Maps and Directions
Map scale and distance
Use a map's scale to turn a length measured on the map into the real distance on the ground, and turn a real distance back into a length on the map.
No map is the size of the place it shows — a map of a town as big as the town would be no use to anybody, and there is nowhere to unroll it. Every map is the real place shrunk down, and the scale is the map telling you by how much. Read the scale and a length measured on the paper turns back into a real distance on the ground.
How a scale is written
A scale says a length on the paper together with the ground distance it stands for: 2 cm stands for 10 km. Going from the map to the ground, you multiply. Going from the ground back to the map, you divide. Nothing else about the map changes what the scale says — it is the same everywhere on that sheet.
Worked example
A map's scale says 2 cm stands for 10 km. Two villages measure 6 cm apart on it. How far apart are they really?
First work out what a single step of the scale's length is worth: 10 shared between 2 gives 5.
This is the number that does all the work. Once you have it, every length on this map is one multiplication away from its real distance.
Try it together
A map's scale says 4 cm stands for 12 km. A river runs 9 cm across the map.
Answer each step with a bare number.
1.The scale gives 12 km for every 4 cm. Share those 12 between the 4 — how many kilometres does each part stand for?
One more thing the scale quietly tells you: how much detail to expect. If a length of paper stands for only a little ground, there is room on the map for streets and wells. If the same length of paper has to cover a great deal of ground, only the big things fit, and the streets are gone. That is why a map of one district and a map of a whole country look so different even when they are printed on the same sheet.
Have a go
Have a go on your own. On a map, 3 cm stands for 6 km. Two towns are 7 cm apart on the map. How far apart are they on the ground, in kilometres?
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.