Roof Pitch Calculator
Result
Roof area in square feet
- Roof area in square metres
- 99.71 m²
- Rafter length in feet
- 13.42 ft
- Rafter length in metres
- 4.09 m
- Pitch angle in degrees
- 26.57 °
- Pitch multiplier
- 1.1180
- Shingle bundles (no waste allowance)
- 33
Roof pitch calculator: give it a pitch written the way a drawing writes it — a rise per 12 inches of run, so 6:12 — together with the length and span of the roof plan, and it answers the three things you need before ordering anything. How steep the roof is in degrees, the pitch multiplier that turns plan area into roof area, and how long the rafters run. The roof area comes back in square feet and square metres, and the rafter length in feet and metres, because those two numbers are read by different people: the one cutting rafters and the one quoting the job. Roof form matters for exactly one of them. A gable roof's rafter spans half the building, a shed roof's rafter spans the whole run, so at the same pitch the shed rafter is twice as long — while the roof area is identical on both, because the plan area the roof covers is the same and the slope only stretches it. That is the part people get wrong, so the multiplier is printed as a number: 6:12 multiplies plan area by 1.118, 12:12 by 1.4142. Any roof slope up to 24:12 can be typed in, including the fractional pitches a drawing sometimes calls out, which the roofing calculator next door cannot do — there the pitch is a dropdown of the eight pitches that actually turn up on a materials list. Use this page to find out how steep and how big the roof is; use that one when the pitch is settled and you want bundles, squares and rolls.
Pitch, angle, multiplier and roof area
| Pitch (rise per 12 in) | Angle (degrees) | Multiplier | Roof area per 100 ft² of plan |
|---|---|---|---|
| 1 | 4.76 | 1.0035 | 100.3 |
| 2 | 9.46 | 1.0138 | 101.4 |
| 3 | 14.04 | 1.0308 | 103.1 |
| 4 | 18.43 | 1.0541 | 105.4 |
| 5 | 22.62 | 1.0833 | 108.3 |
| 6 | 26.57 | 1.118 | 111.8 |
| 7 | 30.26 | 1.1577 | 115.8 |
| 8 | 33.69 | 1.2019 | 120.2 |
| 9 | 36.87 | 1.25 | 125 |
| 10 | 39.81 | 1.3017 | 130.2 |
| 12 | 45 | 1.4142 | 141.4 |
The fourth column is the one to take away: whatever your plan measures, the roof over it is that many square feet for every 100 square feet of plan. 6:12 gives 111.8, 12:12 gives 141.4. The multiplier is √(144 + p²) ÷ 12, so the roof area can be worked out from the plan area alone — no trigonometry needed once you have read the row. Pitch is written here as a rise per 12 inches of run, which is how plans and shingle wrappers write it; a pitch of 12:12 is 45 degrees and its multiplier is exactly √2.
Formula
Roof area = length × span × M, where M = √(144 + pitch²) ÷ 12
- L
- Length of the roof plan, measured along the ridge, in feet
- S
- Span of the roof plan, eave to eave, in feet
- p
- Pitch written as a rise per 12 inches of run (6:12 means p = 6)
- M
- Pitch multiplier: the factor a plan area is stretched by when it is laid on the slope
- θ
- Pitch angle in degrees, arctan(p ÷ 12)
Use it once you know the roof plan and the pitch the drawings call out, and before you order or cut anything. The two numbers people mix up are the multiplier and the angle: a 6:12 roof is 26.57 degrees and stretches the plan by 1.118, which is a fifth of a square over a 1,000 square foot plan, while a 12:12 roof is 45 degrees and stretches it by √2 — a factor that shows up in the rafter length, the roof area and the material order together. If what you need is a slope reading for ground, a driveway or a drain run rather than a roof, the elevation grade calculator in this section does that with a rise and a run; if the pitch is already fixed and the question is how much shingle and underlayment to buy, the roofing calculator answers it and this page does not.
Worked examples
A 6:12 gable roof over a 40 ft by 24 ft plan
- Plan area: 40 × 24 = 960 square feet
- Multiplier: √(144 + 6²) ÷ 12 = √180 ÷ 12 = 13.4164 ÷ 12 = 1.118
- Roof area: 960 × 1.118 = 1,073 square feet (99.71 m²)
- Rafter, gable: the half span 12 ft × 1.118 = 13.42 ft (4.09 m)
- Angle: arctan(6 ÷ 12) = 26.57°
- Bundles, estimated at three bundles per square (100 ft²): 1,073 ÷ 100 = 10.73 squares, and 10.73 × 3 = 32.2 → 33 bundles
This is the default setting on the page, and 6:12 is the pitch you will meet on most house roofs in North America — steep enough to shed water, flat enough to walk. The bundle count is an estimate only: it assumes 3-tab shingles at three bundles to a square and allows nothing for the ridge, the valleys or the cuts around a chimney. Order from the roofing calculator.
The same pitch on a shed roof that spans 30 ft
- Multiplier: √(144 + 4²) ÷ 12 = √160 ÷ 12 = 12.6491 ÷ 12 = 1.0541
- Plan area: 40 × 30 = 1,200 square feet
- Roof area: 1,200 × 1.0541 = 1,265 square feet (117.51 m²)
- Rafter, shed: the whole span 30 ft × 1.0541 = 31.62 ft (9.64 m)
- Angle: arctan(4 ÷ 12) = 18.43°
Compare the rafter with the first example: a gentler pitch (4:12 against 6:12) still gives a much longer rafter, because a shed roof's rafter crosses the entire run instead of half of it. The roof area follows the plan size and the multiplier only — switch the roof form to gable on the page and the area does not move, only the rafter does.
A 12:12 roof (45 degrees) over a 30 ft by 20 ft plan
- Multiplier: √(144 + 12²) ÷ 12 = √288 ÷ 12 = 16.9706 ÷ 12 = 1.4142 — which is √2, because 12:12 is 45°
- Plan area: 30 × 20 = 600 square feet
- Roof area: 600 × 1.4142 = 849 square feet (78.83 m²)
- Rafter: the half span 10 ft × 1.4142 = 14.14 ft (4.31 m)
- Angle: arctan(12 ÷ 12) = 45°
12:12 is the steepest pitch on most charts and the arithmetic behind it is the easiest to remember: the multiplier is √2, so the roof is 41% bigger than the plan it covers. Above about 8:12 a roof is usually walked with fall protection rather than a ladder and hose, and the shingle count on this page is at its least reliable — cutting a steep roof wastes more.
Limitations
The geometry is exact — the multiplier, the angle, the rafter length and the roof area are trigonometry on a rectangle, and they assume the roof plan is a plain rectangle: a hip, a dormer, an L-shaped plan, a roof that steps in over the garage or a curved bay all need to be broken into rectangles and added up, and they will come out bigger than this page says. The rafter length is the slope length from the ridge to the eave plate, so it is the length of the cut member and not the length of the board you buy: it ignores the overhang past the wall, the birdsmouth notch, the ridge thickness and the fact that rafters are cut in pairs. The pitch itself is treated as a rise per 12 inches of run, which is how a drawing gives it — a pitch quoted as a percentage or as a ratio like 1:4 has to be converted before it is typed in. And the bundle figure is a rough estimate, not an order: it is 3-tab shingles at three bundles to a square, with nothing allowed for the ridge caps, the starter course, the valley metal or the waste around penetrations. Real packaging varies by a tenth either way between manufacturers and by more between profiles, so the count on the wrapper always wins over the count on this page.
Frequently asked questions
- What is a 6:12 roof pitch in degrees?
- 26.57 degrees. The rise per 12 inches of run is the tangent of the angle, so the angle is arctan(6 ÷ 12). The common pitches work out as 4:12 = 18.43°, 5:12 = 22.62°, 6:12 = 26.57°, 8:12 = 33.69°, 10:12 = 39.81° and 12:12 = 45°. The chart on this page lists the angle next to every pitch from 1:12 to 12:12 so you can read one off rather than reach for a calculator.
- How do I work out the roof area from the pitch?
- Multiply the plan area by the pitch multiplier, which is √(144 + p²) ÷ 12 for a pitch of p:12. A 6:12 roof stretches the plan by 1.118, so a 960 square foot plan is 1,073 square feet of roof; a 12:12 roof stretches it by 1.4142. The plan area is what the roof covers looking straight down — length along the ridge times the span from eave to eave, not the sloped measurement.
- Does the roof form change the area or only the rafter?
- Only the rafter. A gable roof and a shed roof covering the same plan cover the same area — the slope stretches both by the same multiplier. What changes is how far a single rafter runs: on a gable it crosses half the span from the ridge to the eave, on a shed roof it crosses the whole run from the high wall to the low one, so the shed rafter is twice as long at the same pitch.
- How long are the rafters for a 6:12 roof spanning 24 feet?
- 13.42 feet on a gable roof, measured along the slope from the ridge to where the rafter meets the wall plate. The half span is 12 feet and the multiplier is 1.118. It is not the length of board to buy: add the overhang past the wall, and allow for the birdsmouth notch, the ridge board and the fact that rafters are cut in pairs.
- Can I enter a pitch that is not a whole number?
- Yes, and that is the reason this page takes the pitch as a number rather than a dropdown. Drawings do call out pitches like 6.5:12 or 4.75:12, and the field takes anything from 0.25:12 up to 24:12 with two decimal places. The roofing calculator in this section takes the eight whole pitches that appear on materials lists instead, because there the pitch is one of several fields deciding a delivery.
- Is the bundle count on this page what I should order?
- No. It is an estimate at three bundles of 3-tab shingles per square, with nothing allowed for ridge caps, starter course, valley metal or the waste around vents and chimneys — and packaging varies by about a tenth between manufacturers. Use it to sanity-check a quote, then order from the roofing calculator, which takes the shingle profile, the underlayment and a wastage allowance and returns the count to write on the order.
References
- Approximate Conversions from U.S. Customary Measures to Metric — the chart behind the feet, inches and square feet figures used here — National Institute of Standards and Technology
- The International System of Units (SI) brochure — the metre, the square metre and the degree, the units the roof area and the pitch angle are reported in — Bureau International des Poids et Mesures (BIPM)