How Do You Calculate the Gradient/slope of a Line?

Hero Images/Hero Images/Getty Images

To calculate the gradient of a line, divide the change in height between the beginning and end of the line by the change in its horizontal distance. Arguably the easiest way to do this is to plot the line on a pair of axes. For example, if a line started at (0,0) and ended at (4,4), its change in height would equal 4, and the change in horizontal distance would also equal 4. Divide 4 by 4 to get 1; therefore, the gradient of the line would equal 1.

Gradient, also known as grade, slope, pitch, incline or rise, is a useful measurement with many real-world applications. Steep roads are often marked with gradients to warn drivers in advance before they begin a descent or ascent. Gradients come into play when new roads are planned and constructed. Architects determine gradients during the design process to ensure buildings are safe and aesthetically pleasing.

Gradients are also important in many engineering applications. Components with incorrect gradients don’t always perform correctly within mechanisms or larger structures. Positive and negative gradients are also calculated when topical maps and landscaping plans are created. Many artists use gradients to ensure their pieces are structurally correct.