Roof Pitch & Slope Calculator
US Roof Pitch Chart (1:12 to 18:12): Angle, Grade, Multiplier & Rafter per Foot
Click any row below to load that roof pitch into the calculator.
| Roof Pitch (X:12) | Angle (°) | Slope Grade (%) | Roof Area Multiplier | Common Rafter / ft Run | Hip/Valley / ft Run |
|---|
Roof Pitch, Slope & Rafter Length Formulas
In the United States, roof steepness is expressed as pitch ($X:12$)—the number of vertical inches the roof rises for every 12 inches (1 foot) of horizontal run. Carpenters, roofers, and structural engineers use this ratio to lay out common and hip rafters with a framing square and to convert flat building footprints into actual sloped roof area (measured in 100 sq ft roofing squares).
Core Carpentry & Trigonometric Equations
- Pitch ($X:12$) from Rise and Run:
X = (Total Rise ÷ Total Run) × 12 - Roof Angle in Degrees ($\theta$):
θ = arctan(X ÷ 12) × (180 ÷ π) - Slope Grade Percentage (%):
Grade (%) = (X ÷ 12) × 100% - Roof Pitch Multiplier (Secant of $\theta$):
Multiplier = √[1 + (X ÷ 12)²] = √(144 + X²) ÷ 12 - Common Rafter Length (Pythagorean Theorem):
Rafter Length = √(Run² + Rise²) = Run × Multiplier - Hip / Valley Rafter Factor (90° Corner):
Because the diagonal run of a 12" × 12" corner unit is $\sqrt{12^2 + 12^2} = \sqrt{288} \approx 16.97"$, the hip multiplier is
√(288 + X²) ÷ 12.
Illustrative Worked Example (6:12 Gable Roof on a 24-Foot Wide Building)
A symmetrical gable roof spanning 24 feet has a horizontal run of 24 ÷ 2 = 12 feet (144"). At a 6:12 pitch, total vertical rise is 12 ft × (6 / 12) = 6 feet (72"). The roof angle is arctan(6 / 12) = 26.57° (50% grade).
The pitch multiplier for 6:12 is √(144 + 36) ÷ 12 = 1.1180. Multiplying 12 ft × 1.1180 = 13.416 ft (13' 5") from outer wall plate to ridge center. Adding a 16" horizontal eave overhang adds 16" × 1.1180 = 17-7/8" for a total rafter length of 14' 10-7/8" (order 16-foot lumber stock).
Frequently Asked Questions
What is the difference between roof run and building span?
Building span is the total exterior wall-to-wall width of the building, while horizontal run is the horizontal distance covered by a single rafter from the outer wall plate to the center ridge board. For a standard symmetrical gable roof, Run = Span ÷ 2.
What is the minimum roof pitch allowed for asphalt shingles?
Under the International Residential Code (IRC Section R905.2.2), asphalt shingles may only be installed on roof slopes of 2:12 (9.46°) or greater. Roofs between 2:12 and 4:12 require double-layer underlayment or a self-adhering ice-and-water membrane, while slopes of 4:12 (18.43°) and steeper use standard single underlayment.
How do I use the roof pitch multiplier to estimate roofing shingles?
Measure your building's flat ground footprint in square feet (including eave and gable overhangs) and multiply by the Roof Area Multiplier. For example, a 1,500 sq ft flat footprint with a 6:12 pitch (1.1180 multiplier) equals 1,500 × 1.1180 = 1,677 sq ft of sloped roof surface, or 16.77 roofing squares before waste.
At what pitch is a roof considered non-walkable?
Most roofers classify pitches up to 7:12 (30.26°) as walkable with proper high-traction footwear. Pitches of 8:12 (33.69°) and steeper generally require roof jacks, toe-boards, and personal fall arrest systems.