Rise Over Run Calculator
Rise over run is slope: how far up divided by how far across. A 6 ft rise over a 12 ft run is 6/12, 50% or 26.57°. Enter any two measurements to get the rest, diagonal included.
Slope from rise and run
6/12 pitch
26.57° · 50% · 1 : 2 · diagonal 13.42 ft
A rise of 6 ft over a run of 12 ft is a 6/12 pitch: 26.57°, a 50% slope. The diagonal is 13.42 ft (13 ft 5 in).
- Rise6 ft
- Run12 ft
- Diagonal (rafter or hypotenuse)13.42 ft (13 ft 5 in)
- Pitch (rise per 12 of run)6/12
- Ratio (rise : run)1 : 2
- Percent slope (grade)50%
- Angle26.57°
The diagonal is the straight-line length along the slope, measured on the outside of the triangle. Rafters and ramps need extra for cuts, overhang and thickness; this is the geometry only.
Planning estimate, not a quote. Disclaimer
How rise over run works
Picture a right triangle. The run is the flat side, the distance across. The rise is the vertical side, the distance up. The diagonal is the slanted side that joins them: a roof rafter, a ramp surface or a stair stringer. Slope is the rise divided by the run, and every other way of writing a slope comes from that one number.
Pitch (x/12) = 12 × rise ÷ run
Percent grade = rise ÷ run × 100
Angle = arctan(rise ÷ run)
Ratio = 1 : (run ÷ rise)
Diagonal = √(rise² + run²) = run × √(12² + pitch²) ÷ 12
Example: a rise of 4 ft over a run of 10 ft gives a slope of 0.4. That is 4.8/12 as a roof pitch, a 40% grade, a ratio of 1 : 2.5 and an angle of 21.80°. The diagonal is √(4² + 10²) = 10.77 ft (10 ft 9¼ in).
Find the run or the rise instead
If you know the slope and one length, switch the calculator to Rise and slope or Run and slope. Type the slope the way you have it: as a roof pitch such as 6/12, a ratio such as 1:12, a percent or an angle in degrees.
- Run from rise and slope: a 3 ft rise at 30° needs a run of 5.20 ft (5 ft 2⅜ in), because run = rise ÷ tan(angle).
- Rise from run and slope: a 15 ft run at 8/12 climbs 10.00 ft, because rise = run × pitch ÷ 12.
Common slopes in every form
| Pitch | Percent | Ratio | Angle | Diagonal per 12 in of run |
|---|---|---|---|---|
| 1/12 | 8.3% | 1 : 12 | 4.76° | 12.04 in |
| 2/12 | 16.7% | 1 : 6 | 9.46° | 12.17 in |
| 3/12 | 25.0% | 1 : 4 | 14.04° | 12.37 in |
| 4/12 | 33.3% | 1 : 3 | 18.43° | 12.65 in |
| 6/12 | 50.0% | 1 : 2 | 26.57° | 13.42 in |
| 8/12 | 66.7% | 1 : 1.5 | 33.69° | 14.42 in |
| 9/12 | 75.0% | 1 : 1.33 | 36.87° | 15.00 in |
| 12/12 | 100.0% | 1 : 1 | 45.00° | 16.97 in |
The last column matches the rafter-per-foot figures printed on framing squares and in the Swanson Tool roof pitch reference (13.42 in for 6/12, 16.97 in for 12/12). See the roof pitch chart for every pitch from 1/12 to 18/12.
Where people use rise over run
- Roofing: roofers write slope as rise per 12 inches of run, so 6/12 means 6 inches up for every 12 across. The diagonal is the rafter length along the slope. Turn a pitch into roof area with the roof square calculator or the roof pitch calculator, and find rafter lengths with the rafter calculator.
- Ramps and stairs: the same triangle describes a ramp or a flight of stairs. Rise is the height to climb, run is the horizontal distance, and the diagonal is the ramp surface or stringer length. Rules for how steep a ramp or stair may be come from your local building code, so check it before you build.
- Grade: a path, driveway or yard slope is usually quoted as a percent. Enter the rise and run and read the percent grade, or type a percent and get the rise for a given run.
What the calculator does not do
It gives geometry only. The diagonal is the straight-line length along the outside of the triangle, so add extra for cuts, overhang and material thickness. A run of zero is a vertical wall with no defined slope, and 90° is vertical too, so those are rejected. Lengths are never stored or sent anywhere.
Frequently asked questions
What is rise over run?
The slope of a line: how far it goes up (the rise) divided by how far it goes across (the run). A line that rises 1 foot for every 4 feet across has a rise over run of 1/4, or 0.25.
How do you calculate rise over run?
Divide the rise by the run. 4 ft of rise over 10 ft of run is 0.4. Use the same unit for both, or the calculator converts feet, inches, centimeters and meters for you.
How do I convert rise over run to a percent?
Multiply the slope by 100. A rise of 6 over a run of 12 is 0.5, so the grade is 50%. A 100% grade is a 45° angle.
How do I convert rise over run to degrees?
Take the arctangent of rise ÷ run. A 6 over 12 slope is arctan(0.5) = 26.57°.
How do I find the diagonal (rafter) length?
Use the Pythagorean theorem: the diagonal is the square root of rise squared plus run squared. For a 4 ft rise and 10 ft run that is 10.77 ft, or 10 ft 9¼ in.
Is rise over run the same as roof pitch?
Roof pitch is rise over run with the run fixed at 12. A pitch of 6/12 and a rise over run of 6 ft per 12 ft are the same slope. If your run is not 12, multiply the rise by 12 and divide by the run to get the pitch.
How do I find the run from the rise and the angle?
Divide the rise by the tangent of the angle. A 3 ft rise at 30° gives a run of 5.20 ft.
Related
Other roofing calculators
Sources
- Swanson Tool: Roof pitch reference (rafter length per foot of run) (checked Nov 12, 2026)