About Roof Pitch Calculator (Angle, Rafter Length & Roof Area)
The roof pitch calculator converts any way of stating a roof slope — rise per 12 in of run (the US x/12 pitch), the metric x/10 ratio, the angle in degrees, or the slope percent — into all the others, and classifies the roof as flat, low-slope, conventional, or steep. The slope multiplier sqrt(1 + (x/12)²) that links plan dimensions to sloped dimensions is reported for every pitch.
Two working modes build on the conversion: the rafter mode returns the rise and common rafter length from the horizontal run to the ridge centre plus an optional eave overhang, and the roof area mode converts a plan (footprint) area to the actual sloped roof area, expressed in roofing squares with the number of shingle bundles to order at 3 bundles per square and a waste allowance.
How It Works
- Enter the pitch in whichever notation you have: x/12, x/10, degrees, or percent. The tool normalises it to rise-per-12 and reports the angle atan(x/12), the percent 100·x/12, and the slope multiplier sqrt(1 + (x/12)²).
- The pitch is classified against the common bands: flat below 2/12, low-slope 2/12 to 4/12, conventional 4/12 to 9/12, and steep above 9/12.
- In rafter mode, enter the horizontal run from the wall plate to the ridge centre line. The rise is run x (x/12) and the rafter length is run x multiplier, with an optional horizontal overhang added as overhang x multiplier.
- In area mode, enter the plan footprint area of the roof. The sloped area is plan x multiplier for both gable and hip roofs of the same pitch; the tool converts it to roofing squares (100 ft² each) and shingle bundles at 3 per square, rounded up after applying the waste percentage.
- A chart of the slope multiplier from 0/12 to 18/12 shows where your roof sits on the curve.
Worked Example
A 6/12 roof rises 6 in per 12 in of run, which is atan(0.5) = 26.57 degrees, a 50% slope, and a slope multiplier of sqrt(1 + 0.25) = 1.1180 — a conventional pitch. A rafter with a 12 ft run then has a rise of 6 ft and a length of 12 x 1.1180 = 13.42 ft to the ridge centre. For a house with a 1000 ft² footprint under the same roof, the sloped area is 1000 x 1.1180 = 1118 ft² = 11.18 squares; at 3 bundles per square that is 33.5 bundles, and with 10% waste 36.9, so order 37 bundles of shingles.
Formulas
- Pitch to angle and percent
angle = atan(x / 12), percent = 100 * x / 12- Slope multiplier
m = sqrt(1 + (x / 12)²) = 1 / cos(angle)- Rise and rafter length
rise = run * x / 12, rafter = run * m + overhang * m- Sloped roof area
A_roof = A_plan * m- Roofing squares and shingle bundles
squares = A_roof / 100 ft², bundles = ceil(3 * squares * (1 + waste/100))
Standards & References
- IRC R905.2.2 asphalt shingle minimum slope (2:12)
- IBC / IRC roof classification conventions
- ARMA asphalt roofing estimating practice (3 bundles per square)
Frequently Asked Questions
How do I convert roof pitch to degrees?
Divide the rise by 12 and take the inverse tangent: angle = atan(x/12). A 4/12 pitch is atan(4/12) = 18.4°, a 6/12 pitch is 26.6°, and a 12/12 pitch is exactly 45°. Going the other way, multiply the tangent of the angle by 12 to get the rise per 12 in of run.
What is the roof slope multiplier and how is it used?
The slope multiplier is sqrt(1 + (x/12)²), the ratio of any sloped roof dimension to its horizontal (plan) projection. For a 6/12 roof it is 1.118, so a rafter is 11.8% longer than its run and the roof surface is 11.8% larger than the footprint. Roofers multiply the plan area taken from drawings or satellite measurements by this factor to get the actual shingle area.
How do I calculate rafter length from the run and pitch?
Multiply the horizontal run (from the outside of the wall plate to the ridge centre line) by the slope multiplier: rafter = run x sqrt(1 + (x/12)²). A 12 ft run at 6/12 gives 12 x 1.118 = 13.42 ft, which is the same as the Pythagorean answer sqrt(12² + 6²). Add the eave overhang times the same multiplier, and remember to deduct half the ridge board thickness for the cut length.
How many bundles of shingles do I need per square?
Standard three-tab and most architectural shingles are packaged at 3 bundles per roofing square, where a square is 100 ft² of roof surface. Divide the sloped roof area by 100 to get squares, multiply by 3, then add waste — typically 10% for a simple gable and up to 15% for hip roofs and complex layouts with valleys — and round up to whole bundles.
What is considered a low-slope versus a steep roof pitch?
Common practice groups pitches into flat below 2/12, low-slope from 2/12 to 4/12, conventional from 4/12 to 9/12, and steep above 9/12. Asphalt shingles require at least 2/12 under IRC R905.2.2 (with doubled underlayment up to 4/12), while pitches below that need membrane or built-up roofing. Most walkable production roofs are 4/12 to 6/12; above about 7/12 staging or roof jacks are normally required.
Does a hip roof have more area than a gable roof at the same pitch?
For the same footprint and the same pitch on every plane, the total sloped area is essentially the same — plan area times the slope multiplier — because the hip planes still project onto the same footprint. The practical difference is waste: hips and valleys generate more cut shingles, so estimators carry 12-15% waste on hip roofs against about 10% on a plain gable.