Gradient
Gradient is a measure of the steepness of a slope. Where the contour lines are close together the
slope is steep, where they are wide apart it is gentle.
To calculate the gradient of a slope between two points use the formula:
𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑹𝒊𝒔𝒆 (𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 ℎ𝑒𝑖𝑔ℎ𝑡 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑝𝑜𝑖𝑛𝑡𝑠)
𝑹𝒖𝒏 (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑝𝑜𝑖𝑛𝑡𝑠)
The rise and run MUST be measured in the same units, usually metres
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
𝟐𝟓𝟎𝒎
𝟏
=
𝟏𝟎𝟎𝟎𝒎
𝟒
Watch the following clip for a visual explanation of gradient. This guys is VERY good at explaining how
to do it.
https://www.youtube.com/watch?v=3b3yGololaY&t=20s
Activities
1. Work out the gradient of the slope if Point A has a height of 210
metres, Point B has a height of 70 metres, the distance between the two points is 14cm, and the scale
of the map is 1:100,000.
E.g.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
𝟐𝟏𝟎 − 𝟕𝟎 = 𝟏𝟒𝟎
𝟏
=
𝟏𝟒 𝒙 𝟏𝟎𝟎, 𝟎𝟎𝟎 = 𝟏, 𝟒, 𝟎𝟎𝟎, 𝟎𝟎𝟎 /𝟏𝟎𝟎
𝟏𝟎𝟎
NOTE: Don’t forget to convert CM to METRES. This is why I have divided 1,4,000,000 by 100.
The gradient for this slope tells us that for every 100 metre you walk you will slope will fall by 1 metre,
which means it is not very steep.
2. Work out the gradient of the slope if Point A has a height of 180
metres, Point B has a height of 150 metres, the distance between the two points is 15cm, and the
scale of the map is 1:100,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
3. Work out the gradient of the slope if Point A has a height of 150
metres, Point B has a height of 100 metres, the distance between the two points is 10cm, and the
scale of the map is 1:100,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
4. Work out the gradient of the slope if Point A has a height of 80
metres, Point B has a height of 70 metres, the distance between the two points is 4cm, and the scale of
the map is 1:100,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
5. Work out the gradient of the slope if Point A has a height of 1000
metres, Point B has a height of 750 metres, the distance between the two points is 20cm, and the
scale of the map is 1: 50,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
6. Work out the gradient of the slope if Point A has a height of 640
metres, Point B has a height of 590 metres, the distance between the two points is 15cm, and the
scale of the map is 1:50,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
7. Work out the gradient of the slope if Point A has a height of 50
metres, Point B has a height of 25 metres, the distance between the two points is 4cm, and the scale of
the map is 1:50,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
8. Work out the gradient of the slope if Point A has a height of 90
metres, Point B has a height of 50 metres, the distance between the two points is 8cm, and the scale of
the map is 1:100,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
9. Work out the gradient of the slope if Point A has a height of 1000 metres, Point B has a height of
500 metres, the distance between the two points is 12cm, and the scale of the map is 1:50,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=
10. Work out the gradient of the slope if Point A has a height of 90
metres, Point B has a height of 80 metres, the distance between the two points is 8cm, and the scale of
the map is 1:50,000.
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕 𝒐𝒇 𝑨𝑩 =
=