Convert slope to degrees from rise and run, percent grade, a 1 in N ratio or pitch, or convert an angle in degrees back to percent grade and ratio.
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Slope to Degrees Formula
The following formula is used to calculate the Slope to Degrees.
D = arctan(Y/X) ร 180/ฯ
- Where D is the Slope to Degrees (degrees)
- Y is the slope rise
- X is the slope run
Convert rise and horizontal run to the same units, with run greater than zero. Take the inverse tangent of rise divided by run, then multiply by 180/ฯ when the inverse tangent returns radians.
| Slope (rise/run) | Degrees (ยฐ) |
|---|---|
| 1/12 | 4.764 |
| 1/10 | 5.711 |
| 1/8 | 7.125 |
| 1/6 | 9.462 |
| 1/5 | 11.310 |
| 1/4 | 14.036 |
| 1/3 | 18.435 |
| 3/8 | 20.556 |
| 2/5 | 21.801 |
| 1/2 | 26.565 |
| 5/8 | 32.005 |
| 2/3 | 33.690 |
| 3/4 | 36.870 |
| 4/5 | 38.660 |
| 1 | 45.000 |
| 5/4 | 51.340 |
| 3/2 | 56.310 |
| 2 | 63.435 |
| 3 | 71.565 |
| 4 | 75.964 |
| * Rounded to 3 decimals. Conversion: degrees = arctan(slope) ร (180/ฯ). | |
How to Calculate Slope to Degrees?
The following example problems outline how to calculate Slope to Degrees.
Example Problem #1:
- First, determine the slope rise.
- The slope rise is given as 46.
- Next, determine the slope run.
- The slope run is provided as 30.
- Finally, calculate the Slope to Degrees using the equation above:
D = arctan(Y/X) ร 180/ฯ
The values given above are inserted into the equation below and the solution is calculated:
D = arctan(46/30) ร 180/ฯ โ 56.89 degrees
Example Problem #2:
For this problem, the variables needed are provided below:
slope rise = 70
slope run = 80
This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer.
D = arctan(Y/X) ร 180/ฯ = ?
