Convert angle in degrees to slope percent with ratio and mm/m equivalents.
Why the formula uses tangent
Slope percent expresses the ratio of vertical rise to horizontal run, multiplied by 100. For a right triangle with angle θ at the base, rise = sin(θ) and run = cos(θ), so rise/run = tan(θ). Converting degrees to radians (θ × π / 180) lets the standard math function compute the tangent. Multiplying by 100 turns the decimal ratio into a percent.
Why the percent goes to infinity at 90°
At exactly 90° the slope is vertical: the run (horizontal distance) is zero while the rise is non-zero. Because percent slope divides rise by run, dividing by zero is undefined and the value tends toward infinity as the angle approaches 90°. For example, 89° already gives about 5 729%, and 89.99° gives over 572 957%. In practice, anything above ~85° is treated as a wall rather than a slope.
Reference table
| Degrees | Slope % | Ratio (rise:run) |
|---|---|---|
| 1° | 1.75% | 1:57.29 |
| 5° | 8.75% | 1:11.43 |
| 10° | 17.63% | 1:5.67 |
| 15° | 26.79% | 1:3.73 |
| 30° | 57.74% | 1:1.73 |
| 45° | 100.00% | 1:1 |
| 60° | 173.21% | 1:0.58 |
Frequently asked questions
What is 30 degrees as a slope percent?
A 30° angle corresponds to tan(30°) × 100 ≈ 57.74%. That means for every 100 metres of horizontal run, the rise is about 57.74 metres. In ratio form it is roughly 1:1.73 (rise:run), or approximately 6.93 inches of rise per foot of horizontal run.
What are typical roof pitch angles in degrees and percent?
Flat roofs range from 1° to 5° (1.75%–8.75%), which keeps water drainage without looking pitched. Low-slope roofs sit around 10°–15° (17.63%–26.79%). Standard residential gable roofs usually fall between 20° and 35° (36.4%–70.0%). Steep or alpine roofs often reach 45° (100%) or more.
When does slope percent exceed 100%?
Slope percent crosses 100% at exactly 45°, where rise equals run. Any angle steeper than 45° produces a value over 100%, because the vertical rise is now larger than the horizontal run. For example, 60° gives 173.21%, and 75° gives 373.21%. Percentages above 100% are mathematically valid — they simply describe very steep inclines.
How do I convert slope percent back to degrees?
Switch the tab above to «Percent → Degrees». The math uses the inverse tangent: degrees = atan(percent / 100) × 180 / π. For instance, 25% returns about 14.04°, and 100% returns exactly 45°. Because atan has no upper limit, any positive percent maps to an angle below 90°.
What is the difference between slope percent and slope ratio?
Slope percent expresses rise as a percentage of run (rise ÷ run × 100). Slope ratio writes rise and run as two numbers separated by a colon, such as 1:12 — meaning one unit of rise per twelve units of run. A 1:12 ratio equals about 8.33% or 4.76°, commonly used for wheelchair ramps under the ADA guideline.
Enter an angle in degrees and get the slope as a percent, rise-to-run ratio, millimetres per metre, and inches per foot. The calculator uses the formula tan(theta) x 100 and handles values from 0 to 90 degrees. A few reference points: 5 degrees equals 8.75%, a standard 30-degree roof pitch gives 57.74%, and exactly 45 degrees equals 100% (rise equals run). Angles above 45 degrees produce values over 100%; at 90 degrees the slope becomes vertical and percent is infinite. Toggle the tab to go the other way and convert a percent back to degrees using the inverse tangent. Useful for roofers, ramp designers, surveyors, and anyone checking that a drainage gradient or accessibility ramp meets code.