Slope Converter
Convert a slope between degrees, percent grade, rise:run ratio, roof pitch, radians and per mille. Add a run length to get the rise, and compare with ramp, roof and road references.
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For 1:n enter n (12 for 1:12). For pitch enter the rise per 12 (4 for 4/12). Use a minus sign for downhill.
How to use the Slope Converter
- Enter the slope in any format: 8.33 percent, 12 for a 1:12 ratio, 4 for a 4/12 pitch, or an angle.
- Choose From and To; all other formats appear in the results.
- Add a run length (optional) to get the rise and the sloped length.
- Check the diagram and the closest common reference.
- Copy the results or download the reference table.
Slope formulas
All slope formats describe the same thing, the ratio of vertical rise to horizontal run. With g = rise ÷ run:
- Percent grade = g × 100
- Angle = atan(g) in degrees or radians; back again with g = tan(angle)
- Ratio 1:n: n = 1 ÷ g (run per one unit of rise)
- Pitch x/12: x = g × 12 (inches of rise per foot of run)
- Per mille = g × 1,000, used for railway gradients
- Sloped length = √(run² + rise²)
Example: a ramp that rises 30 in over 30 ft (360 in) has g = 30 ÷ 360 = 0.0833: 8.33%, 4.76°, 1:12 and 1/12 pitch.
Slope equivalents table
| Percent | Degrees | Ratio | Pitch | Inches per foot |
|---|---|---|---|---|
| 1% | 0.57° | 1:100 | 0.12/12 | 0.12 |
| 2% | 1.15° | 1:50 | 0.24/12 | 0.24 |
| 5% | 2.86° | 1:20 | 0.6/12 | 0.6 |
| 8.33% | 4.76° | 1:12 | 1/12 | 1 |
| 10% | 5.71° | 1:10 | 1.2/12 | 1.2 |
| 25% | 14.04° | 1:4 | 3/12 | 3 |
| 33.3% | 18.43° | 1:3 | 4/12 | 4 |
| 50% | 26.57° | 1:2 | 6/12 | 6 |
| 57.7% | 30° | 1:1.73 | 6.93/12 | 6.93 |
| 100% | 45° | 1:1 | 12/12 | 12 |
Which format do different trades use?
- Roads and trails: percent grade on signs; a "6% grade" drops 6 ft per 100 ft.
- Accessibility: ratios such as 1:12 for ramps and 1:48 for cross slopes.
- Roofing: pitch in inches per foot (4/12, 6/12).
- Plumbing and drainage: inches per foot (¼ in/ft) or percent.
- Surveying, geology and physics: degrees or radians.
Building codes change and vary by location. Treat the references as general guidance and check the code that applies to your project.
Frequently asked questions
How do I convert percent grade to degrees?
Divide the percent by 100 to get rise ÷ run, then take the arctangent: angle = atan(percent ÷ 100). A 10% grade is atan(0.10) = 5.71°. To go from degrees to percent, use percent = tan(angle) × 100.
Is a 100% slope vertical?
No. 100% means the rise equals the run, which is a 45° angle. A vertical wall has an infinite percent grade, because the run is zero.
What is a 1:12 slope in degrees and percent?
1:12 means 1 unit of rise for every 12 units of run: 1 ÷ 12 = 8.33%, which is atan(1/12) = 4.76°. It is the maximum slope for a wheelchair ramp under the ADA Standards for Accessible Design.
How do I convert roof pitch to degrees?
Pitch x/12 means x inches of rise per 12 inches of run. The angle is atan(x ÷ 12). A 4/12 roof is 18.43°, a 6/12 roof is 26.57° and a 12/12 roof is 45°.
What does ¼ inch per foot mean as a percent?
¼ inch of drop in 12 inches of run is 0.25 ÷ 12 = 2.08%, or about 1.19°. It is the same slope as 1:48, and as a pitch it is 0.25/12.
Why does doubling the percent not double the angle?
Percent grade is the tangent of the angle, and the tangent grows faster as the angle increases. 50% is 26.57°, but 100% is 45°, not 53°. For small slopes under about 10% the two scale almost in proportion.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.