Slope Angle Degrees Calculator
The slope angle calculator turns a vertical rise and a horizontal run into a slope angle measured in degrees, the form surveyors, roofers and trail builders often need. The method is the standard trigonometric relationship: the slope angle is the arctangent of the rise divided by the run, because the tangent of an angle equals the opposite side over the adjacent side. The run is the horizontal distance, not the distance along the slope, and rise and run must share the same units so the ratio is dimensionless. Degrees and percent grade describe the same slope two different ways, but they are not proportional: a 5 percent grade is about 2.86 degrees, while a 100 percent grade is exactly 45 degrees, the point where the rise equals the run. Enter your own rise and run to convert a measured grade into degrees, check a slope against an angle limit, or set out a cut or fill on site. Every figure here is computed deterministically from the formula shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step and trust the result, plus a reference table linking common grades to their angles.
The slope angle is the arctangent of rise over run: angle = arctan(rise / run). A rise of 5 over a run of 100 gives a slope of 2.86°. A 100 percent grade equals exactly 45 degrees.
Slope angle formula
Angle (degrees) = arctan(rise / run) x (180 / pi)
rise = vertical change in height
run = horizontal distance (not slope distance)
The tangent of the slope angle equals rise over run, so the angle is the arctangent of that ratio. The arctangent returns radians, which are converted to degrees by multiplying by 180 and dividing by pi.
Worked example
A path rises 5 feet over a horizontal distance of 100 feet.
- Ratio = 5 / 100 = 0.05
- Angle in radians = arctan(0.05) = 0.049958
- Angle in degrees = 0.049958 x (180 / pi) = 2.86°
The slope angle is 2.86 degrees, equivalent to a 5 percent grade. These are the calculator's default inputs, so the result above matches the widget exactly.
Grade to angle reference
Common percent grades and their slope angles in degrees.
| Grade (%) | Angle (degrees) |
|---|---|
| 5 | 2.86 |
| 8.33 | 4.76 |
| 12 | 6.84 |
| 100 | 45.00 |
Survey and geodetic standards: US National Geodetic Survey (NOAA).
Slope angle calculator: frequently asked questions
How do I convert slope to degrees?
Take the arctangent of the rise divided by the run. The slope angle in degrees is the angle whose tangent equals rise over run. For a rise of 5 over a run of 100, the angle is the arctangent of 0.05, which is about 2.86 degrees. Most calculators give the answer in radians, so multiply by 180 divided by pi to get degrees.
What is the difference between grade and degrees?
Percent grade is rise over run as a percentage, while the slope angle is the angle in degrees whose tangent is rise over run. They describe the same slope two ways. A 5 percent grade is about 2.86 degrees, and a 100 percent grade is exactly 45 degrees. The two are not proportional, so you cannot simply scale one into the other.
Why is 100 percent grade only 45 degrees?
At a 100 percent grade the rise equals the run, and the angle whose tangent is 1 is 45 degrees. Grade can exceed 100 percent for slopes steeper than 45 degrees, but the angle can never exceed 90 degrees. This is why a steep mountain road at 12 percent grade is still only about 6.8 degrees.
Should I use horizontal run or slope distance?
Use the horizontal run, the flat distance, because the slope angle is defined by the arctangent of rise over horizontal run. If you measured the distance along the slope instead, the angle would come from the arcsine of rise over slope distance. Make sure you know which distance you have before choosing the formula.
What angle is a wheelchair ramp?
A common accessibility limit for ramps is a 1 in 12 slope, which is a grade of about 8.33 percent. As an angle that is the arctangent of 1 divided by 12, roughly 4.76 degrees. Always check the standard that applies to your project, because limits vary by use and jurisdiction.
Official sources
- Survey, leveling and geodetic standards: US National Geodetic Survey (NOAA). 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.