Choose a Solve for task to convert angle, percent grade, 1 in N ratio or pitch, or calculate from rise and horizontal run. Only the independent known values are required.
Related Calculators
- Gradient To Slope Calculator
- Rise And Run Calculator
- Point Slope Form Calculator
- Slope Distance Calculator
- Angle Addition Calculator
- Rotation Calculator (new coordinates by rotation)
- All Math and Numbers Calculators
Angle to Slope Formula
The following formula is used to calculate the slope for a given angle.
Variables:
- S is the slope in percentage
- A is the angle in degrees
To calculate the slope, take the tangent of the angle and multiply by 100 to convert it to a percentage.
| Angle (ยฐ) | Slope (%) |
|---|---|
| 0.5 | 0.87 |
| 1 | 1.75 |
| 1.5 | 2.62 |
| 2 | 3.49 |
| 3 | 5.24 |
| 4 | 6.99 |
| 5 | 8.75 |
| 6 | 10.51 |
| 7 | 12.28 |
| 8 | 14.05 |
| 9 | 15.84 |
| 10 | 17.63 |
| 12 | 21.26 |
| 15 | 26.79 |
| 20 | 36.40 |
| 25 | 46.63 |
| 30 | 57.74 |
| 35 | 70.02 |
| 40 | 83.91 |
| 45 | 100.00 |
| Formula: Slope (%) = tan(Angle in degrees) ร 100. Example: tan(10ยฐ) ร 100 โ 17.63%. | |
What is Angle to Slope?
Angle-to-slope conversion describes steepness: percent grade is 100 times rise divided by horizontal run. Angle and grade determine each other; a length is also needed to determine rise or run. Negative values describe descending slopes. Vertical lines have no finite grade, and a horizontal line has no finite 1 in N ratio. The calculator converts geometry; it does not establish construction or accessibility compliance.
How to Calculate Angle to Slope?
The following steps outline how to calculate the Angle to Slope.
- First, select Slope from angle and enter the angle (A) in degrees or radians.
- Next, calculate the slope using the formula S = tan(A) * 100.
- Alternatively, if you have the rise and run, you can calculate the slope as S = (rise / run) * 100.
- For lengths, select Rise from angle and run or Run from angle and rise, then enter the two known values and choose their units.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Angle (A) = 30 degrees
Run = 10 meters
Select Rise from angle and run with 30ยฐ and 10 m. The slope is about 57.735% and the rise is about 5.773503 m.
