Slope Percentage vs Degrees: Rise, Run and a Conversion Table
Convert slope percentage to degrees with rise and horizontal run. A worked example and short table explain why percent, angle and sloped length differ.
A useful starting point
Slope percent is rise divided by horizontal run times 100; the angle uses arctangent. Keep horizontal run separate from sloped length, and treat the result as geometry rather than approval of a ramp or drainage design.
Slope percentage and degrees are different ways of describing a gradient. A 10% slope is about 5.71°, while a 10° slope is about 17.63%. Using the same number for both gives the wrong geometry.
The FAO measurement guide explains rise, horizontal distance and angle. Our examples apply those relationships with independent illustrative dimensions.
Measure rise and horizontal run
Rise is the vertical change in level. Run is the horizontal distance, not the length along the sloping surface. Use consistent length units; the NIST reference supports that conversion.
The basic relationships are:
- Slope percent = rise ÷ horizontal run × 100.
- Angle in degrees = arctangent(rise ÷ run).
- Sloped length = square root of (rise² + run²).
Work a 300 mm rise
Assume 0.3 m rise over a 4 m horizontal run.
| Quantity | Result |
|---|---|
| Rise/run ratio | 0.075 |
| Slope percentage | 7.5% |
| Angle | about 4.2892° |
| Sloped length | about 4.0112 m |
Enter the values in the slope and gradient calculator. Substituting 4.0112 m as horizontal run would change the meaning of the input.
Compare percent and degrees
The table below is calculated from arctangent, with display values rounded.
| Slope percent | Angle |
|---|---|
| 1% | about 0.573° |
| 2% | about 1.146° |
| 5% | about 2.862° |
| 10% | about 5.711° |
| 100% | 45° |
A 100% slope means equal rise and horizontal run; it does not mean a vertical surface. As the angle approaches 90°, a finite horizontal-run ratio no longer behaves like an ordinary small gradient.
Read roof ratios carefully
GAF's roof field guide distinguishes slope/run and pitch/span terminology. A ratio written on a roof drawing needs its definition, not just a familiar name.
Use the verified angle in the roof-area guide. Do not enter “10” in its angle field when the original drawing means 10%.
Keep a geometric result within scope
The tool uses nonnegative rise or gradient and a positive run. Zero slope is level in the model. It does not approve legal ramp limits, accessible routes, drainage performance, ground stability or structural construction.
Those decisions need the applicable project requirements and specialist review. A conversion table is not a design standard.
Common questions
Can I use centimetres for both rise and run?
Yes, a ratio remains the same when both use the same unit. Convert consistently before comparing with other dimensions.
Is a ratio always written the same way?
No. Label which side is rise and which is run. A bare “1:12” is easy to misread without the drawing's convention. The building-units guide explains related dimensional mistakes.
