Slope to Angle Converter
Slope shows up in three forms depending on the trade, and this converter translates between them. Builders state a roof pitch as rise in 12, engineers quote a percent grade, and geometry and accessibility standards use the angle in degrees. All three describe the same incline, linked by simple trigonometry. The angle a slope makes with the horizontal is the arctangent of the rise divided by the run, while the percent grade is that same ratio multiplied by 100. Enter a rise and a run and the calculator returns both the angle in degrees and the percent grade, so you can read a spec in whatever form you were given and apply it in the form you need. A slope of 3 in 12, for instance, is a 0.25 ratio, which works out to about 14.04 degrees and a 25 percent grade. Note that grade and angle are not the same number: a 100 percent grade is a 45 degree angle, not vertical, because grade rises without limit while the angle is capped at 90. Every figure is computed deterministically from the formula shown below, with a worked example that reconciles exactly to the calculator defaults so you can trust the conversion for layout or design.
Angle comes from the arctangent of rise over run: angle = atan(rise / run). A slope of 3 in 12 is a 0.25 ratio, which is 14.04 degrees and a 25.00% grade.
Slope to angle formula
Ratio = Rise / Run
Angle (degrees) = arctangent(Ratio) x 180 / pi
Percent grade = Ratio x 100
(arctangent is the inverse tangent function)
The tangent of the slope angle equals rise over run, so the arctangent of that ratio recovers the angle. The percent grade is the same ratio scaled to 100.
Worked example
Convert a roof slope of 3 in 12 (rise 3, run 12).
- Ratio = 3 / 12 = 0.25
- Percent grade = 0.25 x 100 = 25.00%
- Angle = arctangent(0.25) = 0.244979 radians
- 0.244979 x 180 / pi = 14.04 degrees
A 3 in 12 slope is 14.04 degrees and a 25.00% grade. These are the calculator's default inputs, so the result above matches the widget exactly.
Common slopes in degrees and grade
The same incline expressed three ways.
| Rise in 12 | Percent grade | Angle |
|---|---|---|
| 1 in 12 | 8.33% | 4.76 degrees |
| 3 in 12 | 25.00% | 14.04 degrees |
| 6 in 12 | 50.00% | 26.57 degrees |
| 12 in 12 | 100.00% | 45.00 degrees |
Measurement and units guidance: US National Institute of Standards and Technology (NIST).
Slope to angle converter: frequently asked questions
How do I convert slope to an angle?
Take the inverse tangent (arctangent) of the rise divided by the run. The result is the angle the slope makes with the horizontal, in degrees. For a slope of 3 in 12, the rise over run is 0.25, and the arctangent of 0.25 is about 14.04 degrees. The percent grade is the same rise over run multiplied by 100, here 25 percent.
What is the difference between grade and angle?
Percent grade is the rise divided by the run, times 100, a ratio. The angle is the geometric angle from horizontal, found with the arctangent. They are not the same: a 100 percent grade is a 45 degree angle, not 90 degrees, because grade grows without bound as the angle approaches vertical while the angle is capped at 90.
Where is this used?
Roofers express pitch as rise in 12, road and rail engineers use percent grade, and accessibility standards specify ramps by ratio or angle. Converting between rise over run, degrees and grade lets you read a specification in whatever form you have and apply it in the form you need.
Does run have to be 12?
No. Roofing conventionally uses a run of 12 for pitch, but any consistent units work because the angle depends only on the ratio of rise to run. A rise of 1 over a run of 4 gives the same angle as 3 over 12, since both ratios equal 0.25.
What is the slope to angle formula?
Angle in degrees equals the arctangent of (rise / run), converted from radians to degrees. Percent grade equals (rise / run) multiplied by 100. Both come from the same rise over run ratio.
Official sources
- Measurement, units and number standards: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.