 m = 2.25 km.
2. Same distance on a smaller scale. On a 1:250,000 map, a distance of 4.5 cm is 4.5 × 250,000 = 1,125,000 cm = 11.25 km. A smaller scale gives a larger ground distance for the same map length.
3. Map distance from ground distance. A route of 37.5 km on a 1:250,000 map is 37.5 km = 3,750,000 cm, divided by 250,000 gives 15 cm on the map.
4. Converting a written scale. “1 cm represents 5 km”: 5 km = 5 × 100,000 = 500,000 cm, so the ratio is 1:500,000.
5. Curved road. A string laid along a road on a 1:50,000 map measures 8.2 cm. The road is 8.2 × 0.5 = 4.1 km long.
6. Area. A field measures 2 cm by 3 cm on a 1:10,000 map. On the ground it is 200 m by 300 m = 60,000 m² = 6 hectares.

How did map scale develop?

Early maps were often not drawn to a consistent scale, and Roman surveyors measured distances along roads. The idea of mapping to an exact scale developed with triangulation surveys in Europe from the 17th and 18th centuries. National mapping agencies, such as the Ordnance Survey in Britain (founded in 1791), produced systematic series of maps at standard scales. In the metric countries, scales such as 1:25,000 and 1:50,000 became common for topographic maps, and today digital maps can be zoomed through scales continuously, often with a bar scale that changes automatically.

Which mistakes are common?

Mistake 1: Mixing up large-scale and small-scale

A large-scale map has a small denominator (1:10,000), not a large area.

Mistake 2: Forgetting to convert units

Convert centimeters to meters or kilometers: 100,000 cm make 1 km.

Mistake 3: Using a written scale on a resized map

When a map is enlarged or reduced, the statement of scale becomes wrong. Only the bar scale changes with it.

Mistake 4: Measuring a curved route with a straight ruler

Use a piece of string or divide the route into short straight segments.