Quick answer: roof pitch is how many inches the roof rises for every 12 inches of horizontal run. A 6:12 roof rises 6 inches per foot. To find roof area, multiply the flat footprint by the slope factor √(1 + (pitch ÷ 12)²). For a 6:12 roof the factor is 1.118, so a 40 × 30 ft footprint becomes about 1,342 ft² of roof, or 13.4 roofing squares (one square is 100 ft²).
The Roof Pitch Calculator and Rafter Length Calculator do these steps for you. This guide shows the math so you can check any result.
Step 1: Measure the pitch
Hold a level horizontally against the underside of a rafter (from the attic) or on the roof surface. Measure 12 inches along the level, then measure straight up or down from the 12 inch mark to the rafter. That vertical distance is the rise, so a 6 inch reading means a 6:12 pitch.
Working from the ground is also possible: measure the rise (ridge height above the eave line) and the run (half the building width for a simple gable roof), then:
Pitch = rise ÷ run × 12 (the "x" in x:12)
Example: a gable roof with a 15 ft run and a 7.5 ft rise has a pitch of 7.5 ÷ 15 × 12 = 6:12.
Step 2: Convert pitch to angle
Angle (degrees) = arctan(pitch ÷ 12)
Step 3: The slope factor
The sloped surface is longer than the flat footprint beneath it. The multiplier is:
Slope factor = √(1 + (pitch ÷ 12)²)
Roof area = footprint area × slope factor
Common values:
| Pitch | Angle | Slope factor |
|---|---|---|
| 3:12 | 14.04° | 1.0308 |
| 4:12 | 18.43° | 1.0541 |
| 6:12 | 26.57° | 1.1180 |
| 8:12 | 33.69° | 1.2019 |
| 12:12 | 45.00° | 1.4142 |
Worked example: a 40 × 30 ft house, 6:12 roof
Assume the roof plan matches the footprint (no overhang) and has a simple gable shape.
- Footprint: 40 × 30 = 1,200 ft².
- Slope factor at 6:12: 1.118.
- Roof area: 1,200 × 1.118 = 1,341.6 ft².
- Roofing squares: 1,341.6 ÷ 100 = 13.4 squares.
Roofers add an allowance for waste, hips, valleys and starter courses. Many suppliers suggest 10 to 15%, with more for complex roofs, but confirm with your supplier. At 10% this roof is 14.8 squares, so order 15 squares of material.
Overhangs add area. Eaves of 1 ft on all sides turn a 40 × 30 footprint into 42 × 32 = 1,344 ft² before the slope factor, so measure the actual roof outline when you can.
Rafter length
For one rafter on a gable roof:
Rafter length = run × slope factor
A 15 ft run at 6:12 gives 15 × 1.118 = 16.8 ft of rafter before adding the eave overhang. Our Rafter Length Calculator adds the overhang.
Minimum pitch for asphalt shingles
Minimum slopes come from building code, not from the shingle itself. The City of Hopkins, Minnesota publishes the IRC section R905.2 requirements. In summary:
- Asphalt shingles are allowed on slopes of 2:12 or greater.
- On slopes from 2:12 up to less than 4:12, double underlayment is required.
- Below 2:12, asphalt shingles are not covered by the standard installation and a different roof system is needed.
Your local code and the shingle manufacturer’s instructions govern. Low-slope roofs may need a different product such as membrane roofing.
Steep roofs
Steep roofs cost more than the footprint suggests. Area grows (a 12:12 roof is 41% larger than its footprint), and installers may need extra safety equipment on steep slopes, so labor often costs more. Ask for quotes by the square with the pitch stated.
Common mistakes
- Measuring the flat footprint only. The roof is always larger than the house below it.
- Using the wrong run. For a gable, the run is half the building width, not the full width.
- Using degrees in a pitch formula. Pitch is a ratio, not an angle.
- Forgetting overhangs, hips, dormers and valleys.
- Ordering exactly 13.4 squares. Shingles are sold in whole bundles (check the label for how many bundles cover one square), so round up and include a waste allowance.
Frequently asked questions
What is a 4/12 pitch in degrees?
18.43°.
How many squares is a 1,500 ft² roof?
15 squares. Add 10% for waste to order about 16.5, which rounds to 17.
What is the slope factor for a 5:12 roof?
√(1 + (5 ÷ 12)²) = √1.1736 = 1.0833. Multiply the footprint by 1.083.
Can I convert roof pitch to percent?
Yes. Percent slope = pitch ÷ 12 × 100, so 6:12 is 50%.
Is a steeper roof better?
Steeper roofs shed water and snow faster but cost more to build and cover. The right pitch also depends on style and local snow and wind rules.
Sources
- City of Hopkins, Minnesota, >Asphalt Shingles, IRC R905.2: minimum slope and underlayment requirements.
- Geometry: the slope factor and angle formulas above are standard right-triangle relations (Pythagorean theorem and arctangent).
Always confirm minimum slopes, underlayment and fastening with the shingle manufacturer and your local building department.