Gradient

Gradient is a mathematical formula usually used to measure how steep or gentle a slope is. It measures how much the elevation of a slope changes as one moves horizontally over the surface. In other words, it measures the rate at which the slope is rising or falling. Gradient is typically expressed as a ratio. The average gradient of a slope can be calculated from contour lines on a topographical map.

To find the gradient, the horizontal distance (run) as well as the vertical distance (rise) between two points need to be determined. The gradient is obtained by dividing the rise over the run as seen in Image 1 below.

Have a look at Image 2, below. Suppose you want to go for a hike from point Y to point X. You want to find out how steep this hike is going to be.

If you are hiking from point Y to point X are you going uphill or downhill? How can you tell?

To find out the gradient we need to divide the rise (vertical difference) by the run (horizontal equivalent).

To find the Rise (vertical interval) we need to subtract the highest elevation with the lowest. 380 – 300 m. This will give us the overall change in elevation between the two points, i.e. 80 metres.

To determine how far apart points X and Y are we need to use the map scale. In this example the distance is 2 kilometres or 2000 metres.

So we need to divide 2000 by 80 and that will give us an answer of 1/25 or 1:25. What this means is that if I were to go for a hike from Y to X for every every 25 metres I travel my elevation would increase by 1 metre. This value is the measure of the average gradient for the distance between the two points. In reality parts of the slope will be steeper and parts gentler than the average slope.

Now watch these two short video clips which will explain clearly how to determine and calculate gradient on a topographical map.

• Use the map (Image 3) below to calculate the gradient from Point A to Point B. It is important to show all your workings.

• Now using the same map, work out the average gradient from Point C to Point D. Show all your working.

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 15 cm, and the scale of the map is 1:100,000.

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 12 cm, and the scale of the map is 1: 50, 000.