Rise over run calculator
Enter a rise and a run and this reads the slope every way a jobsite needs it: as an x/12 pitch, an angle in degrees, a percent grade, and the diagonal length across the two. It is the right-triangle math the CutOnce app runs under its stair, roof, and rafter tools.
Updated
Enter both the way your tape reads: 3, 4, 10 ft, or 3-1/2 in. Rise and run can be any matching units; the ratio is what counts.
- Slope (x/12)
- 9/12
- Angle
- 36.87°
- Grade
- 75%
- Ratio (rise : run)
- 3 : 4
- Diagonal (same units)
- 5
What rise over run actually is
Rise is how far something goes up. Run is how far it goes out. Slope is the ratio between them, and every other way of naming a slope is just that one ratio dressed differently. Carpenters say it as rise per 12 in of run (a 6/12 roof). Surveyors and ramp codes say it as a percent (rise divided by run, times 100). A protractor says it in degrees. They are the same number, so this calculator solves the triangle once and shows all of them.
A worked example: the steepest legal ramp
A wheelchair ramp is capped at 1 in of rise for every 12 in of run. Say you have a 2 ft 6 in rise to clear. Here is the slope read four ways, and the ramp length it takes.
| Rise | 2 ft 6 in | given (the height to clear) |
| Run | 30 ft | given (30 ft of ramp on plan) |
| Slope | 1/12 | rise / run, read as x/12 |
| Angle | 4.76° | atan(rise / run) |
| Grade | 8.3% | rise / run x 100 |
| Diagonal | 30 ft 1-1/4 in | sqrt(rise squared + run squared) |
That 8.3% grade is exactly the ADA and IRC ceiling for a ramp, 1:12. Anything steeper than 30 in of rise over 30 ft of run is over the line, and the fix is always more run, never a steeper slope.
Slope, angle, and grade side by side
The conversions people look up most, all derived from the same ratio the calculator uses. Read across: a 4/12 roof is the same slope as 18.4 degrees or a 33.3% grade.
| Pitch (x/12) | Angle | Grade |
|---|---|---|
| 0.5/12 | 2.39° | 4.2% |
| 1/12 | 4.76° | 8.3% |
| 2/12 | 9.46° | 16.7% |
| 3/12 | 14.04° | 25% |
| 4/12 | 18.43° | 33.3% |
| 6/12 | 26.57° | 50% |
| 8/12 | 33.69° | 66.7% |
| 12/12 | 45° | 100% |
Reading it off a framing square
The reason roof and stair slope is written over 12 is the framing square. Hold the square's 12 in mark (the body) level and read the rise on the tongue, and you have laid out the pitch without any math. That is why a 7/12 cut is set by pinching 7 and 12 on the square: the tool is a physical rise-over-run. This calculator gives you the degrees and grade for the same slope when you need to set a miter saw or check a ramp instead.
Ramps, grades, and the limits that apply
| Accessible ramp, maximum slope | 1:12 (8.3%) | IRC R311.8.1 / ADA |
| Ramp, steepest allowed where space is tight | 1:8 (12.5%) | IRC R311.8.1 exception |
| Handrail required on ramps steeper than | 1:12 (8.3%) | IRC R311.8.3 |
| Below 1:20 a surface is a walkway, not a ramp | 1:20 (5%) | IRC R311.8 |
| Roof, low-slope shingle minimum | 2:12 (9.5 degrees) | IRC R905.2.2 |
These are the residential defaults; your jurisdiction and the accessibility standard that applies can differ, so confirm locally before you pour a ramp or set a roof. The calculator does the geometry; it does not know which limit your project falls under.
Common questions
- How do I turn rise over run into degrees?
- Take the arctangent of the rise divided by the run. A 6 in rise over a 12 in run is atan(6/12) = atan(0.5) = 26.6 degrees. The calculator does it for you, but that is the whole conversion: degrees is just the angle whose tangent is your slope ratio.
- Is percent grade the same as the angle?
- No, and mixing them up is a common jobsite error. Grade is rise divided by run as a percent, so a 100% grade is a 45 degree angle, not 90. A 45 degree slope rises exactly as much as it runs, which is 1:1, which is 100%. Above 45 degrees the grade climbs past 100% fast while the angle only has 45 more degrees to go.
- Why is roof and stair slope written as x/12?
- Because of the framing square. Twelve inches is the fixed run on the square's body, so a slope written over 12 is read straight off the tool with no conversion. It also makes rafter and stair layout portable: a 7/12 pitch lays out the same whether the run is 3 ft or 30.
- What run do I use for a road or driveway grade?
- The horizontal run, measured level, not the distance along the slope. A 10 ft rise over 100 ft of level run is a 10% grade. If you measured 100 ft along the sloped surface instead, the true run is a hair shorter and the grade a hair higher, which is why survey grades always use the level run.
- Can I use feet for one input and inches for the other?
- Put both in the same unit and the ratio comes out right. This calculator reads feet-inch entries and normalizes them, so 2 ft 6 in over 30 ft is handled correctly, but if you type bare numbers, keep them in matching units or the slope will be off by a factor of twelve.
The triangle under every cut
Rise over run is the engine inside the app's stair, rafter, roof-pitch, and hip-and-valley tools. Enter a slope once and CutOnce carries it through the whole layout, then prints the plan with the framing-square settings on it.
Free to download, with a 7-day trial of everything. The web calculator is the teaser; the app draws the plan.
See also