Slope

Slope is the incline (steepness) of a surface or part of a surface. While typically applied to topography, slope may be useful in analyzing other types of surfaces. For example, when slope is calculated for a surface of rainfall, it shows you areas where rainfall is changing and how quickly they are changing (steeper "slopes" are changing faster). You might apply slope calculations within erosion analysis or construction siting.

Slope is calculated as the maximum rate of change in values between each cell and its neighbors. Slope may be expressed as either degrees (e.g., 45 degrees) or percent (e.g., 50%). Degrees is commonly used in scientific applications, while percent is commonly used in transportation studies (e.g., "Caution: 6% grade ahead!").

Slope is a measure of the steepness of a surface and may be expressed in either degrees or percent of slope. In this example, the red cells show steep areas and the green cells show flat areas.

To calculate percent slope, divide the elevation difference (known as the rise) between two points, by the distance between them (known as the run), and then multiply the result by 100.

To calculate degree of slope, imagine rise and run as sides of a right triangle, then the degree of slope is the angle opposite the rise. Since degree of slope is equal to the tangent of the fraction rise/run, it can be calculated as the arctangent of rise/run. Measures of slope in degrees can approach 90 degrees and measures of slope in percent can approach infinity.

The diagram above shows how to mathematically calculate either the degree of slope or the percent of slope.