Slope calculator – the slope of the land on a map

How steep is a plot of land, a field, a ski run, a hiking trail or a driveway? The slope decides whether you can build without terracing, drive a tractor across the field, push a wheelchair up the path, lay a drain with a fall, or cross a snow slope without avalanche risk. A spirit level or a clinometer measures one spot; a topographic map makes you count contour lines. This calculator reads the heights from Terrain Tiles, a free worldwide elevation dataset built from national lidar models, EU-DEM, SRTM and other sources, and works out the slope for you. In the area mode it draws a slope map of a square around the point you click, coloured by slope class, with the mean, median and steepest slope, the direction most slopes face, and how much of the area falls in each class; click inside the square to read the slope, the direction and the height of a single point. In the line mode you click two points and get the average slope between them, the steepest climb and descent along the way and the total height gained and lost. A converter turns percent into degrees, degrees into a ratio such as 1:12, or rise and distance into a slope, without the map. Download the slope map as an Esri ASCII grid or a georeferenced PNG for QGIS, ArcGIS or CAD, the line as GeoJSON or KML, or copy a link that reopens the same view.

How to use it

1. Search for a town or postcode, or pan the map to the land you want to measure.
2. Choose "Area (slope map)" and the size of the square, then click on the map to place its centre.
3. Read the mean and steepest slope and the share of the area in each class; click inside the square for the slope at one point.
4. Or choose "Two points (line)" and click the start and the end to get the average and steepest slope along the line.
5. Switch between degrees and percent, download the slope grid, the image or the line, or copy the share link.

How accurate is it?

Where the heights come from

Terrain Tiles mix the best open elevation model for each place: the Environment Agency's 2 m lidar in England, USGS 3DEP at about 10 m in the United States, 10 m national models in Austria and Norway, EU-DEM at 25 m in most of the rest of Europe and SRTM at about 30 m in much of the world. The tool reads them on a square grid in the area's UTM zone with at most 400 cells along a side: 1.25 m cells for a 500 m square and 12.5 m cells for a 5 km square, but never finer than a pixel of the tiles, so the real resolution is that of the source model. The panel shows the grid and the tile level used.

How the slope is computed

For every cell the gradient comes from its eight neighbours, weighted 1–2–1 (Horn 1981), the method used by ArcGIS Slope, GDAL gdaldem slope and QGIS. The slope is the steepest rise over ground distance, corrected for the UTM scale factor, and the aspect is the direction the ground falls towards, turned from grid north to true north. On a plane the method is exact; on real terrain it gives the slope averaged over about three cells. Between two points the heights are sampled every pixel along the geodesic, and the steepest stretch is measured over at least 30 m or three pixels, so one noisy pixel does not show as a cliff.

Slopes are smoothed by the data

A 25–30 m model cannot see a 3 m embankment, a terrace wall, a ditch or a rock step: the slope it gives is the average over the pixel, so short steep features look gentler than they are, and the maximum slope is usually too low. The finer the source model, the steeper the steepest cells. For a building permit, a road design, a ramp or an avalanche decision, measure on site or use a 1–2 m lidar model (Denmark's DHM, England's LIDAR Composite, Germany's DGM1, France's RGE ALTI, the USGS 1 m DEM) and your local rules.

Good to know

Percent is not degrees

A 100 % slope is 45°, not 90°. Road signs, building codes and drains use percent or 1:n; mountaineering, avalanche bulletins and geology use degrees. Check which one a rule means before you compare, and use the converter under the map.

Average versus steepest slope

The average slope between two points only uses the heights at the ends. A path that climbs and drops on the way is steeper than its average; the line mode shows the steepest climb and descent and the total climb, and the elevation profile shows the whole shape.

Buildings, trees and water

Most of the models behind Terrain Tiles are bare ground, but in some places SRTM includes forest and towns, and lakes are flat. Slopes at forest edges, along buildings and at shorelines can therefore be steps in the data, not in the ground.