Roof Pitch Chart: Angle, Slope Multiplier, and Rafter Length per Foot of Run

What the numbers in a pitch mean

The second number in a U.S. pitch is always 12. It is a fixed unit of horizontal distance, so pitches compare directly: an 8:12 roof climbs twice as fast as a 4:12 roof. Run is the horizontal distance, not the distance along the rafter. On a gable roof with equal slopes, the run is half the building width, measured from the outside face of the wall to the ridge centerline.

Pitch, angle, and percent grade describe the same slope. Angle is the arctangent of rise divided by 12. Grade is rise divided by 12, times 100, so 4:12 is 33.3 percent and 12:12 is 100 percent. The IRC uses both forms. It states the asphalt shingle limit as 2 units vertical in 12 units horizontal and gives the equivalent 17 percent slope.

Older plans and some trades use fractional pitch, which divides the rise by the full span instead of the run. Span is twice the run, so 1/4 pitch is 6:12, 1/3 pitch is 8:12, and 1/2 pitch is 12:12. Confirm which convention a drawing uses before ordering material. Stair layout uses the same rise-over-run idea with different limits, covered in the IRC stair code guide.

Roof pitch chart, 1:12 to 18:12

Rafter length per foot of run is the hypotenuse of a triangle with one leg of 12 in. and the other leg equal to the rise. For 6:12 that is the square root of 12 squared plus 6 squared, or 13.42 in. These are the same figures printed in the rafter table on a framing square.

The calculator labels rise under 2 as Flat, 2 up to 4 as Low Pitch, 4 through 9 as Conventional, and 10 and above as Steep. Those labels are for orientation only. Roof coverings have their own minimums, listed further down.

Converting degrees to pitch

Inclinometers, phone apps, and aerial measurements report degrees. Rise per 12 in. of run equals 12 times the tangent of the angle.

A reading of 30 degrees works out to 6.93:12, so the roof is most likely built at 7:12, which measures 30.26 degrees. Treat a phone reading as an estimate, because it depends on how the phone sits against the surface. Confirm with a level and tape as described under site checks.

Rafter length from run

The multiplier also converts plan dimensions to roof surface. A 1,000 sq ft footprint under a 6:12 roof has 1,118 sq ft of surface. Overhangs are horizontal dimensions too, so they take the same factor. The roofing squares guide covers turning that surface area into bundles and underlayment rolls.

Hips and valleys use a different factor

A hip or valley rafter runs along the diagonal of the plan corner, so its horizontal run is 1.4142 ft for every 1 ft of common run. Its length per foot of common run is 12 times the square root of (2 plus rise/12 squared), in inches. That gives 18.00 in. at 6:12, 18.76 in. at 8:12, and 20.78 in. at 12:12. The factors apply to equal-pitch roof planes that meet at 90 degrees in plan. A hip cut with the common multiplier comes out about 25 percent short at 6:12, since 13.42 in. is 75 percent of 18.00 in.

Worked example: 28 ft wide building, 6:12 roof

The building is 28 ft wide and 40 ft long, with 12 in. overhangs on the eaves and gable ends. The roof has equal 6:12 slopes.

1. Run: 28 ft ÷ 2 = 14 ft = 168 in.
2. Multiplier: the square root of (1 + 0.5 squared) is the square root of 1.25, which is 1.1180.
3. Rafter to the ridge centerline: 168 in. × 1.1180 = 187.83 in., or 15 ft 7 13/16 in.
4. Overhang: 12 in. × 1.1180 = 13.42 in. along the slope. The rafter with overhang is 201.25 in., or 16 ft 9 1/4 in.
5. Ridge deduction: a 1.5 in. ridge board takes 0.75 in. of horizontal run from each rafter. Along the slope that is 0.75 × 1.1180 = 0.84 in. The layout length is 200.41 in., or 16 ft 8 7/16 in.
6. Rise from the top plate line to the ridge centerline: 14 ft × 6 in. = 84 in., or 7 ft.

The calculator reports the 201.25 in. figure from step 4 and leaves the ridge deduction to the framer. For roof area, the plan including overhangs is 30 ft by 42 ft, or 1,260 sq ft. Multiplying by 1.1180 gives 1,408.7 sq ft of roof surface. With 10 percent waste that becomes 1,549.6 sq ft, or 15.5 squares, which is 47 bundles at three bundles per square. Waste percentages for different materials are in the material waste guide.

Minimum pitch for common roof coverings

Each steep-slope covering has a minimum pitch below which it is not allowed, or below which extra measures are required. The table lists commonly cited minimums from IRC 2021 Chapter 9.

Shingles are not allowed below 2:12. Roofs at lower slopes use membrane systems such as modified bitumen, EPDM, or TPO, and the deck still needs positive drainage.

What to check on site

• Measure pitch with a level and tape. Hold a level horizontal against the underside of a rafter in the attic, or against the roof surface. Mark 12 in. along the level and measure straight up or down to the rafter at that mark. That distance is the rise. A speed square gives the same reading on its pitch scale.
• Measure the span at the top plates. Run is taken from the outside of the wall plate, not from the siding or the foundation. If the ridge is off center or the two slopes differ, calculate each side with its own run and pitch.
• Size rafters from the horizontal span. IRC rafter span tables are written for the horizontal projection. Use the run, not the sloped length, to look up a member size.
• Round stock lengths up. Dimension lumber commonly comes in 2 ft length steps. A layout length of 16 ft 8 7/16 in. needs 18 ft stock.

Common mistakes

• Treating a sloped measurement as the run. In the example, the rafter to the ridge is 15.65 ft along the slope. Multiplying that by the slope factor again gives 17.50 ft, which is 1.85 ft (about 22 in.) too long. Convert every measurement to a horizontal dimension first. A correct sloped length is only 11.8 percent longer than its run at 6:12.
• Using the span instead of the run. A 28 ft span times 1.118 gives 31.30 ft, twice the length of one rafter. Divide the building width by 2 for a symmetrical gable.
• Reading fractional pitch as rise over 12. A plan note that says 1/4 pitch means 6:12, not 4:12. Ask which convention applies if a drawing does not say.
• Forgetting that overhangs are sloped too. A 12 in. horizontal overhang adds 13.42 in. along the rafter at 6:12, not 12 in.
• Skipping the ridge deduction. Without it, each rafter is about 0.84 in. long in this example, and the ridge ends up higher than the plan shows.
• Rounding the multiplier early. Using 1.12 instead of 1.118 adds 0.33 in. to a 168 in. run. Carry four decimals through the calculation and round the final length.

To run a different span, pitch, or overhang, use the roof pitch and rafter length calculator.

Frequently asked questions