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Roof Pitch Calculator

Convert between the three ways of describing a roof’s slope: pitch as inches of rise per 12 inches of run, angle in degrees, and slope percent. Enter any one, plus the horizontal run, to get the rafter length too.

Quick examples

Horizontal distance, not the length along the slope.

Horizontal distance from the wall plate to the ridge; add any overhang.

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Roof pitch (rise per 12)6 /12
Written as
6/12
Angle
26.57 °
Slope
50%
Pitch multiplier
1.118
Rafter length
13.42 ft

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      Formula

      Pitch = rise ÷ run × 12
      Angle = arctan(rise ÷ run)
      Slope % = rise ÷ run × 100
      Pitch multiplier = √(1 + (rise ÷ run)²)
      Rafter length = run × pitch multiplier

      How to use it

      1. Choose what you know: rise and run, a pitch such as 6/12, or an angle.
      2. Enter the values; rise and run can be in any unit.
      3. Enter the horizontal rafter run, which is half the building span for a gable roof.
      4. Read the pitch, angle and rafter length.

      Worked examples

      A roof that rises 6 inches for every 12 inches of run, with a 12 ft rafter run

      Roof pitch (rise per 12)
      6 /12
      Written as
      6/12
      Angle
      26.57 °
      Slope
      50%
      Pitch multiplier
      1.118
      Rafter length
      13.42 ft

      A 45° roof over a 10 ft run

      Roof pitch (rise per 12)
      12 /12
      Written as
      12/12
      Slope
      100%
      Pitch multiplier
      1.4142
      Rafter length
      14.14 ft

      A shed roof that rises 4 ft over a 16 ft run

      Roof pitch (rise per 12)
      3 /12
      Written as
      3/12
      Angle
      14.04 °
      Slope
      25%
      Rafter length
      16.49 ft

      Common pitches in degrees

      2/12 = 9.46°. 3/12 = 14.04°. 4/12 = 18.43°. 5/12 = 22.62°. 6/12 = 26.57°. 8/12 = 33.69°. 10/12 = 39.81°. 12/12 = 45°.

      Most houses fall between 4/12 and 9/12. Asphalt shingles are generally not used below 2/12, and between 2/12 and 4/12 manufacturers require special underlayment.

      About the rafter length

      The length given is the theoretical line length from the outside of the wall plate to the center of the ridge. A real rafter is shortened by half the ridge board’s thickness and lengthened by any overhang, so add the overhang to the run before calculating.

      Questions people ask

      What angle is a 6/12 pitch roof?

      26.57 degrees. The roof rises 6 in for every 12 in of horizontal run, a 50% slope.

      How do I measure roof pitch?

      Hold a level horizontally against the roof or a rafter, mark 12 in along it, and measure straight down from that mark to the roof surface. That vertical distance in inches is the pitch.

      How long is a rafter for a 12 ft run at 6/12?

      13.42 ft, or about 13 ft 5 in: 12 ft × 1.118. Add extra for the overhang.

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