Roofing Calculator
Roofing Calculator works out Pitch and Rise per 12 in of run from How the roof size is given, How the pitch is given and Rise. The default figures on this page give squares to buy of 1.160; 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 4:12 -> slope factor = sqrt(4^2 + 12^2) / 12 = 1.054093
- Slope angle = atan(4/12) = 18.4349 deg (33.333% grade)
- Hip / valley factor = sqrt(4^2 + 2 x 12^2) / 12 = 1.452966
- Hip / valley rafter angle = atan(4 / (12 x sqrt(2))) = 13.2627 deg; seat cut = 90 - 18.4349 = 71.5651 deg
- Plan area 100 sq ft x 1.054093 = 105.41 sq ft of roof = 1.054 squares
- Waste 10%: 115.95 sq ft = 1.16 squares
- Bundles = ceil(1.16 squares x 3) = 4
- Underlayment = ceil(115.95 / 400) = 1 roll(s)
- Ridge + hip + valley = 10 ft -> ceil(10/20) = 1 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 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 Calculator
Enter How the roof size is given, How the pitch is given, Rise and Run. Pitch updates as you type, and “Use a worked example” loads checked figures you can adjust. 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.
4:12 pitch geometry example
With How the roof size is given: planArea, Footprint area: 100, Rise: 4, Run: 12, the calculator returns Slope (pitch) factor: 1.05409255, Roof angle: 18.4349488, Hip / valley factor: 1.45296631. This example is checked against an independent source in the test suite.
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 roof size is given, How the pitch is given, Rise, Run, Slope angle and Slope.
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
How do I calculate my roof angle?
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. Open “How this is worked out” beside the result to see each step for your own figures.
What pitch is a 22.5 degree roof?
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. On this page it is computed from How the roof size is given, How the pitch is given and Rise and shown as Pitch, Rise per 12 in of run and Slope (pitch) factor.
What is the typical roof pitch for a 34-degree roof?
On the figures this page opens with — rise 4, run 12 and footprint area 100 ft2 — the squares to buy is 1.16. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
How many degrees is a 4'12" roof slope?
It needs How the roof size is given, How the pitch is given, Rise, Run, Slope angle and Slope. Nothing else is required, and the figures stay in your browser.
What information do I need for the Roofing Calculator?
You need How the roof size is given, How the pitch is given, Rise, Run, Slope angle, Slope, Building length and Building width. The page opens with default figures that give squares to buy of 1.160, so you can see the scale before entering your own.
What does this Roofing 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.