Roof Pitch Calculator — Angle, Slope Factor & Rafter Length
Find your roof angle in degrees, the slope factor for estimating roofing materials, and the rafter length from a X:12 pitch or any rise-to-run ratio. Enter the building span to calculate actual rafter length in feet.
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Pitch 6:12 — slope factor 1.118
- 1
Pitch ratio (rise ÷ run)
6 ÷ 12 = 0.5 - 2
Slope factor
√(1 + 0.5²) = 1.118Multiplies the flat footprint area to give the actual sloped roof surface. - 3
Roof angle
arctan(0.5) × 180 ÷ π = 26.57
How does this calculator work?
Roof angle = arctan(rise/run); slope factor = √(rise²+run²)/run. For a 6:12 pitch: angle ≈ 26.6°, slope factor ≈ 1.118. Actual rafter length = (building width / 2) × slope factor. Multiply the footprint area by the slope factor to estimate roofing material surface area (add 10–15% waste allowance).
Formula
How this is calculated
Roof pitch is traditionally expressed in the United States as a ratio X:12 — meaning X inches of rise for every 12 inches of horizontal run. A 6:12 pitch rises 6 inches for every foot of horizontal span, producing a 26.6° angle. In metric or non-standard notation, pitch can be expressed as rise:run in any consistent unit.
The slope factor (also called the "roof multiplier") is the ratio of rafter length to horizontal run: √(rise² + run²) / run. Multiply the footprint area of the roof by the slope factor to get the actual surface area that must be covered with shingles or tiles — an essential step for estimating materials. A 6:12 pitch has a slope factor of 1.118, meaning the sloped surface is 11.8% larger than the flat footprint.
The rafter length for a given building is the horizontal half-span (span ÷ 2) multiplied by the slope factor. This is the theoretical centreline length; add overhang and subtract half the ridge board thickness for a precise cut length. Rafters must also be checked for structural requirements — maximum span, species and grade of timber, and live/dead load — which this calculator does not cover.
Frequently asked questions
In North America, pitches between 4:12 and 9:12 (18.4°–36.9°) are most common for residential roofs. Pitches below 3:12 (14°) are considered "low slope" and require special waterproofing membranes rather than standard shingles. Pitches above 12:12 (45°) are steep-slope and require safety equipment to work on.
The slope factor tells you exactly: multiply the building footprint area by the slope factor to get actual roof surface area. A 12:12 pitch (45°, slope factor 1.414) requires 41% more shingles than the same footprint would suggest. Contractors add a waste factor (typically 10–15%) on top of this for cuts and overlaps.
No — the rafter length calculated here is based on the building half-span only. To include an overhang, add the horizontal overhang distance multiplied by the slope factor. Then subtract half the ridge board thickness (if the rafters meet at a ridge board) to get the final cut length measured along the rafter.
Also known as
TG we-Calculate Editorial Team. (2026). Roof Pitch Calculator — Angle, Slope Factor & Rafter Length [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/roof-pitch-calculator
TG we-Calculate Editorial Team. "Roof Pitch Calculator — Angle, Slope Factor & Rafter Length." TG we-Calculate. 2026. https://we-calculate.com/calculator/roof-pitch-calculator.
TG we-Calculate Editorial Team, "Roof Pitch Calculator — Angle, Slope Factor & Rafter Length," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/roof-pitch-calculator
@misc{wecalculate_roof_pitch_calculator, title = {Roof Pitch Calculator — Angle, Slope Factor & Rafter Length}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/roof-pitch-calculator}}, year = {2026}, note = {TG we-Calculate} }
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