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The slope is a term which has several definitions, a priori it is the inclination, generally measured in percentage (a slope of 30%). By extension, some call slope the angle $ a $ (a slope of 15 degrees).

The percentage value is the elevation for a horizontal distance $ h $ of 100 units.

How to calculate a slope (in percentage)?

The slope $ p_\% $ (in % percent) is calculated by the ratio of the height $ h $ by the width $ w $ (multiplied by 100 to get a percentage): $$ p_\% = 100 \times \frac{h}{w} $$

Example: Calculate the slope for a vertical distance of 10m and a horizontal distance of 50m: $ p = 10/50 = 0.2 $ or $ 20% $

How to calculate a slope (in degrees)?

The slope $ p° $ (in ° degrees) is calculated by trigonometric functions: $$ p° = \arctan \left( \frac{h}{w} \right) \times \frac{180}{\pi} $$

Example: Calculate the slope for a vertical distance of 10m and a horizontal distance of 50m: $ p° = \arctan(10/50) \approx 0.19 \text{ rad} \approx 11.3° $ (multiply radians by $ 180/\pi $ to get a value in degrees)

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Cite as source (bibliography): Slope Calculator on dCode.fr [online website], retrieved on 2023-02-08, https://www.dcode.fr/slope-calculator