Math CentralQuandaries & Queries


Question from cecil:

convert grade percent to degrees

Hi Cecil.

It's actually not too complicated at all. Road incline grades are given in percentage, which is the rise over run percentage. This is the same thing as the tangent, expressed as a percentage. So 100% grade means tan x = 1, where x is the angle in degrees. Thus, convert from percentage to decimal by dividing by 100, then take the arctan (also called "inverse tangent") of that to get the degrees. Be sure your calculator is set for "degrees" trigonometric functions rather than radians or gradians.

Example: 10% grade: arctan (0.10) = 5.7 degrees.

Hope this helps,
Stephen La Rocque.

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