Slope and Gradient Calculator
Calculate slope or gradient in percent and degrees. For roads, roofs and ramps. Online calculator with solution path and worked examples.
Result
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Formulas
Slope (%) = (Height difference / Horizontal distance) × 100
Slope (°) = arctan(Height difference / Horizontal distance)
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
How is slope percentage calculated?
Slope percentage equals (vertical rise / horizontal distance) times 100. A 10% slope means 10 meters of rise over 100 meters of horizontal distance.
How do I convert between degrees and percent slope?
Percent equals tangent of angle in degrees times 100. Degrees equals arctangent of percent divided by 100. A 45-degree angle equals 100% slope; a 100% slope does not mean vertical.
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
Quick Answer
The gradient calculator computes the slope in percent, degrees and ratio from the height difference and horizontal distance.
What is the Slope and Gradient Calculator?
The gradient calculator computes the slope in percent, degrees and ratio from the height difference and horizontal distance.
How does the Slope and Gradient Calculator work?
Enter the height difference and horizontal distance. Slope in % = (height / distance) * 100. The calculator also shows the angle in degrees and the ratio (e.g. 1:10).
Key Data and Facts
Slope % = (height difference / horizontal distance) * 100. 100% slope = 45 degrees. Road construction max. approx. 12%. Roof pitch: 15-45 degrees typical.
Step-by-Step Guide
How to calculate incline and decline step by step: 1. Measure the height difference and the horizontal distance: the height difference is the vertical distance between the start and end points. The horizontal distance is the level distance (not the slope itself). 2. Incline in percent: incline (%) = (height difference / horizontal distance) x 100. 3. Incline in degrees: angle = arctan(height difference / horizontal distance). Conversion: 100 % incline = 45 degrees. 10 % ≈ 5.7 degrees. 4. Ratio: 10 % incline = ratio 1:10 (1 m of height over 10 m of distance). 5. Applications: road construction: maximum incline on a motorway about 6 %, on a country road about 12 %. Wheelchair ramp: max. 6 % (DIN 18040). Roof pitch: flat roof 2-5 degrees, steep roof 35-45 degrees. Drainage pipe: min. 1-2 % decline. 6. Sloped distance (incline length): L = square root(height2 + distance2).
Calculation Example
Ramp with 0.5 m height and 8 m length: slope = (0.5 / 8) x 100 = 6.25%. Angle = arctan(0.5/8) = 3.58 degrees. Ratio 1:16.
Sources · E-E-A-T
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Mathematics
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