Calculate slope from rise and run as an angle in degrees, percent grade, pitch and ratio, or find the rise or run from a known slope or diagonal.
Rise and Run Formula
For a positive horizontal run, convert rise and run to the same length unit before using these formulas. Zero rise with positive run is flat; zero run is outside this finite-slope calculator’s range.
Slope ratio = Rise / Run
Angle = arctan(Rise / Run)
Percent grade = (Rise / Run) * 100
Pitch = (Rise / Run) * 12
When you instead know the slope, the calculator rearranges these relationships to solve for the missing side:
Run = Rise / tan(Angle)
Rise = Run * tan(Angle)
Rise = L * sin(Angle) Run = L * cos(Angle)
The variables are:
- Rise is the vertical change between two points.
- Run is the horizontal change between the same two points.
- Angle is the slope angle measured from horizontal, in degrees.
- Percent grade is the rise divided by the run, written as a percentage.
- Pitch is the rise for every 12 units of run, the form used for roof slopes.
- L is the diagonal or slope distance, the straight line connecting the two points.
If you enter rise and run, the calculator returns the slope ratio, angle, percent grade, and pitch at once. If you enter a slope value and one length, it solves for the other length. If you enter the diagonal length and a slope, it splits that diagonal into its rise and run. You can supply the slope as an angle, a percent grade, or a pitch, and each form is converted internally before the missing value is found.
Slope Conversion Reference
The same slope can be written four ways. This table lines up common values so you can move between angle, ratio, grade, and pitch.
| Angle (deg) | Ratio (rise:run) | Percent grade | Pitch (per 12) |
|---|---|---|---|
| 4.76 | 1:12 | 8.33% | 1 in 12 |
| 14.04 | 1:4 | 25% | 3 in 12 |
| 18.43 | 1:3 | 33.3% | 4 in 12 |
| 26.57 | 1:2 | 50% | 6 in 12 |
| 45 | 1:1 | 100% | 12 in 12 |
Where Rise and Run Are Used
The rise and run pair uses different notation across trades. The following values illustrate conversions only; they are not recommended slopes, universal design limits or a compliance check. Applicable ramp, roof, stair and road requirements depend on the project and governing standards.
| Use | Common slope form | Illustrative conversion |
|---|---|---|
| Ramp slope | Ratio | 1:12 = 8.33% ≈ 4.76° |
| Roof slope | Pitch | 6 in 12 = 50% ≈ 26.57° |
| Stairs | Angle | 30° ≈ 57.74% grade |
| Road grade | Percent grade | 6% ≈ 3.43° |
Example Problems
Example 1. A roof rises 3 units for every 12 units of horizontal run. Set the slope ratio as Rise / Run = 3 / 12 = 0.25. The angle is arctan(0.25) = 14.04 degrees, the percent grade is 0.25 * 100 = 25%, and the pitch is 0.25 * 12 = 3 in 12.
Example 2. You know a run of 10 feet and a slope angle of 30 degrees, and you need the rise. Rise = Run * tan(Angle) = 10 * tan(30) = 10 * 0.5774 = 5.77 feet.
Frequently Asked Questions
What is the difference between rise and run? Rise is the vertical distance between two points, and run is the horizontal distance between the same two points. Dividing rise by run gives the slope, which you can then express as an angle, a percent grade, or a roof pitch.
How do I turn rise and run into an angle? Take the inverse tangent of the rise divided by the run. For a rise of 5 and a run of 12, the angle is arctan(5 / 12) = 22.6 degrees. Make sure your device is set to degrees rather than radians.
What does a pitch of 6 in 12 mean? It means the surface rises 6 units for every 12 units of horizontal run, which is a slope ratio of 1:2, a percent grade of 50%, and an angle of about 26.57 degrees.
