Slope is the measure of how steep a terrain surface is at a given location — the maximum rate of change in elevation between a cell and its neighbors. It is the most fundamental derivative computed from a digital elevation model (DEM) and is reported either in degrees (0–90°) or as percent slope (rise over run × 100).
Why it matters
Slope underpins a huge range of geological and engineering analyses: landslide and erosion susceptibility, site suitability, infrastructure corridor screening, drainage modeling, and terrain classification. Many thresholds in practice are slope-based — for example flagging ground steeper than 15° or 30° for stability review.
How it is computed
Slope is calculated from the elevation gradient in the x and y directions across a 3×3 moving window. The standard Horn (1981) method, used by GDAL and ArcGIS, fits a plane to the eight neighbors. Percent slope and degrees relate by degrees = arctan(percent / 100): a 100% slope equals 45°, not 90°.
In QGIS or GDAL you can generate a slope raster from a DEM with gdaldem slope input_dem.tif slope.tif, adding -p for percent output.
Common pitfall
If the DEM is in a geographic CRS (degrees, e.g. EPSG:4326) while elevation is in meters, the horizontal and vertical units don't match and slope values come out wrong unless a z-factor or scale is applied. Always run slope on a projected DEM (meters), or set the correct -s scale. Slope also changes with cell size — a coarser DEM smooths and lowers apparent steepness.