Roof Pitch Calculator

Pitch, degrees and slope percent describe the same slope

Roof pitch is the inches of rise for every 12 inches of horizontal run, so a 6/12 roof climbs six inches per foot. Degrees and slope percent say the same thing in different units: 6/12 is about 26.6 degrees, or 50 percent.

Which unit you see depends on who you're talking to. Roofers and shingle wrappers say x/12, phone apps report degrees, and engineers use percent.

The area multiplier decides how much roof you buy

The area multiplier is the number that affects your cost. A sloped roof is bigger than the flat footprint under it, and the gap grows as the pitch gets steeper. At 4/12 you're adding about 5 percent. At 12/12 you have 41 percent more roof than footprint, which is why a steep house needs so many more bundles. The roof pitch guide goes deeper on the pitch bands and what each one costs to roof.

The hip and valley factor is for the diagonal lines. Where two planes of the same pitch meet at a corner, the hip (or the valley, on an inside corner) runs longer than the common rafters beside it. Multiply the common rafter's horizontal run by the factor to get the length of the hip, which you need for ridge cap counts and valley metal.

How do you measure roof pitch?

Measure it from the attic with a 12-inch level. Hold one end of the level (a two-footer with a mark at 12 inches works too) against the underside of a rafter, center the bubble, and measure straight up from the 12-inch mark to the rafter. A reading of six inches means 6/12. Enter it in the "12-inch level" tab.

If you can't get into the attic, a phone app reads the angle from the ground, give or take a degree or two. The house plans are better still, since the framer worked from them. If you know a rafter's length and its level run from wall plate to ridge, the rafter tab works out the rise with the Pythagorean theorem. A 15-foot rafter on a 12-foot run has nine feet of rise, so the pitch is 9/12.

Stay off the roof itself unless it's low and dry and you have good boots. Even a one-story fall can injure you. If you're not sure whether those are rafters or trusses up there, see truss vs rafter, and parts of a roof names every piece you're looking at.

Every roofing material has a minimum pitch

The tool checks your pitch against the minimums in Chapter 9 of the International Residential Code (section R905), which most US towns adopt, sometimes with local changes. The minimums are:

• Asphalt shingles: 2/12, with double underlayment from 2/12 up to 4/12.
• Clay and concrete tile: 2 1/2/12, also with double underlayment below 4/12.
• Wood shingles, wood shakes and metal shingles: 3/12.
• Slate: 4/12.
• Standing seam metal: 1/4/12.
• Membranes (TPO, EPDM, modified bitumen, built-up): at least a quarter inch of fall per foot.

The code text for slate, tile, shingles and metal panels is quoted in the R905 roof covering requirements (California's version of the IRC, with the same slope numbers). The wood minimums are laid out in this summary of IRC R905.7 and R905.8.

The minimum isn't the same as the ideal. Many installers would rather see cedar at 4/12 so it dries out after rain, and the Cedar Shake and Shingle Bureau's shake exposure table only lists roofs at 4/12 and up.

How the pitch math works

• Pitch = rise ÷ run × 12. From an angle: 12 × tan(angle). From a rafter: rise = √(rafter² − run²), then the same formula.
• Angle = arctan(pitch ÷ 12). Slope % = pitch ÷ 12 × 100.
• Area multiplier = √(1 + (pitch ÷ 12)²). Rafter length = run × multiplier. Roof area = footprint × multiplier.
• Hip/valley factor = √(pitch² + 288) ÷ 12, for two planes of equal pitch meeting square. Hip length = common run × factor.

Here is the worked example with the default numbers. Six inches of rise over 12 of run gives 6 ÷ 12 × 12 = 6/12. The angle is arctan(0.5), about 26.57 degrees, and the slope is 50 percent. The multiplier is √1.25, about 1.118, so a 12-foot run gives a rafter of 12 × 1.118 = 13.42 feet, overhang not included.

The hip factor works out evenly. √(36 + 288) = 18, divided by 12 is 1.5, so a 12-foot run means an 18-foot hip. The 1,500 square foot footprint becomes 1,500 × 1.118 = about 1,677 square feet, or about 16.8 squares before waste. The roof cost calculator turns that number into materials and a price range.

Roof pitch table, 1/12 to 18/12

The table covers whole pitches from 1/12 to 18/12. Multiply your footprint by the area multiplier to get roof area, or your common run by the hip factor to get hip length.