Roof Pitch Formulas
\(\text{Pitch Ratio } (X) = \frac{\text{Vertical Rise (in)}}{\text{Horizontal Run (ft)}}\) \(\text{Slope Angle } (\theta) = \arctan\left(\frac{X}{12}\right) \times \frac{180}{\pi}\) \(\text{Pitch Multiplier Factor } (M) = \sqrt{1 + \left(\frac{X}{12}\right)^2}\) \(\text{Diagonal Slope Length (ft)} = \text{Run (ft)} \times M\) \(\text{Sloped Roof Area (sq ft)} = \text{Flat Footprint Area (sq ft)} \times M\)
Standard Roof Pitch Multiplier & Angle Reference Table
| Roof Pitch | Angle (Degrees) | Pitch Multiplier Factor | Flat Area (1,000 sq ft) | Sloped Roof Area | Shingle Bundles Needed (3 bndl/sq) |
|---|---|---|---|---|---|
| 3/12 Pitch | 14.04° | 1.031 | 1,000 sq ft | 1,031 sq ft | 31 Bundles |
| 4/12 Pitch | 18.43° | 1.054 | 1,000 sq ft | 1,054 sq ft | 32 Bundles |
| 5/12 Pitch | 22.62° | 1.083 | 1,000 sq ft | 1,083 sq ft | 33 Bundles |
| 6/12 Pitch | 26.57° | 1.118 | 1,000 sq ft | 1,118 sq ft | 34 Bundles |
| 7/12 Pitch | 30.26° | 1.158 | 1,000 sq ft | 1,158 sq ft | 35 Bundles |
| 8/12 Pitch | 33.69° | 1.202 | 1,000 sq ft | 1,202 sq ft | 37 Bundles |
| 9/12 Pitch | 36.87° | 1.250 | 1,000 sq ft | 1,250 sq ft | 38 Bundles |
| 10/12 Pitch | 39.81° | 1.302 | 1,000 sq ft | 1,302 sq ft | 40 Bundles |
| 12/12 Pitch | 45.00° | 1.414 | 1,000 sq ft | 1,414 sq ft | 43 Bundles |
How to Use This Roof Pitch Calculator
- Enter total Vertical Rise in inches (height from top plate level to ridge peak).
- Enter total Horizontal Run in feet (distance from wall plate to ridge peak).
- Specify flat Building Footprint Area in square feet.
- Review the calculated X/12 pitch ratio, slope angle in degrees, pitch multiplier factor, and sloped roofing square footage.
Frequently Asked Questions
What is roof pitch?
Roof pitch is the measure of the steepness of a roof slope, expressed as inches of vertical rise per 12 inches (1 foot) of horizontal run (e.g., a 6/12 pitch rises 6 inches for every 12 inches of run).
How do you calculate roof pitch ratio?
Pitch Ratio = Total Rise (in inches) / Total Run (in feet). For example, 72 inches of rise over 12 feet of run = 72 / 12 = 6/12 pitch.
How do you convert roof pitch to degrees?
Pitch angle in degrees = arctan(Pitch / 12) × (180 / π). For example, a 7/12 pitch equals arctan(7/12) = 30.26 degrees.
What is a roof pitch multiplier factor?
The pitch multiplier is the ratio of sloped roof length to flat horizontal run: Multiplier = √(1 + (Pitch/12)²). Multiplying flat attic footprint area by this factor gives true sloped roof surface square footage.
What is considered a low slope vs steep slope roof?
Flat roofs are 0/12 to 2/12 pitch. Low-slope roofs are 2/12 to 4/12. Standard residential roofs are 4/12 to 9/12. Steep-slope roofs are 10/12 to 18/12 pitch.
Why is roof pitch important for shingle installation?
Standard asphalt shingles require a minimum 4/12 pitch for proper water drainage without special underlayment. Pitch also determines snow load shed and wind resistance ratings.
Is my roof pitch calculation saved on external servers?
No. All calculation logic executes locally in your browser.