Calculate slope in percent and degrees
Enter the difference in height and the horizontal length to find the slope. You get both the percentage and the angle in degrees.
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Measure the length horizontally
The slope describes how much a surface rises relative to the horizontal distance. It can be used for a ramp, terrain or a sloping surface in a drawing. The calculator needs the height difference h and the horizontal length L.
L must be measured horizontally. If you measure along the sloping surface itself, you get a different length that cannot be put directly into the formula. Use the distance under the sloping surface and the height between its end points. The two measurements must describe the same stretch.
Formulas for percent and angle
The slope in percent is found with p = 100 × h / L. The formula compares the rise with the horizontal length and converts the ratio to a percentage. It shows how large the height difference is relative to the horizontal extent of the stretch.
The angle is found with θ = atan(h / L). The atan function converts the ratio between height and horizontal length into an angle. The calculator shows the angle in degrees. A percentage and an angle thus describe the same slope in two different ways.
Example of the slope of a ramp
A ramp rises 1 m over 10 m horizontally. First the ratio is found: 1 / 10 = 0.1. The slope is 100 × 0.1 = 10%. For the angle, atan(1 / 10) = atan(0.1) is used, which is about 5.7 degrees. The calculation gives the geometry of the ramp and does not determine whether it meets requirements for a particular use.