🏠 Roof Pitch Calculator
By ToolNimba Construction Team · Updated 2026-06-19
Enter the rise and run to find the roof pitch, angle, and rafter length.
Roof pitch is how steep a roof is, written as the rise (vertical height) for every 12 units of run (horizontal distance). Enter your rise and run and this calculator returns the pitch in the standard x-in-12 notation, the slope angle in degrees, the slope as a percent, and the rafter length you need per unit of run. It is handy whether you are framing a new roof, ordering shingles, or just trying to read a builder's plan.
What is the Roof Pitch Calculator?
Roof pitch describes the steepness of a roof as a ratio of vertical rise to horizontal run. In North American framing the run is fixed at 12, so a roof that climbs 6 units of height over 12 units of horizontal distance is a "6 in 12" pitch, often written 6:12 or 6/12. The 12 is not inches in any literal sense, it is just the agreed-upon base, so a 6:12 pitch and a 1:2 ratio are the same slope expressed two ways. The rise is always the first number and the run the second.
The slope angle is what a protractor would read at the eaves, and it comes straight from trigonometry: angle = arctan(rise ÷ run). A 6:12 pitch works out to arctan(0.5) = 26.57 degrees, while a 12:12 pitch is a perfect 45 degrees because the rise equals the run. Slope is also sometimes given as a percent, which is simply rise ÷ run x 100, so 6:12 is a 50% slope. These are three names for one quantity: the x-in-12 number, the angle, and the percent all describe exactly the same steepness.
The last piece builders care about is rafter length, the sloping distance a rafter actually spans. Because the rafter is the hypotenuse of a right triangle whose legs are the rise and run, its length is sqrt(rise² + run²) by the Pythagorean theorem. For a 6:12 pitch the rafter covers sqrt(6² + 12²) = sqrt(180) = 13.42 units for every 12 units of run, or about 1.118 units of rafter per unit of horizontal run. Multiplying that factor by the building's horizontal span gives the rough rafter length before you add overhang and account for the ridge.
When to use it
- Converting a roof pitch like 4:12 into a degree angle so you can set a saw or read a plan.
- Estimating rafter length from the building span before buying lumber.
- Checking whether a roof is steep enough for a given shingle or low-slope membrane product.
- Comparing two roof designs by their slope angle, percent, or x-in-12 pitch.
- Working backward from a measured angle to the x-in-12 pitch a contractor will recognize.
How to use the Roof Pitch Calculator
- Enter the rise, the vertical height the roof climbs.
- Enter the run, the horizontal distance over which it climbs (use 12 for standard x-in-12 pitch).
- Read off the pitch in x-in-12 notation, the slope angle in degrees, and the slope percent.
- Use the rafter length per unit of run, or the total over your run, to estimate lumber.
- Tap a preset like 6:12 to load a common pitch instantly.
Formula & method
Worked examples
A roof rises 6 units over a run of 12 (a 6:12 pitch).
- ratio = rise ÷ run = 6 ÷ 12 = 0.5
- x-in-12 = 0.5 x 12 = 6, so the pitch is 6 in 12
- angle = arctan(0.5) = 26.57°
- slope percent = 0.5 x 100 = 50%
- rafter over the run = sqrt(6² + 12²) = sqrt(180) = 13.42
Result: Pitch 6 in 12, angle 26.57°, slope 50%, rafter 13.42 over the 12 run
A steeper roof rises 9 units over a run of 12 (a 9:12 pitch).
- ratio = 9 ÷ 12 = 0.75
- x-in-12 = 0.75 x 12 = 9, so the pitch is 9 in 12
- angle = arctan(0.75) = 36.87°
- slope percent = 0.75 x 100 = 75%
- rafter over the run = sqrt(9² + 12²) = sqrt(225) = 15.00
Result: Pitch 9 in 12, angle 36.87°, slope 75%, rafter 15.00 over the 12 run
Common roof pitches with angle, slope percent, and rafter length per unit of run
| Pitch (x in 12) | Angle (degrees) | Slope (percent) | Rafter per unit run |
|---|---|---|---|
| 2:12 | 9.46° | 16.67% | 1.0138 |
| 3:12 | 14.04° | 25.00% | 1.0308 |
| 4:12 | 18.43° | 33.33% | 1.0541 |
| 6:12 | 26.57° | 50.00% | 1.1180 |
| 8:12 | 33.69° | 66.67% | 1.2019 |
| 9:12 | 36.87° | 75.00% | 1.2500 |
| 12:12 | 45.00° | 100.00% | 1.4142 |
Roof slope ranges and typical use
| Category | Pitch range | Notes |
|---|---|---|
| Flat / low-slope | Under 2:12 | Needs a membrane (TPO, EPDM); shingles are not rated here |
| Conventional | 4:12 to 9:12 | Standard asphalt shingle range, easy to walk and frame |
| Steep-slope | 9:12 and above | Sheds snow and water well; harder and less safe to walk |
Common mistakes to avoid
- Reading the x-in-12 number as inches of length. A 6:12 pitch does not mean 6 inches of anything specific. The 12 is a fixed base for the ratio, so 6:12 simply means 6 units of rise for every 12 units of run. The pitch is a slope, not a measurement.
- Swapping rise and run. Rise is the vertical height and run is the horizontal distance, and rise always comes first. Entering them the wrong way round flips the slope, turning a gentle 4:12 into a very steep 12:4.
- Confusing rafter length with run. The run is the flat horizontal distance, while the rafter is the longer sloping member. On any pitched roof the rafter is always longer than the run, by the factor sqrt((rise/run)² + 1).
- Forgetting overhang and ridge in lumber estimates. The rafter length from this tool covers the run only. Real rafters also include the eave overhang and a small allowance at the ridge, so add those before cutting to length.
Glossary
- Rise
- The vertical height a roof gains, measured from the level of the eaves up toward the ridge.
- Run
- The horizontal distance over which the rise occurs, usually taken as half the building span. The standard base is 12.
- Pitch
- The steepness of a roof, expressed as rise over a run of 12, for example 6 in 12 (written 6:12 or 6/12).
- Slope angle
- The roof angle from horizontal in degrees, equal to arctan(rise ÷ run).
- Rafter
- The sloping structural member that runs from the wall plate to the ridge; its length is the hypotenuse sqrt(rise² + run²).
Frequently asked questions
What is roof pitch?
Roof pitch is the steepness of a roof, given as the vertical rise for every 12 units of horizontal run. A roof that rises 6 units over a run of 12 is a 6:12 (or "6 in 12") pitch. It is the same idea as a slope, just written in the convention roofers use.
How do I convert roof pitch to an angle in degrees?
Take the arctangent of rise divided by run: angle = arctan(rise ÷ run). For a 6:12 pitch that is arctan(6 ÷ 12) = arctan(0.5) = 26.57 degrees. This calculator does the conversion for you as soon as you enter the rise and run.
What does "rise over run" mean?
Rise over run is the ratio of how far a roof climbs vertically (rise) to how far it travels horizontally (run). It is the fraction that defines the slope, and multiplying it by 12 gives the familiar x-in-12 pitch notation.
How do I find the rafter length from the pitch?
The rafter is the hypotenuse of a right triangle with the rise and run as its legs, so rafter length = sqrt(rise² + run²). For a 6:12 pitch over a 12 run that is sqrt(180) = 13.42 units. Add overhang and ridge allowance for the real cut length.
What is a good roof pitch?
For asphalt shingles, a pitch between 4:12 and 9:12 is common and easy to work with. Below about 2:12 a roof is considered low-slope and needs a membrane rather than shingles, while 9:12 and steeper sheds water and snow well but is harder and less safe to walk.
Is a 12:12 pitch a 45 degree roof?
Yes. When the rise equals the run the triangle is symmetric, so a 12:12 pitch is exactly 45 degrees: arctan(12 ÷ 12) = arctan(1) = 45 degrees. It is one of the steepest pitches in common residential use.