Roof Pitch Calculator
Convert between rise-over-run and degrees, then turn a footprint into real roof area — with the slope factor, rafter length, squares and shingle bundles you need to order.
How to use this calculator
- Get the pitch. If you know it ("it's a 6/12"), enter 6. If you measured with a level and tape in the attic, use the measured mode: hold a level horizontal, mark 12 in along it, and measure straight up to the rafter.
- Enter the building footprint, not the roof. The whole point of the slope factor is that it converts the flat plan area into the sloped surface area.
- Set the waste allowance. 10% suits a simple gable. Go to 15% for hips, valleys and dormers, where every course needs cutting.
- Read the squares figure. Roofing is quoted and sold by the square — 100 sq ft — and architectural shingles run three bundles to the square.
The formula
Pitch is a ratio: rise over a 12 in run. Everything else follows from it.
angle = arctan( rise ÷ 12 )
slope factor = √( 1 + (rise ÷ 12)² )
roof area = footprint area × slope factor
rafter length = run × slope factor
The slope factor is just Pythagoras: a sloped surface is the hypotenuse over the same horizontal distance. That is why a 12/12 roof has 41% more surface than its footprint.
| Pitch | Angle | Slope factor | Character |
|---|---|---|---|
| 1/12 | 4.8° | 1.0035 | Membrane only |
| 2/12 | 9.5° | 1.0138 | Shingle minimum |
| 4/12 | 18.4° | 1.0541 | Common, walkable |
| 6/12 | 26.6° | 1.1180 | Very common |
| 8/12 | 33.7° | 1.2019 | Steep, roof jacks |
| 10/12 | 39.8° | 1.3017 | Steep |
| 12/12 | 45.0° | 1.4142 | Very steep |
Worked example
A 40 × 30 ft gable roof at 6/12, 10% waste:
- Angle: arctan(6 ÷ 12) = 26.57°
- Slope factor: √(1 + 0.5²) = 1.1180
- Footprint: 40 × 30 = 1,200 sq ft
- Roof surface: 1,200 × 1.1180 = 1,342 sq ft
- With 10%: 1,476 sq ft = 14.8 squares
- Bundles: 14.8 × 3 = 45 bundles
- Rafter run is half the 30 ft span: 15 × 1.1180 = 16.77 ft per common rafter
Ordering off the 1,200 sq ft footprint instead of the 1,342 sq ft roof would have left you 1.4 squares short — four bundles, and a second delivery.
Measuring pitch without climbing on the roof
From inside the attic, hold a 12 in level against the underside of a rafter, keep the bubble centred, and measure vertically from the 12 in mark up to the rafter. That vertical distance in inches is the pitch. A smartphone inclinometer app held flat against a rafter gives the angle directly, which this calculator converts.
Frequently asked questions
What is a 6/12 roof pitch in degrees?
A 6/12 pitch is 26.57 degrees. The pitch is the rise in inches over a 12 inch run, so the angle is the arctangent of 6 divided by 12. For reference, 4/12 is 18.43 degrees, 8/12 is 33.69 degrees and 12/12 is exactly 45 degrees.
How do I measure roof pitch from the attic?
Hold a 12 inch level horizontally against the underside of a rafter with the bubble centred, mark the 12 inch point, then measure straight up from that mark to the rafter. If the vertical distance is 6 inches, the pitch is 6/12. This is safer and usually more accurate than measuring on the roof surface.
What is the slope factor and why does it matter?
The slope factor is the number you multiply a flat footprint area by to get the actual sloped roof area. It is the square root of 1 plus the square of rise over run. A 6/12 roof has a factor of 1.118, so a 1,200 square foot footprint carries 1,342 square feet of roof. Ordering material off the footprint is the classic way to come up short.
How many bundles of shingles do I need per square?
Three for most architectural and standard three-tab shingles, since a bundle covers about 33.3 square feet and a square is 100. Heavier designer and premium shingles can run four or five bundles per square, so check the wrapper.
What is the minimum pitch for asphalt shingles?
Generally 2/12, and between 2/12 and 4/12 manufacturers typically require a doubled underlayment for the warranty to hold. Below 2/12 shingles are not appropriate at all and the roof needs a membrane system. Confirm against the shingle manufacturer instructions and your local code.
Guides
- How to Measure Roof Pitch (Safely, From the Attic)
- How Many Shingles Do I Need? Squares, Bundles and the Slope Factor
- Hip Roof vs Gable Roof: Calculating the Area
- How Much Underlayment and Ice Shield Do You Need?
- What Is a Good Roof Pitch?