Roof Pitch Calculator
Enter the rise per 12 inches of run (and the footprint area) to get the pitch angle, percent grade, rafter factor and the true sloped roof area for shingles and sheathing.
Last updated: 2026-09-22
How the calculation works
- Pitch notation (rise per 12) converts to angle via arctangent and to percent grade directly.
- The area factor is the hypotenuse ratio: for each horizontal foot of run, the roof surface spans √(1 + (rise/12)²) feet.
- Multiplying the plan-view footprint by this factor gives the actual shingle/sheathing area — what material orders need.
- The chart draws the slope line so the pitch is visible, not just numeric.
Formula
angle = atan(rise / 12) slope % = rise / 12 × 100 area_factor = √(12² + rise²) / 12 roof_area = footprint × area_factor rafter = run × area_factor
| Symbol | Meaning | Unit |
|---|---|---|
rise/12 | Pitch — vertical inches per 12 horizontal | in/in |
factor | Roof area multiplier (√(run² + rise²)/run) | — |
run | Horizontal distance (half the span) | ft or in |
Worked example
Interpreting the result
Shingles and sheathing are ordered by the sloped area — the factor here is the correction most do-it-yourself estimators forget, and it's 2% at 2/12 but 20% at 8/12 and 41% at 12/12. Steep pitches (8/12+) also add staging and labor cost per square. The rafter factor converts horizontal run to board length: take half the building span (plus overhang), multiply, and that's the rafter length before birdsmouth cuts.
Assumptions
- Gable or hip roof approximated as a single uniform pitch — valleys and hips add cutting waste, not area.
- Footprint measured to the outside of the wall plate line.
- Overhangs excluded — add their area (perimeter × overhang × factor) separately for orders.
Limitations
- Complex roofs (dormers, multiple pitches, gambrel) need per-surface takeoffs.
- Low-slope membranes and standing-seam systems have different waste factors than shingles.
- No snow/wind load implications — pitch selection for loads is a structural decision.
Why roofers think in 12s
Pitch-per-12 is a carpenter's convention that survives because a framing square is 12 inches on each leg — set the square on the rafter, mark 12 along the blade and the rise on the tongue, and the diagonal gives the true rafter line. No trigonometry needed on site. The convention also makes mental math possible: every 12 inches of run costs a predictable board length, and squares of shingles convert from footprint by a factor any estimator can carry in their head for common pitches. Metric markets use degrees or percent grade; when reading international drawings, a 30° roof is roughly 7/12 and a 25% grade is about 3/12.
Frequently asked questions
How do I convert roof pitch to degrees?
Take the arctangent of rise/12. A 6/12 pitch is atan(0.5) = 26.57°, a 12/12 is 45°, and a 4/12 is 18.43°. Roofers quote pitch; engineers quote degrees — this calculator shows both.
How much bigger is the roof than the footprint?
It depends on pitch: multiply by 1.014 at 2/12, 1.054 at 4/12, 1.118 at 6/12, 1.202 at 8/12, and 1.414 at 12/12. The calculator computes this factor exactly and applies it to your area.
What is the minimum pitch for shingles?
Standard asphalt shingles need 2:12 minimum, and between 2:12 and 4:12 manufacturers require double underlayment. Below 2:12 the roof must switch to a membrane system (modified bitumen, TPO) because shingles rely on slope to shed water.