Title: Roof pitch calculator | Cercha
Description: Convert roof rise and horizontal run to an angle, pitch multiplier, and rafter-length factor. Check the geometry before carrying it into a takeoff.
Canonical: https://cercha.pages.dev/tools/roof-pitch-calculator/
# Roof pitch calculator
You have a rise and horizontal run from a roof plan and need the angle or slope factor for your takeoff. Enter both measurements in inches. This calculator returns degrees, rise per twelve inches of run, and the factor that converts a horizontal length to a sloping length.
## Use the matching rise and run
Keep the two dimensions on the same roof segment. Run is horizontal distance, not the distance along the roof. [GAF defines roof slope](https://www.gaf.com/en-us/blog/your-home/how-to-measure-a-roofing-square-3faec381-6f6f-49ff-841f-114c59108f2a) as vertical rise for every twelve inches of horizontal run. A six-inch rise across a twelve-inch run is therefore a 6:12 slope.
You can enter another run length. The tool converts that ratio to the twelve-inch convention. For a triangle example with three inches of rise and four inches of run, it returns 9:12, an angle of 36.87 degrees, and a factor of 1.25. Its sloping segment is five inches long. These are geometry examples, not project dimensions.
## Read the factor before using it
The pitch multiplier and rafter-length factor are the same number here. Both divide the triangle’s sloping length by its horizontal run. The angle follows the inverse tangent of rise divided by run, using the [right-triangle relationships in OpenStax](https://openstax.org/books/precalculus-2e/pages/5-4-right-triangle-trigonometry).
Multiply a horizontal segment by the full factor before rounding your takeoff. The displayed slope length applies only to the segment you entered. It does not include a ridge deduction, seat cut, or an overhang you did not measure. Keep those details in the framing plan.
For a roof with several slopes, record each segment separately. Do not apply one segment’s factor to the entire roof without checking the plan. Open the formula disclosure to see the equations and the rounding rule beside the result.
## Keep geometry separate from sizing
Use this result to check numbers on your takeoff. Ask the project’s designer to resolve member size, span, loads, connections, and assembly questions. This calculator has no inputs for those decisions. A calculated angle also does not tell you whether a roofing product suits that slope.
## Check the inputs and results
| Planned input | Unit or rule |
| --- | --- |
| Rise | Nonnegative inches |
| Horizontal run | Positive inches for the same segment |
| Angle | arctan(rise ÷ run), converted to degrees |
| Rise per twelve inches | 12 × rise ÷ run |
| Length multiplier | √(1 + (rise ÷ run)²) |
| Sloping segment length | √(rise² + run²), in inches |
Use the same unit for rise and run, and keep run greater than zero. Keep each roof segment separate. This calculation adds no waste or order rounding.
## Carry the geometry into the roof scope
Enter rise and run in the same length unit. [NIST’s conversion table](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8) provides unit references. Keep degrees, the rise/run ratio, and the length multiplier labeled separately.
Use the [roof-truss parts guide](/guides/parts-of-a-roof-truss/) when discussing component boundaries. [APA’s framing reference](https://www.apawood.org/applications-systems/fully-sheathed-wall-systems/advanced-framing/) covers assembly choices; this geometry estimate does not select them.
Ask the [roofing sub](/trades/roofing/) about the selected covering using [PNNL’s asphalt-roof guidance](https://basc.pnnl.gov/resource-guides/asphalt-shingle-roofs). Keep roof-wall interfaces in a separate review with the [PNNL flashing reference](https://basc.pnnl.gov/resource-guides/step-and-kick-out-flashing-roof-wall-intersections).
Return to the [construction tools hub](/tools/) for the other quantity checks and printable records.
## Where Cercha fits
Use the Cercha app’s Search filters to find a framing or roofing trade by trade, ZIP code, and radius. Review the profile’s portfolio, then use Messages to discuss the scope you need checked. Keep the dimensions and the drawing reference with that conversation.
- Vertical rise (in): 6
- Horizontal run (in): 12
Rise per 12 in run (in): 6.000000; Angle (degrees): 26.565051; Estimated angle (degrees): 26.57; Pitch multiplier: 1.118034; Rafter-length factor: 1.118034; Segment slope length (in): 13.416408
## How this is calculated
Slope = rise ÷ run. Pitch per 12 = 12 × slope. Angle (degrees) = atan(slope) × 180 ÷ π. Pitch multiplier = rafter-length factor = √(1 + slope²). Segment slope length = run × multiplier.
Rise and run are inches on the same right triangle. Tangent is rise over run. The factor is the hypotenuse divided by horizontal run. The two factors are equal for a uniform slope. This is pure geometry.
Outputs show six decimals; the main angle shows two. No purchase ceiling is applied. Multiply lengths by the full factor before rounding.
Ordinary displays round half up: an exact halfway value rounds upward. Display rounding never changes the purchase ceiling.
[OpenStax: Precalculus 2e: Right Triangle Trigonometry](https://openstax.org/books/precalculus-2e/pages/5-4-right-triangle-trigonometry). Tangent is opposite divided by adjacent; the multiplier and length follow right-triangle geometry.
[GAF: How to Measure a Roofing Square](https://www.gaf.com/en-us/blog/your-home/how-to-measure-a-roofing-square-3faec381-6f6f-49ff-841f-114c59108f2a). Roof slope is vertical rise per 12 inches of horizontal run. Include overhangs in a roof takeoff.
Estimate only. Rise and run must describe the same segment. The slope length is a geometric line length. It excludes cuts, ridge deductions, seat geometry, and overhang choices. It does not size rafters or establish material eligibility.
Estimate only. No structural sizing, loads, spans, strengths, or code-compliance decisions are calculated.
Geometry estimate only. Enter rise and horizontal run for the same segment. This tool does not size rafters or select roof assemblies.
Print this calculator from the HTML page.
## Build your connections
[Ask about the beta]()
## Sources
1. Jay Abramson. (2021, December 21). *Precalculus 2e: Right Triangle Trigonometry*. OpenStax. https://openstax.org/books/precalculus-2e/pages/5-4-right-triangle-trigonometry
2. Annie Crawford. (2021, March 23). *How to Measure a Roofing Square*. GAF. https://www.gaf.com/en-us/blog/your-home/how-to-measure-a-roofing-square-3faec381-6f6f-49ff-841f-114c59108f2a
3. NIST. (2025, August 18). *Guide to the SI, Appendix B.8*. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8
4. APA: The Engineered Wood Association. (n.d.). *Advanced Framing*. Retrieved October 14, 2026, from https://www.apawood.org/applications-systems/fully-sheathed-wall-systems/advanced-framing/
5. Pacific Northwest National Laboratory. (n.d.). *Asphalt Shingle Roofs*. Building America Solution Center. Retrieved October 14, 2026, from https://basc.pnnl.gov/resource-guides/asphalt-shingle-roofs
6. Pacific Northwest National Laboratory. (n.d.). *Step and Kick-Out Flashing at Roof-Wall Intersections*. Building America Solution Center. Retrieved October 14, 2026, from https://basc.pnnl.gov/resource-guides/step-and-kick-out-flashing-roof-wall-intersections