Calculating a gradient
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 \(75\%\)