Kōkiri Learn

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.

  • Ratio scale: 1:50,000 means the real world is 50,000 times bigger than the map. - Scale bar: a little ruler printed on the map; you can measure against it without any maths. - Large-scale map: shows a small area in lots of detail, like 1:500 for a school. - Small-scale map: shows a big area with less detail, like a map of the whole Pacific.
  • 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.

  • Lines close together: the land is steep. - Lines far apart: the land is gentle or flat. - Circles inside circles: a hill or a peak. - V shapes pointing uphill: a valley or stream.
  • 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.

    Used in: Find Your Way: Maps, Angles and Coordinates