Gradient compares vertical change with horizontal distance; contour spacing helps locate steeper ground.
A contour joins points of equal elevation. Check the reference height, or datum, such as mean sea level. Then read the height units and contour interval. Close contours indicate a faster height change over distance than widely spaced contours on the same map. Closed contours need labelled heights or depression markings to distinguish a hill from a hollow.
Measure horizontal map distance using the scale. Gradient = vertical change divided by horizontal distance. If A is 40 m high, B is 60 m high and their horizontal separation is 100 m, the gradient is 20/100 = 0.2, or 20%. As a ratio this is 1 in 5.
Do not confuse a 20% gradient with an angle of 20 degrees. Do not use sloping ground distance when the calculation requires horizontal distance. The average gradient between endpoints can also hide short, steeper sections.
In fieldwork, use contours to plan routes, compare slope positions and interpret runoff pathways. Check the actual path and barriers on the ground; a map at coarse resolution may omit small steps or drainage features.
Step by step
Find the rise
Subtract the two endpoint elevations using the same vertical datum.
Find horizontal distance
Convert the mapped separation using the scale bar.
State the form
Give a decimal, percentage or 1-in-N ratio with clear working.
Worked example: Keep both distances in metres
A path rises 15 m over 0.3 km horizontally. Convert 0.3 km to 300 m, then calculate 15/300 = 0.05 = 5%, or 1 in 20. Mixing metres with kilometres would give the wrong result.
Watch out for this
A contour line traces a river of that height.
A contour joins points of equal elevation. A river usually flows downhill across successive contours.
Check your understanding
What is the gradient of a 10 m rise over 200 m horizontally?
- 5%, or 1 in 20.
- 20%, or 1 in 5.
- 10 degrees.