Calculate percent slope from rise and run, convert between degrees, gradient, roof pitch and pipe fall, or find required rise/run.
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Percent Slope Formula
Percent slope expresses how much a surface rises or falls over a horizontal distance, as a percentage. The calculator uses three formulas depending on which mode you choose.
% slope = (rise / run) * 100
angle (deg) = arctan(rise / run)
surface length = sqrt(run^2 + rise^2)
- rise: vertical change between the two points. Use a negative value for downhill.
- run: horizontal distance between the two points, measured level, not along the slope.
- angle: slope angle in degrees from horizontal.
- surface length: distance measured along the sloped surface itself.
Rise & Run mode takes your two measurements, converts them to the same unit, then applies rise divided by run times 100.
Convert Slope mode takes a value in degrees, gradient (1 in N), roof pitch (X:12), or pipe fall (in/ft) and converts it to a percent. Degrees use tan(angle) × 100. Gradient uses 100 ÷ N. Roof pitch and pipe fall both use X ÷ 12 × 100.
Find Rise/Run mode reverses the formula. Given a target percent slope and one known distance (run, rise, or sloped surface length), it solves for the other two using the slope ratio r = % ÷ 100 and the Pythagorean relationship above.
Common Slope Values and Limits
Use these tables to interpret a result or set a target.
| Percent | Degrees | Gradient | Roof pitch |
|---|---|---|---|
| 1% | 0.57° | 1 in 100 | 0.12:12 |
| 2% | 1.15° | 1 in 50 | 0.24:12 |
| 5% | 2.86° | 1 in 20 | 0.6:12 |
| 8.33% | 4.76° | 1 in 12 | 1:12 |
| 10% | 5.71° | 1 in 10 | 1.2:12 |
| 25% | 14.04° | 1 in 4 | 3:12 |
| 50% | 26.57° | 1 in 2 | 6:12 |
| 100% | 45° | 1 in 1 | 12:12 |
| Application | Typical slope |
|---|---|
| Sanitary sewer pipe (4 in) | 1% to 2% |
| Driveway, paved | 2% to 15% |
| Lawn drainage away from foundation | 5% over first 10 ft |
| ADA accessible ramp (max) | 8.33% (1:12) |
| Accessible walking surface (max) | 5% (1:20) |
| Low-slope roof | 2% to 25% |
| Steep-slope roof | over 25% |
| Highway, rural maximum | 6% to 7% |
Examples and FAQ
Example 1: Driveway grade. A driveway rises 4 ft over a horizontal run of 50 ft. Percent slope = 4 ÷ 50 × 100 = 8%. The angle is 4.57°. That is steeper than the 5% accessible-route limit but workable for vehicles.
Example 2: Sewer pipe fall. You need 2% slope on a 30 ft pipe run. Required fall = 0.02 × 30 = 0.6 ft, or 7.2 inches. That works out to 0.24 inches per foot.
Is 1:12 the same as 8.33%? Yes. A 1:12 ratio means 1 unit of rise for every 12 units of run, which is 1 ÷ 12 × 100 = 8.333%.
How do I convert percent slope to degrees? Take the arctangent of the percent divided by 100. A 10% slope is arctan(0.10) = 5.71°. The relationship is not linear, so 100% slope is 45°, not 90°.
Can percent slope be over 100%? Yes. Anything steeper than 45° produces a percent above 100. A 200% slope is about 63.4°.
Should I measure along the slope or horizontally? The formula uses horizontal run, not surface length. If you only have the sloped distance, use the Find Rise/Run mode and select "Sloped surface length" to back out the true run and rise.
