Slope & Grade Calculator
With rise (vertical) 12 inch, run (horizontal) 144 inch, slope & grade comes to 8.33 % — grade. It is reached in 5 steps, the last of which is 12 / 144 * 100, and each one is printed on the page with its numbers filled in. The formula is the one published by US Access Board, not an approximation fitted to it.
Grade percentage, angle in degrees, ratio and roof pitch from a rise and a run.
Formula and sources checked · How we check
Rise (vertical) 12 inch, Run (horizontal) 144 inch
8.33 %
Grade for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Grade
12 / 144 * 1008.333 %- Angle from horizontal
atan(12 / 144) * 180 / pi4.764 °- Ratio — one unit of rise per this much run
144 / 1212- Roof pitch, rise per 12 of run
12 / 144 * 121 /12- Length along the slope
sqrt(pow(12, 2) + pow(144, 2))144.499 in
Ask about this in the chatRoof Pitch to Angle and Grade Chart
Worked example
12 in of rise over 12 ft of run is an 8.33% grade, 4.76°, a 1:12 ratio — exactly the maximum slope the ADA allows for a wheelchair ramp. Anything steeper needs a longer run or a landing.
How to work it out yourself
- 1.Measure the rise and the run in the same units — a level held horizontally and a tape held vertically is enough.
- 2.Divide rise by run and multiply by 100 for the grade percentage.
- 3.For the angle, take the arctangent of rise over run and convert from radians to degrees.
- 4.For a ratio, divide run by rise: a 1:12 ramp rises one unit for every twelve of run.
Grade, angle and pitch over a 12 ft run
| Rise (vertical) (inch) | Grade | Angle from horizontal | Roof pitch, rise per 12 of run |
|---|---|---|---|
| 1 | 0.69 % | 0.4 ° | 0.08 /12 |
| 2 | 1.39 % | 0.8 ° | 0.17 /12 |
| 3 | 2.08 % | 1.19 ° | 0.25 /12 |
| 4 | 2.78 % | 1.59 ° | 0.33 /12 |
| 6 | 4.17 % | 2.39 ° | 0.5 /12 |
| 8 | 5.56 % | 3.18 ° | 0.67 /12 |
| 12 | 8.33 % | 4.76 ° | 1 /12 |
| 18 | 12.50 % | 7.13 ° | 1.5 /12 |
| 24 | 16.67 % | 9.46 ° | 2 /12 |
Rise in inches over a 144 in run. 12 in of rise is the 1:12 maximum the ADA allows for a ramp.
The formula
- Grade
12 / 144 * 100 - Angle from horizontal
atan(12 / 144) * 180 / pi - Ratio — one unit of rise per this much run
144 / 12 - Roof pitch, rise per 12 of run
12 / 144 * 12 - Length along the slope
sqrt(pow(12, 2) + pow(144, 2))
Source: US Access Board — ADA accessibility standards for ramps, International Residential Code — site drainage and slope
Questions people actually ask
- Grade, angle or ratio — which do I need?
- Grade for drainage and roads, ratio for accessibility ramps, angle for cutting anything. They describe the same slope: 8.33% is 1:12 is 4.76°, and only the last is what a mitre saw understands.
- What slope does a yard need to drain?
- The IRC wants ground falling at least 6 in over the first 10 ft away from a foundation — a 5% grade. Hard surfaces can go as low as 2%, but below that water sits rather than runs.
- Is a 100% grade a vertical wall?
- No, it is 45°. Grade is rise divided by run, so equal rise and run is 100%. A vertical face has infinite grade, which is why steep terrain is described in degrees instead.
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Read first
- How to Use a Protractor — Lining up the vertex, choosing between the two scales — the one to read starts at zero on your baseline — and reading an angle past 180° without inverting it.
- What a Shingle Roof Costs — Squares, bundles, tear-off and the pitch multiplier that makes a steep roof cost more twice over — once for the area, once for the labour of standing on it.
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