Roof Pitch Calculator
Convert roof pitch ratios (X/12) into slope angles in degrees, grade percentages, and rafter board cut lengths.
| Standard Pitch Ratio | 6 / 12 Pitch (6 in 12) |
| Percentage Grade Slope | 50.0% Grade |
| Roof Pitch Area Multiplier | 1.1180 |
| Total Vertical Ridge Rise | 7.50 ft (90.0 inches) |
| Slope Classification | Conventional Slope (Walkable) |
How Roof Pitch is Measured and Expressed
Roof pitch represents the steepness of a roof. In the United States and North America, pitch is traditionally expressed as the number of vertical inches the roof rises for every 12 horizontal inches (1 foot) of run.
For example, a 6/12 pitch means that for every 12 inches you move horizontally toward the center ridge of the house, the roof climbs 6 inches vertically.
The Mathematics of Roof Geometry
Here are the mathematical formulas used to convert roof pitch into angles, percentage grade, and rafter cut lengths:
Percentage Grade (%) = (Rise / 12) * 100
Pitch Multiplier = Math.sqrt(1 + (Rise / 12)²)
Total Rise (Feet) = Horizontal Run (Feet) * (Rise / 12)
Rafter Length (without overhang) = Horizontal Run (Feet) * Pitch Multiplier
Total Rafter Length = (Horizontal Run + (Overhang in Inches / 12)) * Pitch Multiplier
Step-by-Step Worked Calculation Example
Suppose you are building a gable roof with a 6/12 pitch, a 15-foot horizontal run, and a 12-inch overhang:
- Slope Angle:
atan(6 / 12) = atan(0.5) = 26.57 degrees - Pitch Multiplier:
sqrt(1 + 0.5²) = sqrt(1.25) = 1.1180 - Total Vertical Rise:
15 ft * 0.5 = 7.5 feet (90 inches) - Run including overhang:
15 ft + 1 ft overhang = 16 feet total run - Total Rafter Cut Length:
16 ft * 1.1180 = 17.89 feet (17 ft 10-5/8 in)
Master Roof Pitch Conversion & Material Compatibility Table
Look up common roof pitches to view their exact angles, multipliers, and compatible roofing materials:
| Pitch (X/12) | Angle (Degrees) | Slope Grade (%) | Pitch Multiplier | Classification | Compatible Materials |
|---|---|---|---|---|---|
| 1 / 12 | 4.76° | 8.3% | 1.0035 | Flat / Low Slope | EPDM Rubber, Built-Up TPO |
| 2 / 12 | 9.46° | 16.7% | 1.0138 | Low Slope | Standing Seam Metal, Double Underlayment |
| 3 / 12 | 14.04° | 25.0% | 1.0308 | Low Slope | Metal Panels, Special Underlayment Shingles |
| 4 / 12 | 18.43° | 33.3% | 1.0541 | Conventional | Standard 3-Tab & Architectural Shingles |
| 6 / 12 | 26.57° | 50.0% | 1.1180 | Conventional | Asphalt Shingles, Metal, Concrete Tile |
| 8 / 12 | 33.69° | 66.7% | 1.2019 | Conventional | All Standard Roofing Products |
| 10 / 12 | 39.81° | 83.3% | 1.3017 | Steep Slope | Architectural Shingles, Slate, Cedar Shake |
| 12 / 12 | 45.00° | 100.0% | 1.4142 | Steep Slope | Slate, Clay Tile, Standing Seam Metal |
| 14 / 12 | 49.40° | 116.7% | 1.5366 | Very Steep | Special Mansard / Alpine Framing |
| 18 / 12 | 56.31° | 150.0% | 1.8028 | A-Frame / Tower | A-Frame Siding / Metal Panels |
Roof Slope Classifications Explained
- Flat and Low-Slope Roofs (0/12 to 3/12): Common in commercial buildings and modern residential additions. Water drains slowly, so continuous waterproof membranes (like TPO, PVC, or EPDM) are required instead of overlapping shingles.
- Conventional Slope Roofs (4/12 to 8/12): The most popular residential roof profile. These roofs shed water and light snow effectively, are relatively safe for roofers to walk on, and accommodate standard asphalt shingles.
- Steep Slope Roofs (9/12 and above): Common on Tudor, Victorian, and Alpine homes. They offer dramatic curb appeal and shed snow instantly, but require safety harnesses and specialized staging during installation and repair.
5 Tips for Measuring and Framing Roofs
Frequently Asked Questions
A 6/12 roof pitch means the roof rises 6 vertical inches for every 12 horizontal inches (1 foot) of run. This creates an angle of approximately 26.57 degrees with a 50% slope grade.
Divide the vertical rise by 12, take the arctangent (atan) in radians, and convert to degrees by multiplying by 180 / π. For example: atan(6 / 12) * (180 / 3.14159) = 26.57 degrees.
A pitch multiplier (or slope factor) is the ratio of true sloped rafter length to flat horizontal run. Multiplying flat roof square footage by this multiplier gives the exact sloped square footage needed to order shingles and underlayment.
Standard building codes permit shingles on 2/12 to 4/12 pitches only if you install two full layers of asphalt-saturated underlayment or a continuous self-adhered waterproof membrane across the entire deck before nailing shingles.
In modern carpentry, pitch and slope are often used interchangeably to refer to rise over 12 inches of run. Historically, pitch referred to total rise over total building span (e.g. 1/4 pitch), whereas slope refers to rise over run (e.g. 6/12).