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How to Calculate Gradient

Updated April 06, 2018

The gradient is another name for the slope of a line. The gradient measures how steep the line elevates or descends. A positive gradient means the line goes up, while a negative number means the slope goes down. The higher the number, either positive or negative, the more steep the slope. For example, a line with a gradient of -10 slopes downward more steeply than a line with a gradient of -3.

Compute the vertical change, also known as the rise. For example, if you are given two points on a coordinate plane, you would calculate the vertical change by subtracting the first y-coordinate from the second y-coordinate. If your coordinates are (5,7) and (8, 13), you would subtract 7 from 13 to get 6.

Compute the horizontal change, also known as the run. Similar to the rise, if you are given two points on a coordinate plan, you would calculate the horizontal change by subtracting the first x-coordinate from the second x-coordinate. Continuing the example, if your coordinates are (5,7) and (8, 13), you would subtract 5 from 8 to get 3.

Divide the vertical change (rise) by the horizontal change (run) to calculate the gradient. Finishing the example, you would divide 6 by 3 to find the gradient equals 2.

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About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."