Roof Pitch Calculator
Roof pitch describes the steepness of a roof, expressed as the ratio of vertical rise to 12 inches of horizontal run (for example, 6:12 means the roof rises 6 inches for every 12 inches of run). Pitch affects the choice of roofing material, water drainage performance, attic space, and the amount of material required. This calculator converts a rise-per-12-run value into the pitch angle in degrees, the roof area multiplier (used to convert flat plan area to actual sloped surface area), and the rafter length per foot of run. The angle in degrees is found using the arctangent of (rise / run). The area multiplier is the hypotenuse of the rise/run triangle divided by the run (the run being 1 for the unit triangle). Pitches below 2:12 are classified as low-slope and require specific roofing systems. Pitches of 4:12 to 12:12 are typical residential slopes. Pitches above 12:12 are steep slope and may require special installation techniques. The International Building Code and the National Roofing Contractors Association provide guidance on minimum pitch requirements for different roofing materials.
Roof pitch formulas
Pitch ratio = Rise : 12
Angle (deg) = atan(Rise / 12) x (180 / pi)
Multiplier = sqrt(Rise^2 + 12^2) / 12
Rafter per ft of run = sqrt((Rise/12)^2 + 1)
Total rafter length = Rafter per ft x Total run (ft)
Worked example (6:12 pitch)
Rise = 6, Total run = 12 ft.
- Pitch = 6:12
- Angle = atan(6/12) x (180/pi) = 26.57 degrees
- Multiplier = sqrt(36+144)/12 = sqrt(180)/12 = 1.12
- Rafter per ft = sqrt(0.25 + 1) = 1.12 ft
- Total rafter = 1.12 x 12 = 13.42 ft
Common roof pitches reference
| Pitch | Angle | Multiplier | Category |
|---|---|---|---|
| 2:12 | 9.46 deg | 1.03 | Low slope |
| 4:12 | 18.43 deg | 1.05 | Conventional |
| 6:12 | 26.57 deg | 1.12 | Conventional |
| 8:12 | 33.69 deg | 1.20 | Conventional |
| 10:12 | 39.81 deg | 1.30 | Steep |
| 12:12 | 45.00 deg | 1.41 | Steep (45 deg) |
Frequently asked questions
What is roof pitch?
Roof pitch is the slope of a roof expressed as the ratio of vertical rise to horizontal run, always measured over a 12-inch run. A 6:12 pitch rises 6 inches for every 12 inches of horizontal distance. Pitch can also be expressed as a decimal or as an angle in degrees.
What are common residential roof pitches?
Common residential roof pitches range from 4:12 (low slope) to 12:12 (steep, 45 degrees). A 6:12 pitch is very common. Pitches below 2:12 are considered flat or low-slope roofs and require special roofing materials. Pitches above 12:12 are considered steep slope.
How does roof pitch affect the amount of roofing material needed?
A steeper roof has more actual surface area than its flat footprint suggests. The roof area multiplier converts the flat plan area to the actual sloped area. For a 6:12 pitch, the multiplier is approximately 1.118. Multiply the flat (plan) area by this factor to get the true roof surface area.
How do I find the rafter length from roof pitch?
The rafter length for one foot of horizontal run equals the square root of (1 squared + pitch fraction squared), where pitch fraction = rise/12. For a 6:12 pitch: square root of (1 + 0.25) = 1.118 ft of rafter per foot of run. Multiply by the total run to get the full rafter length.
What is the difference between pitch and slope?
In common use, pitch and slope are often used interchangeably. Technically, pitch is the ratio of rise to span (the full width of the building), while slope is rise over run (half the span). In the construction trades, X:12 notation refers to rise over run (slope). This calculator uses the common trade convention of rise per 12 inches of run.
Sources
- National Roofing Contractors Association (NRCA): Roofing Manual.
- International Building Code (IBC): minimum roof slope requirements by material.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. Consult a licensed contractor for structural roof design.