How to calculate terrain slope: percent, degrees and permille
Slope looks like a simple ratio, but the elevation source, horizontal distance and field line matter.
Field takeaways
- Percent slope is vertical difference divided by horizontal distance, multiplied by 100.
- Permille is useful for drainage and pipe grades.
- Degrees are angular slope and should not be confused with percent.
- GNSS height and DEM elevation need control for precise work.
- MapLab Survey helps read two-point and along-line slope in the field.
The basic formula
Percent slope is the vertical difference divided by the horizontal distance, times 100: a 2-metre rise over 50 metres of horizontal distance is a 4 percent slope. Per mille multiplies the same ratio by 1000, so the same example is 40 per mille. Degrees express the ratio as the angle — its arctangent.
Percent, per mille or degrees?
- Percent — roads, ramps and general terrain; the most widely understood.
- Per mille — channels, pipes and drainage; makes small gradients readable.
- Degrees — topography, slopes and technical drawings; never to be confused with percent.
State the unit in every report. A gradient given without its unit is an argument waiting to happen.
Watch the elevation source
Phone altitude, RTK ellipsoidal height, orthometric level and DEM sources such as SRTM are not the same thing. For drainage, channel inverts, foundation levels or road platforms, write down what the level was produced against. For quick scouting a DEM or phone level gives an idea; precise application needs control points and a proper method.
Reading slope in the field
Draw a line between two points in MapLab Survey, or pick an existing one, and read the gradient; take a profile along the line and watch for sudden jumps. A jump can be real topography — or a data-source artefact. Marking the critical spots with photos and notes pays off when the office looks at the drawing later.
The honest limit
A slope figure is exactly as good as the levels feeding it. Debating a 0.5 percent gradient with levels that are 30 cm off is not safe; on small gradients, a small level error becomes a large decision error. That is why low-gradient drainage and pipe work may need tighter levelling or control measurement.
See it in action
MapLab Survey | Professional Mobile GIS, GPS Surveying & Land Measurement App
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MapLab Survey handles RTK/GNSS point capture, drawing, area and volume calculations and coordinate conversion, then exports to DXF, KML/KMZ, GeoJSON, Shapefile, GeoPackage, NCZ or CSV. Capture, calculation and export work offline. Live NTRIP corrections and online basemaps need a connection.
Frequently asked questions
How is percent slope calculated?
Vertical difference divided by horizontal distance, multiplied by 100.
Is percent the same as degrees?
No. Degrees are angular slope.
What is permille slope?
The same ratio multiplied by 1000.
Is phone elevation enough?
For reconnaissance only. Precise work needs control.
Technical references
The field guidance in this article is aligned with the technical and official references below.
Related: Creating an elevation profile · GNSS Z and elevation · Contour lines · MapLab Survey