Gradient is a measure of how steep a slope is.

The greater the gradient the steeper a slope is.

The smaller the gradient the shallower a slope is.

To calculate the gradient of a slope the following formula and diagram can be used:

$gradient=\frac{{vertical\,height}}{{horizontal\,distance}}$

## Example 1

$gradient\,of\,line\,AB=\frac{{vertical\,height}}{{horizontal\,distance}}$

$vertical height=4cm$

$horizontal distance=7cm$

$gradient = \frac{4}{7}$

Gradient is usually expressed as a simplified fraction. It can also be expressed as a decimal fraction or as a percentage.

## Example 2

$gradient\,of\,line\,CD = \frac{{vertical\,height}}{{horizontal\,distance}}$

$vertical\,height = 6\,cm$

$horizontal\,distance = 8\,cm$

$gradient = \frac{6}{8}$

The fraction $$\frac{6}{8}$$ can be simplified to $$\frac{3}{4}$$

$$\frac{3}{4}$$ is also equal to $$0.75$$ and $$75\%$$

Gradient $$= \frac{3}{4}$$ or $$0.75$$ or $$75\%$$