Roof pitch & rafter calculator

Rafter 14' 5-9/16"6/12 · 26.57° · 50%

Pitch: 6/12
Angle: 26.57°
Slope: 50%
Rafter per foot of run: 13.416"
Rafter run: 11' 11-1/4"
Line length: 13' 4-3/16"
Tail (overhang): 13-7/16"
Rafter length: 14' 5-9/16"
Ridge height above plate: 5' 11-5/8"

These sketches are here to help you order material and price the work quickly. They are not engineered or shop drawings — always build from your approved project drawings.

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Pitch (inches per 12")

Building spanRidge board thicknessOverhang (level)

Length is along the top edge of the rafter, plate line to ridge face plus the tail — lay out the birdsmouth and plumb cuts from it. Rafter size and spacing are structural: use the IRC span tables or an engineer.

Show the math▾

Angle
atan(pitch ÷ 12)
atan(6 ÷ 12) = 26.57
Slope factor
√(1 + (pitch ÷ 12)²) — rafter length per unit of run
√(1 + (6 ÷ 12)²) = 1.1180
Rafter run
(span − ridge board) ÷ 2
( 24' 0" − 1-1/2" ) ÷ 2 = 11' 11-1/4"
Line length
run × slope factor
11' 11-1/4" × 1.118 = 13' 4-3/16"
Tail
level overhang × slope factor
1' 0" × 1.118 = 1' 1-7/16"
Rafter length
line length + tail (before plumb cuts)
13' 4-3/16" + 1' 1-7/16" = 14' 5-9/16"
Ridge height
run × pitch ÷ 12
11' 11-1/4" × 6 ÷ 12 = 5' 11-5/8"

Where the numbers come from

Pitch, angle and rafter length: angle = atan(pitch ÷ 12) · rafter = run × √(1 + (pitch ÷ 12)²) · 6/12 = 26.57°, 13.42" per foot of runRight-triangle geometry: the rafter is the hypotenuse of run and rise. "Unit length" (rafter inches per 12" of run) is what a framing square's rafter table shows — 6/12 = 13.42, 8/12 = 14.42, 12/12 = 16.97. The length here is the line length; birdsmouth and plumb cuts are laid out from it. Rafter size and spacing are structural — use the IRC span tables or an engineer.

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Pitch, angle, percent and common rafter length for a gable roof.