Loading…
Calculate roof pitch, slope, angle, rafter length, area and material needs from rise and run.
Calculate roof pitch, slope, angle, rafter length, area and material needs from rise and run.
Enter values above and click Calculate — results will appear here with the formula explained.
Roof pitch is rise over run, usually expressed as X:12 (e.g., 6:12). Slope is rise/run as decimal, angle is arctangent in degrees. Rafter length is the hypotenuse of rise and run, scaled to your building width. A 6:12 pitch means 6 inches of rise per 12 inches of run, which is a 26.57° angle and 0.5 slope — the reference conversions worth memorizing are 4:12 ≈ 18.4°, 6:12 ≈ 26.6°, 8:12 ≈ 33.7° and 12:12 = 45°.
Pitch decides what the roof can do. Low slopes (below 4:12) shed water slowly and demand membrane or sealed-seam systems rather than standard shingles; most shingle manufacturers require at least 2:12 with special underlayment and fully endorse 4:12 and up. Steeper pitches shed snow and water faster but need more material, stronger fastening against wind uplift, and safety equipment for anyone walking them — up to 6:12 is generally walkable, 7:12–9:12 is steep work, and 10:12+ means harnesses and staging.
Snow country raises the stakes: flatter roofs accumulate drift loads that can exceed design capacity, while steep metal roofs shed snow in sudden slides that endanger entries and landscaping (snow guards exist for exactly this). Local building codes encode minimum pitches, live loads and fastening schedules for the region's weather history — this calculator handles geometry, but code compliance and structural sizing belong to the local code book and, for anything beyond a shed, a professional.
Material quantity follows area, and area follows pitch more than people expect. Steepening from 4:12 to 12:12 on the same footprint multiplies roof area by roughly 1.34× (the ratio of rafter factors 1.4142 ÷ 1.0541), which multiplies shingles, underlayment, flashing and labor with it. The waste factor input exists because cuts around valleys, hips, dormers and ridges consume real material: 5% suits simple gables, 10% is the common default, and 15% fits hip roofs and cut-up designs.
Rafter math is right-triangle geometry scaled to the building. The unit rafter — hypotenuse per 12 inches of run — times the horizontal run gives the rafter length before overhang; add the eave overhang (typically 12–24 inches horizontally, converted through the same triangle) for the full board length. Ridge boards, birdsmouth cuts and collar ties then come from framing tables, not from pitch alone — pitch gives the angles, span tables give the lumber sizes.
When comparing quotes, normalize by squares (1 square = 100 sq ft) of installed area including waste, and confirm each bidder's assumed pitch, overhang and waste match — a cheaper quote built on 5% waste versus a realistic 15% is not actually cheaper. Re-run this calculator with the contractor's numbers to verify the area behind the price before signing.
Calculate roof pitch, slope, angle, rafter length, area and material needs from rise and run. Formula: Pitch = rise:run. Example: 6 inches rise, 12 inches run = 6:12 pitch, 0.5 slope, 26.57°, 13.42-inch rafter per foot of run.
Roof pitch is rise over run, usually expressed as X:12 (e.g., 6:12). Slope is rise/run as decimal, angle is arctangent in degrees. Rafter length is the hypotenuse of rise and run, scaled to your building width. A 6:12 pitch means 6 inches of rise per 12 inches of run, which is a 26.57° angle and 0.5 slope — the reference conversions worth memorizing are 4:12 ≈ 18.4°, 6:12 ≈ 26.6°, 8:12 ≈ 33.7° and 12:12 = 45°.
Pitch decides what the roof can do. Low slopes (below 4:12) shed water slowly and demand membrane or sealed-seam systems rather than standard shingles; most shingle manufacturers require at least 2:12 with special underlayment and fully endorse 4:12 and up. Steeper pitches shed snow and water faster but need more material, stronger fastening against wind uplift, and safety equipment for anyone walking them — up to 6:12 is generally walkable, 7:12–9:12 is steep work, and 10:12+ means harnesses and staging.
Snow country raises the stakes: flatter roofs accumulate drift loads that can exceed design capacity, while steep metal roofs shed snow in sudden slides that endanger entries and landscaping (snow guards exist for exactly this). Local building codes encode minimum pitches, live loads and fastening schedules for the region's weather history — this calculator handles geometry, but code compliance and structural sizing belong to the local code book and, for anything beyond a shed, a professional.
Material quantity follows area, and area follows pitch more than people expect. Steepening from 4:12 to 12:12 on the same footprint multiplies roof area by roughly 1.34× (the ratio of rafter factors 1.4142 ÷ 1.0541), which multiplies shingles, underlayment, flashing and labor with it. The waste factor input exists because cuts around valleys, hips, dormers and ridges consume real material: 5% suits simple gables, 10% is the common default, and 15% fits hip roofs and cut-up designs.
Rafter math is right-triangle geometry scaled to the building. The unit rafter — hypotenuse per 12 inches of run — times the horizontal run gives the rafter length before overhang; add the eave overhang (typically 12–24 inches horizontally, converted through the same triangle) for the full board length. Ridge boards, birdsmouth cuts and collar ties then come from framing tables, not from pitch alone — pitch gives the angles, span tables give the lumber sizes.
When comparing quotes, normalize by squares (1 square = 100 sq ft) of installed area including waste, and confirm each bidder's assumed pitch, overhang and waste match — a cheaper quote built on 5% waste versus a realistic 15% is not actually cheaper. Re-run this calculator with the contractor's numbers to verify the area behind the price before signing.
6 inches rise, 12 inches run = 6:12 pitch, 0.5 slope, 26.57°, 13.42-inch rafter per foot of run. For a 24-foot wide building (12-foot run each side), rafter is about 13.42 feet, roof area about 322 sq ft per side. A steeper 12:12 on the same building gives 45°, a 16.97-inch unit rafter and roughly 407 sq ft per side — about 26% more area and material for identical footprint.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error