Roof Pitch Chart
Authoritative reference chart converting standard roof pitches (1/12 to 24/12) into slope angles in degrees, slope percentages, rafter line lengths, and surface area multipliers.
1. Master Roof Pitch Conversion Table (1/12 to 24/12)
Calculated using standard imperial right-triangle trigonometry (12-inch horizontal run).
| Pitch (X/12) | Angle (Degrees) | Slope (%) | Pitch Multiplier | Unit Rafter (in/ft) |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.33% | 1.0035 | 12.042" |
| 2/12 | 9.46° | 16.67% | 1.0138 | 12.166" |
| 3/12 | 14.04° | 25% | 1.0308 | 12.369" |
| 4/12 | 18.43° | 33.33% | 1.0541 | 12.649" |
| 5/12 | 22.62° | 41.67% | 1.0833 | 13" |
| 6/12 | 26.57° | 50% | 1.118 | 13.416" |
| 7/12 | 30.26° | 58.33% | 1.1577 | 13.892" |
| 8/12 | 33.69° | 66.67% | 1.2019 | 14.422" |
| 9/12 | 36.87° | 75% | 1.25 | 15" |
| 10/12 | 39.81° | 83.33% | 1.3017 | 15.62" |
| 11/12 | 42.51° | 91.67% | 1.3566 | 16.279" |
| 12/12 | 45° | 100% | 1.4142 | 16.971" |
| 13/12 | 47.29° | 108.33% | 1.4743 | 17.692" |
| 14/12 | 49.4° | 116.67% | 1.5366 | 18.439" |
| 15/12 | 51.34° | 125% | 1.6008 | 19.209" |
| 16/12 | 53.13° | 133.33% | 1.6667 | 20" |
| 17/12 | 54.78° | 141.67% | 1.7341 | 20.809" |
| 18/12 | 56.31° | 150% | 1.8028 | 21.633" |
| 19/12 | 57.72° | 158.33% | 1.8727 | 22.472" |
| 20/12 | 59.04° | 166.67% | 1.9437 | 23.324" |
| 21/12 | 60.26° | 175% | 2.0156 | 24.187" |
| 22/12 | 61.39° | 183.33% | 2.0883 | 25.06" |
| 23/12 | 62.45° | 191.67% | 2.1619 | 25.942" |
| 24/12 | 63.43° | 200% | 2.2361 | 26.833" |
2. What Does X/12 Mean in Construction Framing?
In traditional North American carpentry and architectural drafting, roof pitch describes slope as a ratio of vertical rise in inches for every 12 inches of horizontal run. A standard 12-inch horizontal base was established because 12 inches equals exactly 1 foot, allowing carpenters to quickly scale rafter line lengths per foot of building span.
Pitch = (Vertical Rise ÷ Horizontal Run) × 12Example: If a roof rises 5 feet over a 10-foot half-span: (5 ÷ 10) × 12 = 6/12 pitch.
Angle (θ) = arctan(Rise ÷ 12) × (180 ÷ π)Example: For a 6/12 pitch: arctan(6 ÷ 12) = arctan(0.5) = 26.5651 degrees.
3. The Roof Pitch Multiplier (Hypotenuse Factor) Formula
The roof pitch multiplier (also known as the slope factor or rafter multiplier) is the mathematical ratio of the sloped hypotenuse to the adjacent horizontal run. Because a right triangle follows the Pythagorean theorem (A² + B² = C²), the multiplier represents the unit hypotenuse for a 1-unit horizontal base:
To estimate actual sloped roof surface area from a flat architectural footprint, multiply the horizontal area (including eave and rake overhangs) by the pitch multiplier. For a full walkthrough, explore our guide on how to calculate roof square footage.
4. Detailed Engineering Analysis of Common Pitches
4/12 Roof Pitch (18.43° / 33.33% Slope / 1.0541 Multiplier)
A 4/12 slope is one of the most significant thresholds in roofing. Under OSHA 29 CFR 1926.500, 4:12 is the upper boundary for low-slope roofs. Under 2024 IRC Section R905.2.2, 4:12 is the minimum slope permitted for standard single-layer asphalt shingle underlayment. Slopes below 4:12 down to 2:12 require special enhanced double-layer underlayment.
5/12 Roof Pitch (22.62° / 41.67% Slope / 1.0833 Multiplier)
A 5/12 pitch is a conventional residential slope frequently selected for ranch-style homes and split-levels. It provides reliable precipitation runoff while maintaining moderate attic volume. Under OSHA, 5:12 is classified as a steep roof requiring standard fall protection during framing and re-roofing operations.
6/12 Roof Pitch (26.57° / 50.00% Slope / 1.1180 Multiplier)
A 6/12 pitch represents the single most common residential roof slope in North America. It rises 6 inches per foot of run (a 50% grade). It provides rapid water and snow shedding, ample attic storage headspace, and accommodates all standard roofing materials including architectural shingles, standing-seam metal, and concrete tile.
8/12 Roof Pitch (33.69° / 66.67% Slope / 1.2019 Multiplier)
An 8/12 slope is a steep residential pitch popular on colonial, Victorian, and Cape Cod architectural styles. It sheds heavy snow loads quickly and adds 20.2% more surface area relative to a flat horizontal footprint. Roofers utilize roof brackets (roof jacks) and safety harnesses on 8/12 pitches.
12/12 Roof Pitch (45.00° / 100.00% Slope / 1.4142 Multiplier)
A 12/12 pitch forms a true 45-degree right isosceles triangle where vertical rise equals horizontal run (100% grade). Multiplier is exactly √2 ≈ 1.4142 (+41.4% surface area). Highly common on classic Cape Cod architecture, chalets, and steep decorative gables.
Frequently Asked Questions
What does a 6/12 roof pitch mean?
A 6/12 roof pitch (often written 6:12) means the roof rises 6 inches vertically for every 12 inches (1 foot) of horizontal run. In geometric terms, this equals an angle of 26.57 degrees, a 50% grade slope, and a roof pitch multiplier of 1.1180.
How do I convert roof pitch to degrees?
To convert roof pitch to degrees, divide the vertical rise by the horizontal run (12 inches), then calculate the arctangent (inverse tangent) of that fraction and convert radians to degrees: Angle = arctan(Rise / 12) × (180 / π). For example, for an 8/12 pitch: arctan(8 / 12) = arctan(0.6667) ≈ 33.69 degrees.
What is a roof pitch multiplier (slope factor)?
A roof pitch multiplier (also known as a slope factor or rafter factor) is the ratio of the sloped hypotenuse length to the horizontal run length. Derived from the Pythagorean theorem, the formula is Multiplier = √(1 + (Rise / 12)²). Multiplying your flat horizontal roof footprint by this multiplier gives the true sloped roof surface area.
What angle is a 4/12 roof pitch in degrees?
A 4/12 roof pitch equals exactly 18.43 degrees (arctan(4/12) × 180/π). It has a slope percentage of 33.33% and a pitch multiplier of 1.0541.
What angle is an 8/12 roof pitch in degrees?
An 8/12 roof pitch equals exactly 33.69 degrees (arctan(8/12) × 180/π). It has a slope percentage of 66.67% and a pitch multiplier of 1.2019.
What angle is a 12/12 roof pitch in degrees?
A 12/12 roof pitch equals exactly 45.00 degrees (arctan(12/12) × 180/π). It has a slope percentage of 100.0% and a pitch multiplier of 1.4142 (√2).
What is the difference between a low-slope and a steep-slope roof?
Under OSHA 29 CFR 1926.500 and the International Residential Code (IRC), a low-slope roof is defined as a slope of 4:12 or less (≤ 18.43°). A steep-slope (steep roof) is defined as any slope greater than 4:12 (> 18.43°). Slopes below 4:12 require enhanced water-resistive underlayment or continuous membrane assemblies.