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\%