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Construction & Home
Roof Pitch Calculator — Pitch, Slope Angle & Area Multiplier
Find roof pitch in x/12, the angle in degrees, and the area multiplier for ordering shingles
A roof pitch calculator turns two simple measurements — rise and run — into the three numbers every roofer, framer and shingle buyer needs: the pitch as x/12, the slope angle in degrees, and the roof-area multiplier that scales your flat floor-plan area up to the real sloped surface. Get the pitch wrong and you'll order the wrong number of shingle squares, cut your rafters to the wrong length, or buy the wrong walkability gear.
In US roofing, pitch is written as rise over a fixed run of 12 inches — a "6/12" ("six-twelve") roof rises 6 inches for every 12 inches of horizontal run. That's the language every supplier and framer speaks, so the first job is to convert your measured rise and run into that x/12 form.
Pitch (x/12) = rise ÷ run × 12. If you measure a 4-inch rise over a 12-inch run, that's 4 ÷ 12 × 12 = a 4/12 pitch. Measure a 13-inch rise over a 24-inch run and you get 13 ÷ 24 × 12 = a 6.5/12 pitch.
The slope angle is the same triangle expressed in degrees:
Angle = arctan(rise ÷ run) × 180 ÷ π.
A 6/12 roof works out to 26.57°, a 4/12 to 18.43°, and a 12/12 (a perfect 45-degree "square" roof) to exactly 45°. Angle is what you set on a miter saw or a speed square.
The number that quietly drives your material order is the roof-area multiplier (also called the slope factor or line-length factor):
Multiplier = √(rise² + run²) ÷ run.
A roof's footprint — the area you'd measure on the ground or off a floor plan — is always smaller than its actual sloped surface, because the roof is the hypotenuse of that rise-run triangle. The multiplier is exactly that hypotenuse ratio. A 6/12 roof has a multiplier of 1.118, so a 1,500 sq ft footprint is really 1,500 × 1.118 = 1,677 sq ft of roof to cover. A 4/12 is 1.054; a 12/12 is 1.414 (√2). Skip this factor and you'll under-order shingles, felt and ice-and-water shield on every steep roof.
This calculator takes your rise and run (in inches, the way you'd read them off a level and a tape), and returns the pitch, the angle and the multiplier together. Enter your roof footprint and it will also show the true sloped area — the figure you hand to the supplier or feed into a roofing-squares estimate. For the actual shingle, felt and rafter quantities, pair it with the roofing and rafter calculators; this tool owns the pitch, slope and multiplier math those estimates depend on.
📖 See also: How to Calculate a Tip (and Split the Bill)
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• Pitch (x/12) = rise ÷ run × 12 • Slope angle (degrees) = arctan(rise ÷ run) × 180 ÷ π • Roof-area multiplier (slope factor) = √(rise² + run²) ÷ run • True sloped area = footprint area × multiplier • Reference points: 4/12 → 18.43°, multiplier 1.054 • 6/12 → 26.57°, multiplier 1.118 • 12/12 → 45.00°, multiplier 1.414 (√2)
📰 Formula
• Pitch (x/12) = rise ÷ run × 12 • Slope angle (degrees) = arctan(rise ÷ run) × 180 ÷ π • Roof-area multiplier (slope factor) = √(rise² + run²) ÷ run • True sloped area = footprint area × multiplier • Reference points: 4/12 → 18.43°, multiplier 1.054 • 6/12 → 26.57°, multiplier 1.118 • 12/12 → 45.00°, multiplier 1.414 (√2)
🧪 Worked examples
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Example 4
⚠️ Common mistakes
- Writing pitch as rise-over-run as a fraction (6/12 means 6 in rise per 12 in run, not the fraction 1/2).
- Measuring run as the sloped roof length instead of the horizontal distance.
- Using the multiplier on the wrong area — apply it to the flat footprint, not to a length.
- Confusing the angle in degrees with the x/12 pitch number; a 45° roof is 12/12, not 45/12.
- Forgetting the multiplier entirely and under-ordering shingles on a steep roof.
💡 Tips
- Measure rise with a level: hold it level off the roof, mark 12 in along it, then measure straight down to the surface — that drop is your rise per 12 of run.
- Roofs at 6/12 and lower are generally walkable; 7/12 and steeper usually need roof jacks or staging.
- A 12/12 roof is a 45° "square" roof — its multiplier is √2 ≈ 1.414, the steepest common residential pitch.
- Apply the multiplier to your footprint area first, then add the usual 10% shingle waste — the two stack.
- Low slopes under about 2/12 are out of range for standard shingles and need a membrane roof instead.
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<iframe src="https://www.calcnimbus.com/embed/roof-pitch-calculator" width="100%" height="500" frameborder="0" style="border:1px solid #eee;border-radius:12px"></iframe>
❓ Frequently asked questions
What does a 6/12 roof pitch mean?
A 6/12 pitch means the roof rises 6 inches for every 12 inches of horizontal run. It works out to a slope angle of 26.57 degrees and a roof-area multiplier of 1.118, and it is the most common residential pitch.
How do I calculate roof pitch from rise and run?
Divide the rise by the run, then multiply by 12, to get the pitch as x/12. A 4-inch rise over a 12-inch run is 4 ÷ 12 × 12 = a 4/12 pitch. Always measure run as the horizontal distance, not the sloped length.
How do I convert roof pitch to degrees?
The slope angle equals arctan(rise ÷ run) × 180 ÷ π. A 6/12 roof is arctan(6 ÷ 12) = 26.57°, a 4/12 is 18.43°, and a 12/12 is exactly 45°. This calculator does the conversion for you.
What is the roof area multiplier and why does it matter?
The multiplier, or slope factor, is √(rise² + run²) ÷ run. It scales your flat roof footprint up to the true sloped surface area. A 6/12 roof has a multiplier of 1.118, so a 1,500 sq ft footprint is really 1,677 sq ft of roof to shingle.
How do I find the actual roof area to order shingles?
Measure the building footprint the roof covers, then multiply by the slope-factor multiplier for your pitch. Add a waste factor of about 10% on top, then divide by 100 to get roofing squares for the supplier.
What is the steepest walkable roof pitch?
Roofs up to about 6/12 (26.57°) are generally walkable for most people. From 7/12 (30.26°) up, you typically need roof jacks, toe boards or staging to work safely, and the surface gets harder to shingle.
What is the difference between roof pitch and roof slope?
In everyday US roofing they're used interchangeably, both expressed as x/12. Strictly, slope is the rise over run (the x/12 ratio) while pitch is sometimes defined as rise over the full span; this calculator uses the common x/12 slope convention.
What pitch is a 45 degree roof?
A 45-degree roof is a 12/12 pitch, because the rise equals the run. Its area multiplier is √2 ≈ 1.414, meaning the sloped surface is about 41% larger than the flat footprint beneath it.
Is a roof pitch calculator different from a roofing calculator?
Yes. A roof pitch calculator gives you the pitch, the slope angle and the area multiplier from rise and run. A roofing calculator uses that multiplier to estimate shingle squares, bundles and felt. Use the pitch result as the input to the roofing or rafter estimate.