Rise over Run

The grade of a slope is exactly what it sounds like-- a slope.


Grade is expressed in the following equation:

% grade = rise/run x 100

A slope with a grade of 9% is one in which 9 feet of altitude is gained for every 100 feet of distance travelled, which is actually steeper than it seems. A handicap ramp, which must rise 1 inch for every foot travelled, has a grade of 8.3%. The steepest road in San Francisco, Filbert Street, has a grade of 31.5%, meaning that when driving on this road, one gains 4 inches in elevation for every foot they travel.

This also means that the road climbs at an 18.4 degree angle, because the negative tangent of 4 over 12 is 18.4. The tangent, a trigonometric function, can tell us the angle based on rise over run, or the rise or run based on the angle and one of the value. The tangent function is opposite over adjacent. To elaborate, this means that the equation must be set up like this:

tan(angle) = (opposite side) / (adjacent side)

Reworded, the equation becomes:

tan(angle) = (rise) / (run)

And that is how the trigonometric function of tangent finds it's way into rise over run, and subsequently, grade.