Grade (slope)

The grade (US) or gradient (UK) (also called slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance.

Slopes of existing physical features such as canyons and hillsides, stream and river banks, and beds are often described as grades, but typically the word "grade" is used for human-made surfaces such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle routes. The grade may refer to the longitudinal slope or the perpendicular cross slope.

Nomenclature

There are several ways to express slope:

as an angle of inclination to the horizontal. (This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.)

as a percentage, the formula for which is

100

×

rise

run

{\displaystyle 100\times {\frac {\text{rise}}{\text{run}}}}

, which is equivalent to the tangent of the angle of inclination times 100. At a slope angle of 45 degrees, the run is equal to the rise. Expressed as a percentage, the slope of this angle is 100 percent.