Before viewing this page, it would be helpful to learn Linear Graphs.

Gradient or Slope

Gradient =

Rise

Run

where
Rise is the vertical height
Run is the horizontal height.

Civil engineers use this formula to work out the gradient of roads. Carpenters use this formula to calculate the slope of a step.

Example One - Gradient

The world's most dangerous road is the Yungas Road in Bolivia in South America. More than 200 people are killed each year. Not only is it steep in parts but it is also in an area of high blinding rainfall. Calculate the gradient (steepness) of a part of the road with a rise of 215 metres and a run of 500 metres.

Answer:

Gradient =

Rise

=

215

= 0.43

Run

500

Gradient between Two Given Points

Gradient = m =

y_{2} – y_{1}

x_{2} – x_{1}

where (x_{1}, y_{1}) and (x_{2}, y_{2}) are two points on a linear or straight-line graph.

Notice that the Rise is the difference between the y-values and the Run is the difference between the x-values.

Example Two - Positive Gradient

What is the gradient between the points (2,1) and (4,5)?