Maps and scale

A map of Australia. Here is the city of Melbourne, and here is Perth, and here is Sydney. Do you think it’s a good map? No, not really, eh? It’s drawn pretty roughly.

Let’s change it and make it more thorough. Like this. Yes, now it looks like Australia. This is what Australia looks like in reality. Although, this is not correct either.

Something’s missing. Let’s add the green forests, the sandy yellow deserts, and some rivers. And here there should be a mountain range. Now! Perfect.

The Australia of reality. Unless we should add some more cities, of course. Here is Cairns, and here, in the north, is Darwin. And then there’s an island south of Australia called Tasmania. Let’s add that too.

And we can go on like this. We can add, or remove, more and more details to or from the map, depending on what we want the map to tell us. A map is never the reality. It is an image of the reality, a representation. If we want a map with many small details, like streets and houses, we need to enlarge the map, we need to zoom in.

Let’s zoom in to the city of Perth. Now we can see details like streets, lakes, and parks. And if we zoom in even more, we can make a map of a garden. This garden has a pool in the centre, with a couple of trees around it. Nice.

There are other details on the map. This, for example. It looks like a small compass, and marks the directions north, south, east, and west on this map. North points upwards, as it does on almost every map. And then there are some numbers here.

One, colon, 45 million. This means one centimetre on the map corresponds to 45 million centimetres in reality. That’s the scale of this map. We say that the scale is one to 45 million. Let’s have a deeper look at how this works.

The distance between Perth and Melbourne is… 6 centimetres on this map. And the scale is one to 45 million. So, one centimetre on the map is 45 million centimetres in reality. This means 6 centimetres corresponds to: 6 times 45 000 000 centimetres. This is 270 000 000 centimetres.

That’s the same thing as 2 700 000 metres, or 2700 kilometres. This is the real distance between Perth and Melbourne. Let’s look at another example from the city of Perth. Here is that garden with a pool. If you want to swim in the river instead, and want to go there by bike, how far is it?

First we measure the distance with a ruler. 4 centimetres. Then we look at the scale. One to 75 thousand. To get the distance in reality we calculate 4 times 75 000.

This is 300 000, and now we have the answer in centimetres. And 300 000 cm, this is the same as 3000 metres, or 3 kilometres. Keep in mind that with the ruler, we measure and straightest way between two points. This way goes over houses and gardens, so no one can cycle that way. A bird can fly like that, though, and this distance is called “as the crow flies”.

For a cyclist, the way to the river will be longer than 3 kilometres. You can calculate the other way around too. Here is a map of a soccer pitch. The pitch is 90 metres long in reality. On the map it is … 2 centimetres.

What is the scale of this map? You can calculate this by dividing the distance on the map by the distance in reality. We need to measure in the same units, so that both distances are in metres or both in centimetres. 90 metres, that’s 9000 centimetres. Now, we can divide.

2 divided by 9000. This can be simplified to one divided by 4500. And there’s the scale. One to 4500. One centimetre on the map corresponds to 4500 centimetres in reality.