Roofing Angles Calculator
Roofing angles calculator works out Pitch and Rise per 12 in of run from How the pitch is given, Rise and Run. The default figures on this page give squares to buy of 14.758; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
9 steps
- Pitch 6:12 -> slope factor = sqrt(6^2 + 12^2) / 12 = 1.118034
- Slope angle = atan(6/12) = 26.5651 deg (50% grade)
- Hip / valley factor = sqrt(6^2 + 2 x 12^2) / 12 = 1.5
- Hip / valley rafter angle = atan(6 / (12 x sqrt(2))) = 19.4712 deg; seat cut = 90 - 26.5651 = 63.4349 deg
- Plan area 1200 sq ft x 1.118034 = 1341.64 sq ft of roof = 13.416 squares
- Waste 10%: 1475.8 sq ft = 14.758 squares
- Bundles = ceil(14.758 squares x 3) = 45
- Underlayment = ceil(1475.8 / 400) = 4 roll(s)
- Ridge + hip + valley = 40 ft -> ceil(40/20) = 2 cap bundle(s)
Its 9 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
Keep this result
Save it, change one figure, then compare the two
The calculation stays free. Save this scenario, adjust one assumption, save that too, and put them side by side to see exactly what the change costs you. A free account keeps 5 scenarios and 2 comparisons; Personal makes both unlimited and adds exports and private links. Nothing is saved unless you press Save.
What the roofing angles calculator calculates
Derives roof pitch factor and slope angle, converts a building footprint into true roof area and roofing squares, and quantifies shingle bundles, underlayment, ridge cap, drip edge, fasteners and replacement cost.
How to use this roofing angles calculator
Enter How the pitch is given, Rise, Run and Slope angle. Pitch updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Pitch, Rise per 12 in of run and Slope (pitch) factor.
The method follows NRCA Roofing Manual: Steep-slope Roof Systems (roof area from plan area x slope factor; one square = 100 sq ft), 2021 International Residential Code Section R905.2, Asphalt shingles (slope limits, underlayment, minimum four fasteners per strip shingle in R905.2.5), ASTM D226/D226M, Standard Specification for Asphalt-Saturated Organic Felt Used in Roofing and Waterproofing (Type I #15 felt, 4 squares per roll) and ASTM D3462/D3462M, Standard Specification for Asphalt Shingles Made from Glass Felt and Surfaced with Mineral Granules.
What you can compare
Change one input at a time to see how it affects Pitch, Rise per 12 in of run and Slope (pitch) factor. The inputs you can vary are How the pitch is given, Rise, Run, Slope angle, Slope and Roof shape.
Understanding Pitch, Rise per 12 in of run and Slope (pitch) factor
Rafter, truss and sheathing sizing, and the ice-barrier, underlayment and fastening requirements for your wind zone, are set by the building code adopted locally and by the shingle manufacturer's installation instructions. Confirm quantities against a physical measure-up before ordering.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What information do I need for the roofing angles calculator?
You need How the pitch is given, Rise, Run, Slope angle, Slope and Roof shape. The page opens with default figures that give squares to buy of 14.758, so you can see the scale before entering your own.
What does this roofing angles calculator show?
It shows Pitch, Rise per 12 in of run, Slope (pitch) factor, Roof angle, Slope, Hip / valley factor, Hip / valley rafter angle and Seat (level) cut angle, with the working and any warnings for your entries.
Can I check how the roofing angles calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.