How do I use this calculator?
The basic portion of this calculator allows you to calculate any of the variables shown directly above.
Calculator Operations:
- Enter the horizontal distance and vertical height to calculate the slope length.
- Enter the horizontal distance and slope length to calculate the vertical height.
- Enter the vertical height and slope length to calculate the horizontal distance.
The advanced version of this calculator allows you to calculate both the slope length and angle using the horizontal distance and vertical height.
Use the calculate button when all known values have been entered and use the reset button when you want to clear the values from the calculator.
Calculate a 1:20 slope as a percent grade (5%) and angle in degrees, or find the rise or run for any 1:N ratio in inches, feet, cm, m or mm.
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1:20 Slope Formula
The following formulas are used to calculate the dimensions of a 1:20 slope.
Variables:
- VH is the vertical height (units)
- HD is the horizontal distance (units)
- SL is the slope length (units)
To calculate the vertical height, divide the horizontal distance by 20. To calculate the horizontal distance, multiply the vertical height by 20. To find the slope length, use the Pythagorean theorem with the horizontal distance and the vertical height.
What is a 1:20 Slope?
A 1:20 slope is a gradient or incline of a surface where for every 20 units of horizontal distance, there is a 1 unit change in vertical height. A 1:20 slope is a 5% grade, with an angle of about 2.862405° from horizontal. Under the U.S. ADA Standards §403.3, it is at the maximum running slope for an accessible-route walking surface. Accessibility also depends on cross slope, clear width, stable and slip-resistant surfaces and other applicable requirements. Steeper accessible-route slopes generally require ramp provisions; §405.2 usually limits ramps to 1:12, with limited existing-site exceptions. This calculator checks geometry only.
How to Calculate a 1:20 Slope?
The following steps outline how to calculate the dimensions of a 1:20 slope.
- First, determine either the horizontal distance (HD) or the vertical height (VH) of the slope.
- Use the formulas VH = HD / 20 or HD = VH * 20 to calculate the missing dimension.
- Next, calculate the slope length (SL) using the Pythagorean theorem: SL = √(HD^2 + VH^2).
- Finally, check your calculations with the 1:20 Slope Calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
horizontal distance (HD) = 100 units
Using the formula VH = HD / 20, the vertical height (VH) would be 100 / 20 = 5 units.
Using the Pythagorean theorem, the slope length (SL) would be √(100^2 + 5^2) = √(10000 + 25) = √10025 ≈ 100.12 units.
