Reading slope from contours

Climb 100 metres while walking 500 metres across the map and the slope is 20 percent, an angle of about 11.3 degrees.

Rise over run

Slope is how much the ground rises for each step you take across it. Surveyors call the height difference the rise and the horizontal distance the run. Divide one by the other and you have the gradient. Contour maps give you both numbers. The rise comes from counting contour lines and multiplying by the interval. The run comes from measuring the distance on the map and converting it with the scale. Nothing else is needed, which is why a topographic map can tell you how steep a trail is before you set foot on it.

Percent, ratio and angle

The same slope can be written three ways. As a percent, multiply the gradient by 100: a rise of 100 metres over 500 metres is 20 percent. As a ratio, write the rise as 1: a 20 percent slope is 1 in 5. A Colorado State University field lab gives an example in American units: a gradient of 528 feet per mile is the same as 1 in 10, because a mile is 5,280 feet. As an angle, take the arctangent of the gradient. Twenty percent is about 11.3 degrees, and 100 percent, where the rise equals the run, is exactly 45 degrees.

Notice that percent and angle do not grow together evenly. Doubling a 10 percent slope to 20 percent roughly doubles the angle, but going from 50 to 100 percent only adds about 18 degrees. That is why road signs give percent: the numbers spread out more for the gentle slopes that roads actually have.

Spacing tells you steepness at a glance

Because every contour step is the same height, the distance between lines tells you the slope directly. Lines close together mean the rise happens in a short run, a steep slope. Lines far apart mean a gentle one. On the east hill in the scene, the lines crowd together on the east face and spread out on the west. Measure both sides with the line tool. You should find the east face several times steeper, even though both sides climb to the same summit.

A quick rule of thumb works on any Korean 1:25,000 sheet. The main contours are 10 metres apart in height and 1 millimetre on the map is 25 metres on the ground. So if two neighbouring lines are 1 millimetre apart, the slope is 10 over 25, or 40 percent. At 2 millimetres it is 20 percent, at 4 millimetres 10 percent. The readout in the scene does the same arithmetic for any two points you choose.