Roofing
Roof Pitch Calculator
Convert between rise over run, degrees and the pitch multiplier used to turn footprint into actual roof area.
Result
Roof pitch is conventionally expressed as rise over a 12-inch run. The slope multiplier converts a flat footprint into true surface area. It is the number most area errors come from ignoring.
Get a Free Business AuditHow the calculation works
Pitch is the vertical rise over twelve inches of horizontal run, so a 6/12 roof climbs six inches for every foot travelled. The sloped length of that run is the hypotenuse of the triangle, which is the square root of the rise squared plus the run squared. Divide that by the run and you have the pitch multiplier: the number you multiply flat footprint by to get true roof area. A 6/12 roof gives roughly 1.12, so a hundred square feet of footprint is about 112 square feet of roof.
What moves the number
- Rise over twelve inches of run, which is how pitch is expressed on a quote.
- The multiplier that converts flat footprint into sloped area.
- Whether the pitch changes across the roof, which is common on additions.
Where this one goes wrong
Measuring one plane and applying its pitch to the whole roof. Additions, dormers and porches frequently run at a different pitch, and material ordered from a single figure comes up short.
Before you quote
- Pitch on every plane, not just the main one.
- Whether the pitch pushes the job into steep-slope working, which changes labour and safety requirements.
- Whether the pitch suits the material being proposed, since low slopes rule some products out.
Where the rules come from
Questions
About this calculator
Why does pitch matter to the price?
It changes both quantity and labour. A steeper roof has more surface area over the same footprint, and above a certain pitch the crew needs staging and fall protection that slows everything down.
Can I measure pitch from the ground?
Approximately, from a gable end or with a photograph and a known reference. It is enough to plan with and not enough to order from.
Is there a minimum pitch for shingles?
Yes, and it is set by the manufacturer's installation instructions. Below their stated minimum the warranty does not apply, and low-slope areas need a different product or a different detail.
The formula
slope multiplier = √(1 + (rise ÷ run)²); angle = arctan(rise ÷ run)
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How to use this calculator
- Rise (inches) (in). Enter your own figure; the page starts at 6 in.
- Run (inches) (in). Enter your own figure; the page starts at 12 in.
The result updates as you type, so you can try a figure, see what it does to pitch, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| Rise (inches) | 6 in |
| Run (inches) | 12 in |
What comes out
| Result | Value |
|---|---|
| Pitch main result | 6/12 |
| Angle in degrees | 26.5651 |
| Slope multiplier | 1.118 |
| Slope as a percentage | 50.00% |
A 6/12 pitch is 26.5651°. Multiply the building footprint by 1.118 to get the actual roof surface area.
How sensitive the answer is
Holding everything else steady and changing only rise (inches), this is what happens to pitch. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| Rise (inches) (in) | Pitch |
|---|---|
| 3 in | 3/12 |
| 4.5 in | 4.5/12 |
| 6 in example above | 6/12 |
| 9 in | 9/12 |
| 12 in | 12/12 |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- Rise (inches) (in)
- Measured in in, between 0 and 48, starting at 6 in.
- Run (inches) (in)
- Measured in in, between 0 and 48, starting at 12 in.
What the results tell you
| Result | What it is |
|---|---|
| Pitch | The headline result. A category or planning selection, rather than a measured quantity. |
| Angle in degrees | A number. |
| Slope multiplier | A number. |
| Slope as a percentage | A percentage. |
What this cannot see
Material quantities assume a clean rectangular plane and the waste factor you enter. Valleys, hips, dormers, penetrations and a steep pitch all raise real waste, and a tear-off frequently uncovers decking that was not in the quote.
Keep going
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