Roof pitch calculator

How It Is Calculated

This calculator determines the surface area of a symmetrical gable roof, the rafter length, the slope angle, and the total rise. All intermediate calculations use full precision; final outputs are rounded to the specified number of decimal places using standard rounding (half up).

Step-by-step formulas

1. Convert overhang to feet: O_ft = O_in / 12
2. Horizontal run from ridge to eave: R = (S / 2) + O_ft, where S is the building width (span) in feet.
3. Slope ratio: r = P / 12, where P is the pitch (rise per 12 inches of run).
4. Rafter length: L_raft = R × √(1 + r²)
5. Net roof area (both slopes): A_net = 2 × L_raft × L_bldg, where L_bldg is the roof length along the ridge.
6. Material area with waste: A_mat = A_net × (1 + W / 100), where W is the waste factor in percent.
7. Slope angle: θ = arctan(r) × (180 / π)
8. Total rise: H = (S × P) / 2

Assumptions

• The roof is a symmetrical gable roof (two equal slopes).
• Building width is measured from outer wall to outer wall.
• Roof length is the length of the building along the ridge (no gable end overhang).
• Overhang is the horizontal projection of the rafter beyond the wall.
• Waste factor is a percentage added to the net roof area to account for cut-offs and waste.
• Pitch is the rise in inches per 12 inches of horizontal run.
• Default values: pitch 4/12, building width 30 ft, roof length 50 ft, overhang 12 in, waste 10%.

Worked Example

Inputs: Roof pitch = 4, Building width = 30 ft, Roof length = 50 ft, Overhang = 12 in, Waste factor = 10%.

1. Overhang in feet: O_ft = 12 / 12 = 1 ft
2. Run: R = (30 / 2) + 1 = 15 + 1 = 16 ft
3. Slope ratio: r = 4 / 12 = 0.3333
4. Rafter length: L_raft = 16 × √(1 + 0.3333²) = 16 × √1.1111 = 16 × 1.0541 = 16.87 ft (rounded to 2 decimal places)
5. Net roof area: A_net = 2 × 16.87 × 50 = 1687 ft² (rounded to 1 decimal place)
6. Material area with waste: A_mat = 1687 × (1 + 10/100) = 1687 × 1.1 = 1855.7 ft² (rounded to 1 decimal place)
7. Slope angle: θ = arctan(0.3333) × (180/π) = 18.4° (rounded to 1 decimal place)
8. Total rise: H = (30 × 4) / 2 = 120 / 2 = 60 in (rounded to 1 decimal place)

Results: Net roof area = 1687 ft², Material area (with waste) = 1855.7 ft², Rafter length = 16.87 ft, Slope angle = 18.4°, Total rise = 60 in.

Practical Tips

• Always measure the building width from outer wall to outer wall, not from the center.
• Include the overhang in your measurements to ensure rafters are long enough.
• Use a waste factor of 10–15% for asphalt shingles or tiles; 5–10% for metal roofing.
• For ordering materials, use the material area with waste. For estimating framing lumber, use the rafter length and number of rafters.
• If you need to estimate the number of roofing tiles or shingles, use the Roofing calculator.
• For insulation requirements, the Insulation calculator can help.
• If your project involves a flat roof or different roof shape, adjust the formulas accordingly.