Slope Calculator
Slope is rise divided by run: a 30" rise over a 30' run is 8.33% (1:12, 4.76°), with a line length of 30' 1 1/4". That 1:12 slope is the steepest wheelchair ramp the ADA guideline allows (your local code rules), so every inch of rise needs a foot of run. Type any two of rise, run and slope (percent, degrees, ratio such as 1:12, or roof pitch) in feet and inches or metric, and the calculator finds the third, the angle and the line length.
Updated Runs in your browser: nothing you enter is uploadedHow this tool works
Rise 30" ÷ run 30' = 8.33% (1:12, 4.76°)
8.33% (1:12, 4.76°)
Line length is shown to the nearest 1/16 inch; the exact length is ≈ 361.2478 in.
- Rise
- 2' 6" (762 mm)
- Run
- 30' 0" (9,144 mm)
- Line length
- 30' 1 1/4" (9,175.7 mm)
- Slope (percent grade)
- 8.33%
- Angle from level
- 4.76°
- Ratio (rise : run)
- 1:12
- Roof pitch
- 1 in 12
- Rise per foot of run
- 1"
- Rise per meter of run
- 83.33 mm
Common DIY slopes: ramp, drainage, gutter, stairs
| Use | Ratio (rise : run) | Percent | Angle | Rise per foot of run |
|---|---|---|---|---|
| Wheelchair ramp, the steepest the ADA guideline allows | 1:12 | 8.33% | 4.76° | 1" |
| Walkway that is not counted as a ramp (ADA guideline) | 1:20 | 5% | 2.86° | ≈ 5/8" (0.6 in) |
| Patio, walkway or slab drainage, 1/4" per foot (also the ADA cross-slope limit) | 1:48 | 2.08% | 1.19° | 1/4" |
| Ground next to the house, 6" in the first 10 ft (a common code figure) | 1:20 | 5% | 2.86° | ≈ 5/8" (0.6 in) |
| Gutter, 1/4" per 10 ft | 1:480 | 0.21% | 0.12° | 0.025 in |
| Typical stair, 7" rise and 11" run | 1:1.57 | 63.64% | 32.47° | ≈ 7 5/8" (7.636 in) |
Roof pitch to degrees and percent
| Roof pitch | Percent | Angle | Ratio (rise : run) | Line length per 12" of run |
|---|---|---|---|---|
| 1 in 12 | 8.33% | 4.76° | 1:12 | 12 1/16" (1.003 × the run) |
| 2 in 12 | 16.67% | 9.46° | 1:6 | 12 3/16" (1.014 × the run) |
| 3 in 12 | 25% | 14.04° | 1:4 | 12 3/8" (1.031 × the run) |
| 4 in 12 | 33.33% | 18.43° | 1:3 | 12 5/8" (1.054 × the run) |
| 5 in 12 | 41.67% | 22.62° | 1:2.4 | 13" (1.083 × the run) |
| 6 in 12 | 50% | 26.57° | 1:2 | 13 7/16" (1.118 × the run) |
| 7 in 12 | 58.33% | 30.26° | 1:1.71 | 13 7/8" (1.158 × the run) |
| 8 in 12 | 66.67% | 33.69° | 1:1.5 | 14 7/16" (1.202 × the run) |
| 9 in 12 | 75% | 36.87° | 1:1.33 | 15" (1.25 × the run) |
| 10 in 12 | 83.33% | 39.81° | 1:1.2 | 15 5/8" (1.302 × the run) |
| 11 in 12 | 91.67% | 42.51° | 1:1.09 | 16 1/4" (1.357 × the run) |
| 12 in 12 | 100% | 45° | 1:1 | 17" (1.414 × the run) |
How long a ramp needs to be for a given rise
| Rise | Run at 1:12 | Run at 1:16 | Run at 1:20 |
|---|---|---|---|
| 2" | 2' 0" | 2' 8" | 3' 4" |
| 4" | 4' 0" | 5' 4" | 6' 8" |
| 6" | 6' 0" | 8' 0" | 10' 0" |
| 8" | 8' 0" | 10' 8" | 13' 4" |
| 12" | 12' 0" | 16' 0" | 20' 0" |
| 18" | 18' 0" | 24' 0" | 30' 0" |
| 24" | 24' 0" | 32' 0" | 40' 0" |
| 30" | 30' 0" | 40' 0" | 50' 0" |
How much drop for a run: gutters, patios and the ground by the house
| Run | Gutter, 1/4" per 10 ft | Patio, 1/4" per foot | Ground, 6" per 10 ft |
|---|---|---|---|
| 5 ft | 1/8" | 1 1/4" | 3" |
| 10 ft | 1/4" | 2 1/2" | 6" |
| 15 ft | 3/8" | 3 3/4" | 9" |
| 20 ft | 1/2" | 5" | 1' 0" |
| 30 ft | 3/4" | 7 1/2" | 1' 6" |
| 40 ft | 1" | 10" | 2' 0" |
| 50 ft | 1 1/4" | 1' 1/2" | 2' 6" |
How to work out a slope by hand
- Measure the rise and the run. Rise is how far the surface goes up (or down), measured straight up. Run is the level distance across, not the length along the slope. Use the same unit for both.
- Divide rise by run. 30 inches of rise over a 30 foot (360 inch) run is 30 ÷ 360 = 0.0833, which is 1 up for every 12 across: a 1:12 ratio.
- Multiply by 100 for percent. 0.0833 × 100 = 8.33%. A 100% slope rises as much as it runs.
- Take the arctangent for degrees. The angle is the arctangent of rise ÷ run: arctan(0.0833) = 4.76°. A 100% slope is 45°.
- Find the line length with Pythagoras. The sloped line is the square root of rise² + run²: √(30² + 360²) = 30' 1 1/4" rounded to 1/16 inch.
Frequently asked questions
- How do you calculate slope from rise and run?
- Divide the rise by the run. A 30" rise over a 30' run is 30 ÷ 360 = 0.0833. As a percent that is 8.33%, as an angle 4.76°, and as a ratio 1:12. Use the level run, not the length along the slope.
- How do you convert slope percent to degrees?
- Take the arctangent of the percent divided by 100. 8.33% is arctan(0.0833) = 4.76°, and 100% is 45°. Percent and degrees are not proportional: 50% is 26.57°, not 22.5°. Going the other way, degrees to percent is the tangent × 100.
- What slope is a wheelchair ramp?
- The ADA Standards set the maximum ramp slope at 1:12 (8.33%, 4.76°): 1 inch of rise needs 12 inches of run. A 24" rise needs 24' 0" of run, and in metric a 760 mm rise needs 9,120 mm. That is a guideline for the US: the ADA also limits how much rise one ramp run may have and calls for landings, and your local building code and inspector decide what applies to your project. Gentler is easier to use.
- How much slope does a patio need for drainage?
- A common rule is 1/4" of drop per foot, away from the house: 1:48, about 2.08%, 1.19°. Over a 10 ft patio that is 2 1/2". Guides differ (some accept less, wet climates ask for more), so check what your paver, slab or drain manufacturer and your local code say.
- How much slope do gutters need?
- Gutters are usually pitched about 1/4" for every 10 ft toward the downspout: 1:480, 0.21%. A 40 ft gutter run drops 1" from the high end to the downspout, and a long run is often split with a downspout at each end so the drop stays small. Follow the gutter maker's instructions if they differ.
- How do I convert roof pitch to degrees?
- Roof pitch is rise in inches per 12 inches of run, so take the arctangent of pitch ÷ 12. A 6 in 12 roof is 26.57° and 50%, and every 12 ft of run adds 6' 0" of rise. A 4 in 12 roof is 18.43°, and 12 in 12 is 45°. The roof pitch table above lists all twelve.
- What is the difference between rise, run and line length?
- Rise is the vertical change and run is the horizontal distance; line length (the hypotenuse) is the distance along the slope, √(rise² + run²). It is what you cut for a ramp surface, a rafter or a drain pipe. For a 7" rise over an 11" run (a typical stair) the line is 1' 1 1/16" and the angle 32.47°.
- Does the ratio 1:12 mean 1 up for 12 across?
- Yes: the first number is the rise and the second the run, so 1:12 goes up 1 for every 12 across. Some people write it 1/12 or "1 in 12" and a few write it the other way round (12:1), so check which is meant. Choose the ratio format for "1:12" and the roof pitch format for "6 in 12".
- Does the slope calculator work in metric?
- Yes. Type lengths such as 760 mm, 76 cm or 0.76 m, or pick millimeters, centimeters or meters under "Plain numbers are" and type just 760. A 760 mm rise at 1:12 needs a run of 9,120 mm (29' 11 1/16"). Feet and inches are read too, and both are shown in the results.
How it works
Slope is rise ÷ run. Percent is that × 100, the angle is its arctangent in degrees, the ratio is 1 : (run ÷ rise) and roof pitch is rise per 12 inches of run. The line length is √(rise² + run²). Lengths you type are read as exact fractions of an inch (feet are 12 inches; metric uses 1 inch = 25.4 mm exactly), so 30' 0" is exactly 360 inches. Lengths are shown in feet, inches and a fraction rounded to the nearest 1/16 inch, with millimetres alongside; the difference from the exact length is stated under the answer. Percent, angle, ratio and pitch are rounded to two decimals. A run of 0 (a vertical wall) has no slope and is refused, as are slopes steeper than 10,000 up per 1 across. Rise is measured straight up and run along the level, not along the sloped surface. The ramp, drainage and gutter figures are common guidelines, not code: the ADA Standards apply to accessible routes and your local building code applies to your project. Everything runs in your browser.
Sources
- 2010 ADA Standards for Accessible Design, section 405 Ramps (maximum running slope 1:12)
- International Residential Code, section R401.3 Drainage (6 inches of fall in the first 10 feet away from the foundation)
- NIST Special Publication 811 (1 inch = 2.54 cm exactly)
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