Frame Sums

Reference chart

Roof Pitch Chart & Calculator

Every roof pitch as an angle, a grade and the two multipliers a framer uses: the slope factor for common rafters and roof area, and the hip and valley factor. The calculator below converts any pitch, angle or measured rise and run.

Pitch to degrees, percent and slope factor

Pitch is rise per 12″ of run. Angle = atan(rise ÷ 12). Slope factor = √(rise² + 144) ÷ 12. Hip/valley factor = √(rise² + 288) ÷ 12.
PitchDegreesPercentSlope factorcommon rafter / roof areaHip / valleyWhere you see it
1:124.76°8.3%1.00351.4167Flat / low-slope (membrane roofing only)
2:129.46°16.7%1.01381.4240Low slope (minimum for asphalt shingles is 2:12 with special underlayment; 4:12 standard)
3:1214.04°25%1.03081.4361Low slope (minimum for asphalt shingles is 2:12 with special underlayment; 4:12 standard)
4:1218.43°33.3%1.05411.4530Conventional, walkable
5:1222.62°41.7%1.08331.4743Conventional, walkable
6:1226.57°50%1.11801.5000Conventional, walkable
7:1230.26°58.3%1.15771.5298Conventional, walkable
8:1233.69°66.7%1.20191.5635Conventional, walkable
9:1236.87°75%1.25001.6008Conventional, walkable
10:1239.81°83.3%1.30171.6415Steep; roof jacks or staging to work on
11:1242.51°91.7%1.35661.6853Steep; roof jacks or staging to work on
12:1245.00°100%1.41421.7321Steep; roof jacks or staging to work on
14:1249.40°116.7%1.53661.8333Very steep; requires full staging
16:1253.13°133.3%1.66671.9437Very steep; requires full staging
18:1256.31°150%1.80282.0616Very steep; requires full staging
24:1263.43°200%2.23612.4495Very steep; requires full staging

Your numbers

Pitch

6:12

Conventional, walkable

Angle

26.57°

50% grade

Slope factor

1.118

× run = common rafter length

Hip / valley factor

1.5

× run = hip rafter length

angle = atan(rise ÷ 12); factor = √(rise² + 144) ÷ 12; hip factor = √(rise² + 288) ÷ 12. Roof area = plan area × slope factor.

Questions

How do I convert roof pitch to degrees?

Angle = arctangent of rise over 12. A 6:12 roof is atan(6 ÷ 12) = 26.57°, a 4:12 is 18.43°, a 12:12 is 45°. The chart lists every pitch from 1:12 to 24:12; the calculator does any value, and the other way, degrees back to rise.

What is the slope factor and what is it for?

The ratio of rafter length to horizontal run: √(rise² + 144) ÷ 12. At 6:12 it is 1.118, so every foot of run needs 1.118 feet of rafter, and the roof surface is 1.118 times the plan area. Use it for rafter length, roofing squares and gutter-to-ridge measurements.

How do I measure the pitch of an existing roof?

Hold a level horizontally against the roof or a rafter, mark 12 inches along the level from where it touches, and measure straight down from that mark to the roof. That measurement is the rise per 12. From inside an attic, measure along the underside of a rafter the same way. Enter it in the calculator's rise-and-run mode.

What pitch do I need for shingles or metal?

Asphalt shingles need 4:12 or steeper for standard installation and are allowed down to 2:12 with doubled underlayment; below 2:12 use a membrane. Standing-seam metal goes to 3:12, some profiles to ½:12. Tile and slate want 4:12 or more. Snow country favours 6:12 and up.

What about hip and valley rafters?

They run diagonally, so their run per foot of common run is √2 = 1.414 feet, and their slope factor is √(rise² + 288) ÷ 12: 1.5 at 6:12 against the common rafter's 1.118. The hip column in the chart gives the multiplier for the hip's plan length.

Charts are computed from the formulas and code figures stated on the page (International Residential Code limits where cited). They are planning and take-off numbers, not engineering: species, grade, span tables and local amendments govern anything structural. Confirm with your inspector before you cut.

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