Slope and Gradient Calculator
Enter rise and run, a percentage or an angle to get the slope in percent and degrees, the ratio 1:X and, from rise and run, the sloped length.
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.
Do I enter the horizontal distance or the sloped length?
The calculator expects the horizontal distance, i.e. the level distance on the plan; it works out the sloped length itself as the hypotenuse. Example: a rise of 0.3 m over a horizontal distance of 5 m gives a 6% slope, 3.43°, a ratio of 1 : 16.7 and a sloped length of about 5.01 m. On gentle ramps the difference is small, on steep surfaces it is large: if you measure 5 m along the slope of a 45° roof, the horizontal distance is only 3.54 m.
Guide
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
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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