Roof pitch calculator
Convert a roof's rise and run into pitch, angle and slope, and get the multiplier that turns a footprint into the area of the sloping roof. This is geometry only: no prices are involved.
Results update as you type.Press Calculate for a link you can bookmark. Nothing you enter is stored by us.
Result
Enter a pitch, or pick a common pitch. The example below shows 6/12.
- Pitch
- —
- Angle
- —
- Slope
- —
- Roof-area multiplier
- — Footprint area × this = sloped roof area.
- Hip and valley factor
- — Common run × this = hip or valley length, where equal pitches meet at a right angle.
- Rafter length
- — Common run × roof-area multiplier, before any overhang.
- Hip or valley length
- — For a regular hip or valley, before any overhang.
Roof-area multiplier = √(rise² + run²) ÷ run. For 6/12: √(36 + 144) ÷ 12 = 1.118034.
How to measure your pitch safely
Stay off the roof.You can measure pitch from inside the attic. Walking on a roof is a fall risk, and it can damage shingles.
- Go into the attic with a level and a tape measure. A 24-inch level is the easiest to hold against a rafter. Step only on joists or a floored area.
- Hold the level against the underside of a rafter, with the bubble centered, so the level is horizontal and one end touches the rafter.
- Mark 12 inches along the level from the point where it touches the rafter.
- Measure straight up from that mark to the underside of the rafter. That distance in inches is the rise, and the pitch is rise/12.
No attic access? The pitch shown on the house plans, or in a roofer's measurement report, gives the same number.
What the numbers mean
- Pitch (X/12)
- Inches of rise for every 12 inches of horizontal run. A 6/12 roof rises 6 inches over 12.
- Angle
- The same slope in degrees from horizontal: arctan(rise ÷ run).
- Slope (percent)
- Rise ÷ run × 100. A 6/12 roof is a 50% slope.
- Roof-area multiplier (pitch factor)
- √(rise² + run²) ÷ run. Multiply a roof plane's horizontal footprint by it to get the plane's sloped surface area.
- Hip and valley factor
- √(rise² + 2 × run²) ÷ run. Where two roof planes with the same pitch meet at a right angle in plan, the hip or valley rafter is longer than the common rafter: its length is the common run × this factor. It is a length factor, not an area multiplier, and it doesn't apply where the two pitches differ or the corner isn't square. For 6/12 it is √(36 + 288) ÷ 12 = 1.5.
From pitch to roof area
Keep these quantities separate. They are often confused in quotes and calculators.
- Footprint: the roof's horizontal area seen from above, including overhangs. Measured level, in square feet.
- Roof area: footprint × roof-area multiplier. This is the sloped surface that gets covered.
- Squares: roof area ÷ 100. One roofing square covers 100 square feet of roof (GAF).
- Waste: extra shingles for cutting at edges, hips and valleys, added on top of the roof area. The right allowance depends on the roof's shape and the shingle; it is a material quantity, not part of the roof's area.
Worked example
- Footprint
- 2,000 sq ft, one 6/12 pitch throughout
- Roof area
- 2,000 × 1.118034 = 2,236.07 sq ft
- Squares
- 2,236.07 ÷ 100 = 22.36 squares
A single multiplier is exact only when every roof plane has the same pitch. For roofs with two or more pitches, dormers or other sections, work out each section's footprint and pitch separately and add the areas, or use a contractor's or measurement company's report. The measuring guide walks through the whole method.
Common roof pitches
| Pitch | Angle | Slope | Roof-area multiplier | Hip/valley factor |
|---|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.003 | 1.417 |
| 2/12 | 9.5° | 16.7% | 1.014 | 1.424 |
| 3/12 | 14.0° | 25.0% | 1.031 | 1.436 |
| 4/12 | 18.4° | 33.3% | 1.054 | 1.453 |
| 5/12 | 22.6° | 41.7% | 1.083 | 1.474 |
| 6/12 | 26.6° | 50.0% | 1.118 | 1.500 |
| 7/12 | 30.3° | 58.3% | 1.158 | 1.530 |
| 8/12 | 33.7° | 66.7% | 1.202 | 1.563 |
| 9/12 | 36.9° | 75.0% | 1.250 | 1.601 |
| 10/12 | 39.8° | 83.3% | 1.302 | 1.641 |
| 11/12 | 42.5° | 91.7% | 1.357 | 1.685 |
| 12/12 | 45.0° | 100.0% | 1.414 | 1.732 |
| 14/12 | 49.4° | 116.7% | 1.537 | 1.833 |
| 16/12 | 53.1° | 133.3% | 1.667 | 1.944 |
| 18/12 | 56.3° | 150.0% | 1.803 | 2.062 |
| 24/12 | 63.4° | 200.0% | 2.236 | 2.449 |
Roof shapes and the multiplier
The multiplier works for any roof whose planes share one pitch, because each plane's area is its footprint times the same factor.
GableTwo planes meeting at a ridge. One pitch: the multiplier applies. 
HipFour planes meeting at hips and a short ridge. If all four share one pitch, the multiplier applies. 
ShedOne plane sloping one way. The multiplier applies. 
GambrelTwo different pitches on each side. Measure the lower and upper slopes separately. 
MansardSteep lower slopes under a low-pitched top. Measure each pitch separately. 
Flat (low-slope)The multiplier is close to 1. Low-slope roofs use membrane systems, not shingles.
Limitations
- Geometry doesn't tell you what a roof will cost. Materials, labor, tear-off, access and local requirements all change the price.
- Multipliers assume flat roof planes. They don't account for overhang length you haven't included in the footprint, or for curved roofs.
- Minimum slopes depend on the roofing product and the local code. Many US residential codes allow asphalt shingles only on slopes of 2/12 or more, with two layers of underlayment from 2/12 up to 4/12; for example the codes summarized by the City of Grand Rapids, Michigan and the City of Minneapolis. Your local building department and the shingle's installation instructions decide.
Questions
What does a 6/12 pitch mean?
The roof rises 6 inches for every 12 inches of horizontal run. That is about 26.57 degrees, or a 50% slope.
How are pitch, angle and percent slope related?
They are three ways to write the same ratio of rise to run. Pitch is that ratio × 12, percent slope is the ratio × 100, and the angle is the arctangent of the ratio.
How do I convert roof area to roofing squares?
Divide the roof area in square feet by 100. A 2,236 sq ft roof is 22.36 squares. Use the sloped roof area, not the footprint.
Can one pitch factor calculate a complex roof?
Only if every plane has the same pitch. Sections with different pitches, such as a gambrel's two slopes or a porch roof, need their own footprint and multiplier.
Does roof pitch determine roofing cost?
It affects the quantities, because a steeper roof has more surface for the same footprint, and contractors may charge more to work on steep roofs. But pitch alone can't tell you a price; material choice, tear-off, access and local labor rates matter too.
Why is the hip and valley factor 1.5 for a 6/12 roof?
A hip runs diagonally across the corner, so over 12 units of common run it covers 12 × √2 ≈ 16.97 units in plan while rising the same 6. Its length is √(16.97² + 6²) = √(288 + 36) = 18, and 18 ÷ 12 = 1.5. Multiply your common run by this factor to get the hip or valley length. It applies only where two planes with the same pitch meet at a right angle.
Sources
- Roof Assemblies (Chapter 9, Michigan Residential Code), City of Grand Rapids, Michigan. Read October 21, 2026.
- Roofing and re-roofing with asphalt shingles (handout, last updated May 2016), City of Minneapolis, Minnesota — Construction Code Services. Read October 26, 2026.
- How Many Bundles of Shingles Are in a Square?, GAF (shingle manufacturer). Read October 26, 2026.
Pitch, angle, slope and the two factors are standard right-triangle geometry; the formulas and their tests are on the methodology page.