Map scale

Every map has a certain scale, which lets us convert distances on the map into real distances.

Scale as a ratio

A simpler definition says that the scale gives the ratio of a distance on the map to the real distance. This definition is not precise; a more precise one is at the end of the article. Usually the scale is given either in numerical form or in graphical form. The numerical form looks like this: 1 : 100, which is the ratio map : reality. Such a ratio means that one centimetre on the map is one hundred centimetres in real life. In other words, one centimetre on the map corresponds to one metre in reality. A map with the scale 1 : 100 is therefore a hundred times smaller than reality.

How to calculate the real distance

A typical example: you have a map with the scale 1 : 100,000 and you measure a certain distance on it, for example four centimetres. What is the real distance?

You get the distance in centimetres by multiplying your four centimetres by the number after the colon, that is, by 100,000. That gives you the real distance. For our example the result is 400,000 cm.

Usually we want to know the distance in other units – either metres or kilometres. You get the length in metres by dividing the current result by a hundred (because there are a hundred centimetres in a metre). So the distance is 400,000 / 100 = 4,000 metres. You get the result in kilometres by dividing this value in metres by a thousand (because there are a thousand metres in a kilometre). The result is 4,000 / 1,000 = 4 kilometres.

The answer is that four centimetres on the map represent four kilometres in real life.

Calculator

If you need to convert a distance on the map into a real distance, you can use the following calculator. In the first field enter the second number of the scale (that is, if the map has the scale 1 : 1000, enter a thousand). In the second field enter the number of centimetres on the map. By default the calculator contains the data from the previous example, that is, the scale 1 : 100,000 and 4 centimetres.

How to calculate the distance on the map

You may need the opposite procedure too. You know that some real distance is 15 kilometres and you want to know what distance that is on a map with the scale 1 : 30,000. In the first step we convert kilometres to centimetres. When we multiply the kilometres by a thousand, we get the distance in metres: 15,000. When we multiply this number by a hundred, we get the distance in centimetres: 1,500,000 . In the last step we just divide this number by the scale, that is, we calculate 1,500,000 / 30,000 = 50. The result is that 15 km in real life corresponds to 50 centimetres on the map.

A more precise definition of scale

A more precise definition says that the scale of a map gives the ratio of the reduction of a length measured on the map to the length in reality. What is the difference between this definition and the one given at the beginning of the article?

The problem with scale is linked to the curvature of the map itself. Our Earth is not flat but round. And it is not possible to unfold the surface of a sphere into a rectangle so that the resulting rectangle is not distorted. If you took a globe and peeled off its surface, you would not manage to make a rectangle out of the peeled paper. A standard map, though, is rectangular – how is that possible? Simply, some distances are distorted so that a rectangular map can be made from the surface of a sphere.

In other words – if we made a gigantic rectangular map of the whole Earth at a ratio of 1:1, there would still be distances on that map that did not match reality. The scale of a map therefore cannot give the ratio of a distance on the map to the real distance, because that would not be true even on a map made at a ratio of 1:1. This problem can be seen nicely with Antarctica, which, if it is on the map, usually looks bigger than it is in reality.