How this works
Roof pitch is the steepness of a roof, expressed in three roughly equivalent ways depending on who's talking. American carpenters and roofers say it as "rise over run" with a 12-inch run — a "6:12 pitch" means 6 inches of vertical rise per 12 inches of horizontal run. Architects and engineers usually quote the angle in degrees: a 6:12 pitch is 26.57°. Civil engineering and ramps use percentage: rise/run × 100, so 6:12 is 50%. All three describe the same slope; the calculator above converts between them in either direction.
The fourth number that matters for materials is the slope multiplier (also called the "slope factor" or "rafter multiplier"): √(rise² + run²) / run. It tells you how much MORE area the actual roof surface has than the floor footprint below. A 6:12 roof has a slope multiplier of 1.118 — so a house with a 1,000 sq ft footprint has 1,118 sq ft of roof surface to cover with shingles. For 12:12 (45°) the multiplier is 1.414 — almost 42% more material. This is the number that catches DIYers who size shingles or metal panels off the floor area: every roof is bigger than the building it sits on, and steeper roofs are dramatically bigger.
A few practical points. (1) "Pitch" in some older British and European usage means the same as "slope multiplier" rather than rise/run — context matters when reading old plans. (2) Common residential roof pitches: 4:12 to 8:12 for typical American suburban homes; 9:12 to 12:12 for steep traditional roofs and snow country; 1:12 to 3:12 for low-slope roofs that need different (membrane rather than shingle) materials. Below 2:12 most asphalt shingle warranties become void — a hard cutoff that catches a lot of DIY shed builders. (3) Walkability drops fast with pitch: 6:12 is fine to walk; 9:12 needs roof brackets or a harness; 12:12 you're basically rock-climbing. Plan accordingly when buying ladders and safety equipment.
The formula
Rise and run can be entered in any consistent unit (the calculator uses inches by default but the math is unit-agnostic — only the ratio matters). The slope multiplier is what you use to size shingles, metal panels, underlayment and any roof-area-priced material. Building footprint area in the calculator is optional; entering it computes the roof area for you so you don't have to multiply by hand.
Example calculation
- Roof pitch: 6:12 — six inches of rise per twelve of run.
- Angle = atan(6/12) × 180/π ≈ 26.57°. Percentage = (6/12) × 100 = 50%.
- Slope multiplier = √(36+144)/12 = √180/12 ≈ 1.118. So a 1,500 sq ft footprint = ~1,677 sq ft of roof.
Frequently asked questions
What pitch is right for my project?
Match it to climate, material and aesthetic. For asphalt-shingle American suburban roofs, 4:12 to 8:12 is the standard sweet spot — steep enough for shingles to shed water reliably and shallow enough to walk for maintenance. In snow country (interior US Northeast, Alpine Europe, mountainous Japan), 9:12 to 12:12 sheds snow rather than letting it accumulate to dangerous loads. For sheds, garages, and shop roofs where you want to fit them under existing eaves, 3:12 is a common low-end with metal roofing rather than asphalt. Below 2:12 you're into membrane territory (TPO, EPDM) — different materials entirely and usually a professional install. Aesthetically, 5:12 to 7:12 reads "modern", 8:12 to 10:12 reads "traditional", 12:12+ reads "Victorian / chalet".
How do I size shingles or metal panels from this?
Multiply your floor footprint by the slope multiplier to get actual roof area, then divide by the per-bundle or per-panel coverage and add 10-15% waste. Asphalt shingles cover ~33 sq ft per bundle, so a 1,118 sq ft 6:12 roof needs 1,118 / 33 × 1.10 ≈ 38 bundles. Metal panels are sold by length (matching your rafter length) — slope multiplier × run length gives you the rafter length you need to order. Don't forget hips, valleys, and ridges add to the count: starter strip and ridge cap typically add another 10-15% of roof-edge linear footage in shingle equivalents. The slope multiplier captures the area math, but the linear extras still need separate counting.
Why are some pitches given as a single number (e.g. "30°")?
Outside the US, angle in degrees is the standard way to express pitch — UK building regulations, EU technical drawings, and Japanese 勾配 (kōbai) all default to degrees. The American "rise:run" convention is specific to North American carpentry tradition and shows up almost nowhere else. So if you're reading non-US plans and see "pitch 30°" or "pente 30°" without further qualifier, it's the angle, not 30:12. The rule of thumb: 30° ≈ 7:12, 45° = 12:12 (the steepest "common" residential pitch), 60° ≈ 21:12 (rare, mostly steeple/spire territory). The calculator above accepts any of the three notations and converts in either direction.