Background reading · Mathematics and Statistics
Scale and contours: shrinking the land onto paper
How map scales let you measure real distances, and how contour lines turn a flat sheet of paper into hills and valleys.
A map is a picture of the land shrunk down so it fits in your hand. The trick is to shrink everything by exactly the same amount. That amount is the scale.
Reading a scale
Scales are written as a ratio, like 1:50,000. It means 1 unit on the map stands for 50,000 of the same units on the ground. So 1 cm on a Topo50 map is 50,000 cm in real life. That is 500 m, or half a kilometre.
To find a real distance, measure on the map and multiply by the scale. A track that is 6 cm long on a Topo50 map is 6 × 500 m = 3,000 m, or 3 km. Remember that paths wiggle, so a piece of string laid along the track gives a better measurement than a ruler.
Hills on a flat page
Contour lines are the thin brown lines on a topographic map. Each line joins places that are the same height above sea level. On Topo50 maps there is a contour line every 20 metres of height.
Where the water goes
Contours also tell you where rain will flow. Water always runs downhill by the shortest path, which means it crosses contour lines at right angles. Farmers and land designers use this to plan where to put dams, tracks and trees. One Wairarapa family spent years trying to dry out a paddock that was always muddy, until a surveyor looked at the contours and saw that water from about ten hectares of hillside above all funnelled through that one spot. Once they understood the shape of the land, they turned the wettest corner into a wetland instead of fighting it.
Being able to read contours helps you plan a safe tramp, understand floods and design with the land instead of against it.
Sources and further reading
Written for Kōkiri Learn students in our own words. Check facts against the sources.