Gradient measures steepness. Divide the vertical change by the horizontal distance, with both in the same unit. It appears when a question gives two heights and a map distance and asks how steep a slope is.
This lesson follows reading contours and uses the conversion from map distances, both in scale, distance and relief.
How is gradient calculated, step by step?
- Find the vertical change by subtracting the lower height from the higher one, in metres.
- Convert the map distance to a real horizontal distance with the scale, and change it to metres.
- Divide the vertical change by the horizontal distance.
- Express the answer as the question asks: fraction, 1 in n, or a percentage.
The two lengths must both be in metres. A mismatch is the main source of lost marks in this skill.
Worked example
The numbers here are invented for practice. Point A is at 120 m and point B is at 270 m.
They are 6 cm apart on a 1:25 000 map. Find the average gradient from A to B.
Vertical change: 270 − 120 = 150 m.
Horizontal distance: 6 × 25 000 = 150 000 cm = 1 500 m.
Gradient: 150 ÷ 1 500 = 1/10. That is 1 in 10, or 10%.
Check: over 1 500 m of ground the land rises 150 m. Over each 10 m travelled it would rise 1 m, and 1 500 ÷ 10 = 150. The answer is consistent.
The mistake to watch for
Mistaken answer: the gradient is 150 ÷ 1.5 = 100.
The student put metres on top and kilometres underneath.
The vertical change was in metres and the distance in kilometres. Converting the distance to 1 500 m fixes it. A gradient of 100 would also mean a vertical cliff, which a map with a 6 cm span does not show.
To correct it, write the unit beside each number before dividing. If one says m and the other says km, convert first.
Check yourself
1. The ground rises 80 m over a horizontal distance of 2 km. Find the gradient as a fraction.
Show answer
2 km = 2 000 m. 80 ÷ 2 000 = 1/25, which is 1 in 25 (4%).
2. A road has a gradient of 1 in 8. It climbs 45 m. What horizontal distance does it cover?
Show answer
Horizontal = 45 × 8 = 360 m.
3. Point C is at 340 m and point D is at 190 m. They are 4.5 cm apart on a 1:50 000 map. Find the average gradient.
Show answer
Vertical = 340 − 190 = 150 m. Horizontal = 4.5 × 50 000 = 225 000 cm = 2 250 m. Gradient = 150 ÷ 2 250 = 1/15, so 1 in 15. Check: 2 250 ÷ 15 = 150.
Where this leads next
Use gradients to shape a profile in drawing a cross-section from supplied elevations. The map scale, contour and gradient practice tool and the statistics and distribution explorer are useful for repeated practice.
If gradient answers keep going wrong at the units, a teacher in online one-to-one Geography tuition can check every unit with you.