Slope & gradient converter
A free slope percentage calculator that converts between percent grade, ratio 1:n, degrees and rise-over-run — all from the single relation tan θ = rise ÷ run.
Enter a slope in whichever form you have — a road grade, a 1:12 ramp ratio, an angle, or measured rise and run — and read the other three instantly. Pure geometry, computed in your browser.
Enter one slope value
Grade as a percentage — e.g. an 8% road grade rises 8 m over 100 m run.
Slope (grade)
8%
4.57° from the horizontal
As a ratio
1 : 12.5
Percent
8%
Degrees
4.57°
Ratio 1:n
1:12.5
Rise per 100 m
8 m
| Definition | tan θ = rise ÷ run |
| Percent grade | 100 × tan(4.57°) = 8% |
| Angle | atan(8 ÷ 100) = 4.574° |
| Ratio (run per rise) | 1 : 12.5 |
| Rise per metre of run | 0.08 m |
Slope, grade, gradient and pitch all describe the same geometry. “Percent grade” is the rise as a percentage of the horizontal run — not the angle. A 45° slope is therefore 100%, not 50%. Computed in your browser; no rounding beyond what is shown.
One angle, four ways to write it
Every slope is just a vertical rise over a horizontal run. Fix that ratio and the percent, the angle and the 1:n form all follow from it.
Rise over run
Start from rise ÷ run — the vertical height gained divided by the horizontal distance covered.
Percent & ratio
Percent grade = 100 × rise ÷ run; the ratio 1:n uses n = run ÷ rise, so 8% ≈ 1:12.5.
Angle
The inclination is θ = arctan(rise ÷ run). A 100% grade equals 45°, since tan 45° = 1.
Slope & gradient, answered
How do you convert slope percentage to degrees?+
Percent grade is 100 × tan(θ), so to go the other way the angle is θ = arctan(grade ÷ 100). For example a 10% grade is arctan(0.10) ≈ 5.71°, and a 100% grade is arctan(1) = 45°. Percent and degrees are not the same scale — a 45° slope is 100%, not 50%.
What is the difference between slope percent, ratio and degrees?+
They are three ways of writing the same geometry. Percent grade is the rise as a percentage of the horizontal run (rise ÷ run × 100). A ratio 1:n means 1 unit of rise for every n units of run, so n = run ÷ rise. Degrees is the angle from the horizontal, where tan(θ) = rise ÷ run. This tool converts between all of them.
How is rise over run used to find slope?+
Rise is the vertical height gained and run is the horizontal distance covered. The slope is simply rise ÷ run. Multiply by 100 for percent grade, take the arctangent for the angle in degrees, or divide run by rise for the 1:n ratio.
What does a 1:12 slope mean?+
A 1:12 ratio means the surface rises 1 unit for every 12 units of horizontal run — about 8.33% grade or 4.76°. It is a common maximum for accessible wheelchair ramps in many building guidelines; always confirm the requirement that applies to your project.
Is percent grade the same as the angle in degrees?+
No. Percent grade is the tangent of the angle expressed as a percentage, so the relationship is non-linear. Small slopes are close (5% ≈ 2.86°), but they diverge as the slope steepens: 50% is about 26.57°, and 100% is exactly 45°.
What slopes are typical for roads and drainage?+
Mountain highways often cap sustained grades in the region of 7–12% where terrain allows, while gravity drains and sewers usually need only a gentle fall of a fraction of a percent. Exact limits depend on the governing road or building standard, so treat any figure here as indicative and check the relevant code.
Sources & data note
Based purely on the trigonometric identity tan θ = rise ÷ run, with percent grade = 100·tan θ and the ratio 1:n where n = run ÷ rise. The conversions are exact; any road, ramp or drainage grade limits mentioned are indicative only — confirm the standard or building code that governs your project.