Terrain (DEM)

Slope: Turning Elevation Into Steepness

Concept article · Updated · by Dr. Anant Kumar Pathak

Water runs downhill, soil slips on steep ground, and roads cannot climb past a certain grade — all of which begin with slope, the rate at which elevation changes across the surface.

How it works

Slope is computed from the elevation difference between a cell and its neighbours, usually via Horn's 3×3 algorithm, and expressed in degrees or percent. Flat ground reads near 0°, cliffs approach 90°. It is, mathematically, the first derivative of the elevation surface.

How it is calculated

Slope = Maximum rate of elevation change between a cell and its neighbours (° or %)

What the numbers mean

Typical range: 0–90° (or 0 to ∞ %)

0–5° flat · 5–15° gentle · 15–30° moderate · > 30° steep.

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The data it needs

Derived fromDigital Elevation Model (SRTM / Copernicus, 30 m) — not an optical band index.

Where it is used

Slope feeds landslide and erosion susceptibility, hydrological and runoff modelling, agricultural suitability, and constraint mapping for construction and routing.

Limitations to know

Values depend heavily on DEM resolution — coarser grids flatten steep terrain, and noisy DEMs create speckle.

Slope is only as good as the DEM's resolution: a coarse grid flattens genuinely steep terrain, while a noisy DEM produces speckled, exaggerated values. Match the DEM resolution to the scale of the landforms you care about.

Compute Slope on your own study area

Skip the code. Draw or upload a boundary and Spatial Research Suite runs Slope on live data — with cloud masking, exports and citations built in.

Run this analysis in GISforus →

Frequently asked

Is slope measured in degrees or percent?

Either — degrees (0–90°) is most common in GIS, while percent (rise over run ×100) is common in engineering and agriculture.

Why does slope change with DEM resolution?

Coarser cells average over longer distances, smoothing away steep local relief, so the same hill reads gentler on a coarse DEM.

Primary reference: Horn, B.K.P. (1981). Hill shading and the reflectance map. Proceedings of the IEEE 69(1), 14–47.