This slope percentage calculator turns rise over run into percent slope, degrees, a 1:n ratio and roof pitch, and converts between slope angle and percent grade in both directions. It also returns the slope length, so you can check a roof pitch, a ramp or a drainage fall in one place — free, with no login and no upload.
Rise and run must use the same unit. Leave rise at 0 for a level surface.
Run must be greater than 0, and both values must be positive numbers.
Slope describes how much a surface rises for a given horizontal distance. Given a rise (vertical change) and a run (horizontal distance), the three common expressions of the same gradient are related by simple trigonometry:
Roof pitch is the rise measured over a fixed run of 12, written as x:12 — a convention from imperial construction practice. It is therefore just the percent slope recalculated against a run of 12, and a 1:12 slope is identical to a 1:12 roof pitch.
The slope length is the diagonal distance along the inclined surface. By
Pythagoras' theorem it equals √(rise² + run²). Note that percent slope and slope
length use different denominators: percent slope is based on the horizontal run, not on the
distance along the slope, which is a frequent source of error in quantity take-offs.
To convert degrees to percent slope or percent slope to degrees, the tool applies the inverse
relationship: percent = tan(angle) × 100 and angle = arctan(percent ÷ 100).
A 45-degree slope is therefore 100 percent, while an elevation grade of 5 percent is only
about 2.86 degrees — the two units diverge quickly as the angle rises.
Rise over run is the simplest definition of a slope: divide the vertical change (the rise) by the horizontal distance (the run). The quotient is the gradient as a decimal, and multiplying it by 100 gives the percent slope. A rise of 1 with a run of 12 is 0.0833, so 8.33 percent. Using a rise over run calculator saves re-entry, because the same three numbers produce a percentage, an angle in degrees, a 1:n ratio and a roof pitch in x:12 at once.
One caution: the run is always measured horizontally. If you substitute the slope length — the distance measured along the inclined surface — the percentage comes out too low, and the error grows with steepness. This is the most frequent mistake in drainage falls and in quantity take-offs.
A roof pitch calculator reports the same gradient in the units roofers use: the rise measured over a fixed run of 12, written as x:12. A 4:12 pitch rises 4 units for every 12 units of horizontal run, which is the same as 18.43 degrees or a 33.3 percent slope. Residential roofs commonly sit between 4:12 and 9:12; below 4:12 the roof is treated as low-slope and needs more careful waterproofing, and 2:12 is often quoted as the practical minimum for asphalt shingles.
Because pitch, degrees and percent all describe one angle, the calculator shows all three together, so you can match whichever figure appears on the drawing, the material datasheet or the building code.
Ramps are where slope percentage becomes a legal limit rather than a convenience. The ADA standard in the United States caps the running slope of a wheelchair ramp at 1:12 — one unit of rise for every 12 units of run — which equals 8.33 percent or 4.76 degrees. A ramp slope calculator lets you check a layout against that ceiling: enter the total rise and the available run, and a result above 8.33 percent tells you the ramp needs a longer run, a landing or a switchback.
The same 1:12 reference applies to kerb ramps and accessible routes, while a slope of 1:20 (5 percent) or flatter is generally treated as a walkway rather than a ramp. Always confirm the current edition of the governing code, since thresholds and exceptions are updated periodically.
In excavation, slope is a safety control. An excavation slope calculator checks whether a cut batter is stable for the soil present: firm clay or rock may stand at 1:1 (45 degrees, 100 percent), while loose sand, gravel or previously disturbed fill usually needs 1.5:1 (about 34 degrees, 67 percent) or flatter. Many jurisdictions require a protective system — sloping, shoring or a trench box — once a trench reaches 5 feet (1.5 m) in depth.
Enter the depth and the horizontal offset to get the working slope, then verify it against the applicable excavation standard, because the permitted batter depends on soil classification, moisture content and how long the excavation will stay open.
| Ratio | Percent | Angle | Roof pitch | Typical use |
|---|---|---|---|---|
| 1 : 48 | 2.08% | 1.19° | 0.25 : 12 | Minimum drainage fall for a large pipe |
| 1 : 12 | 8.33% | 4.76° | 1 : 12 | Wheelchair ramp, common minimum roof pitch |
| 1 : 8 | 12.50% | 7.13° | 1.5 : 12 | Steep drainage, short ramps |
| 1 : 6 | 16.67% | 9.46° | 2 : 12 | Minimum roof pitch for standard shingles |
| 1 : 5 | 20.00% | 11.31° | 2.4 : 12 | Gentle cut slope in soil |
| 1 : 4 | 25.00% | 14.04° | 3 : 12 | Low-slope roof |
| 1 : 3 | 33.33% | 18.43° | 4 : 12 | Common residential roof pitch |
| 1 : 2 | 50.00% | 26.57° | 6 : 12 | Retaining and embankment batter |
| 1 : 1 | 100.00% | 45.00° | 12 : 12 | Rock slope, steep roof |
Values are rounded for reference. Always confirm the governing requirement against the applicable design standard for your project.
Percent slope equals rise ÷ run × 100. A rise of 1 metre over a run of 12 metres is 8.33%.
Angle = arctan(percent ÷ 100). So 100% becomes arctan(1) = 45°. In reverse, percent = tan(angle) × 100.
One unit of rise for every 12 units of run — 8.33% or 4.76°. It is the standard ratio form for ramps and drainage, and equals a 1:12 roof pitch.
Roof pitch is the rise over 12 units of run, written x:12. A 4:12 pitch rises 4 units for every 12 units of horizontal run.
Slope length = √(rise² + run²), by Pythagoras' theorem — the diagonal distance along the slope, which is what you need when ordering roofing, pipe or fencing.
As a general guide: under 2% nearly level, 2–5% gentle, 5–10% moderate, 10–20% steep, above 20% very steep. Always check the applicable design standard, as acceptable limits vary by application.
Enter the rise and the horizontal run in the same unit. The slope percentage calculator divides the rise by the run and multiplies by 100, then shows the same gradient as an angle, a 1:n ratio and a roof pitch in x:12. Measure the run horizontally, not along the sloping surface.
The ADA standard caps a ramp's running slope at 1:12 — 8.33% or 4.76°. A slope of 1:20 (5%) or flatter is treated as a walkway rather than a ramp. Confirm the current edition of the governing code, as thresholds are updated periodically.
Rise over run is the vertical rise divided by the horizontal run — a slope of 1 in 4, written 1:4. Multiply by 100 to get the elevation grade: a rise of 1 over a run of 4 is 25 percent. The same gradient is 14.04 degrees and a roof pitch of 3:12.
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