Gradient of a slope

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:

\[gradient=\frac{{vertical\,height}}{{horizontal\,distance}}\]

Diagram of a triangle showing vertical and horizontal dimensions.

Example 1

Diagram of a triangle showing values of vertical and horizontal sides.

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

\[vertical height=4cm\]

\[horizontal distance=7cm\]

\[gradient = \frac{4}{7}\]

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

Example 2

Diagram of a triangle showing values of its vertical and horizontal sides.

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

\[vertical\,height = 6\,cm\]

\[horizontal\,distance = 8\,cm\]

\[gradient = \frac{6}{8}\]

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 \(75\%\)