Cut length (ridge to tail)
17' 10 7/8"
Ridge center to wall line
18' 0"
Length per foot of run
18"
Hip pitch
6 / 16.97 (19.47°)
Cheek (side) cut, top edge from square
46.69°
Cheek cut, saw bevel on the plumb line
45°
Drop the hip seat (or back the hip)
1/4"
Framing square (tongue / body)
6 / 17
How the Rafter Calculator works
A rafter calculator tells you how long to cut each rafter and at what angles. Enter the roof pitch (inches of rise per 12" of run) and either the run, from the outside of the wall to the center of the ridge, or the span, wall to wall, which is twice the run. You get the common rafter cut length, the plumb and level cuts and the birdsmouth, and for hip roofs the hip or valley rafter and every jack rafter.
Each foot of run takes √(12² + rise²) inches of rafter; for a 6/12 roof that is √180 = 13.42", a slope factor of 13.42 ÷ 12 = 1.118. Run in feet × that figure is the length from the ridge center to the outside of the wall, measured along the top edge. Subtract half the ridge thickness × the slope factor, and add the level overhang × the slope factor for the tail. The plumb cut is atan(rise ÷ 12) from square. A hip runs at 45° in plan, so it covers 16.97" per foot of common run and its length per foot is √(288 + rise²).
Example: a 6/12 roof with a 24 ft span (12 ft run) and a 1 1/2" ridge board. Length per foot of run = √(144 + 36) = 13.416", so ridge center to wall is 12 × 13.416 = 161.0" (13' 5"). The ridge deduction is 3/4" × 1.118 = 0.84", leaving a cut length of 160 3/16" (13' 4 3/16"). A 12" overhang adds 12 × 1.118 = 13.42", for 173 9/16" (14' 5 9/16") overall. The plumb cut is atan(6 ÷ 12) = 26.57° and the level cut 63.43°. On the same roof a hip rafter is √(288 + 36) = 18" per foot: 12 × 18 = 216" less a 1 1/8" ridge deduction = 214 7/8" (17' 10 7/8") before its overhang.
Lengths are measured along the measuring line, the top edge above the outside of the wall. Cut one pattern rafter, test it at the ridge and the wall, then mark the rest from it, and keep the same HAP (height above plate) on every rafter so the roof plane stays straight. Hip and jack results assume both roof planes have the same pitch. The calculator does not size rafters: lumber size and allowable span come from the IRC R802 rafter span tables or an engineer, and your local code may differ.
Roof Pitch Chart: common sizes at a glanceFrequently asked questions
How do you calculate rafter length?
Multiply the run in feet by the rafter length per foot of run, √(12² + rise²). For a 6/12 pitch that is 13.42" per foot, so a 12 ft run gives 161" to the ridge center. Then deduct half the ridge thickness along the slope and add the overhang tail; the calculator does both and gives the cut length.
What does a 6/12 roof pitch mean?
The roof rises 6" for every 12" it runs level. That is an angle of 26.57° and a slope factor of 1.118, so every foot of run needs 13.42" of rafter. On a speed square, pivot to 6 on the COMMON scale to mark the plumb cut.
How deep can a birdsmouth cut be?
Framers commonly keep the notch to no more than 1/3 of the rafter depth, and IRC R802.7.1 also limits notches in rafters, so check it and your local code. The seat needs at least 1 1/2" of bearing on wood (IRC R802.6). Example: a 2x8 (7 1/4") on a 2x4 wall (3 1/2" seat) at 6/12 has a 1 3/4" heel cut, a notch of about 1 9/16" (22% of the depth) and a HAP of 6 3/8".
How do you figure a hip rafter length?
On an equal-pitch roof the hip runs at 45° in plan, so it covers 16.97" (12 × √2) for every foot of common run. Its length per foot of common run is √(288 + rise²): exactly 18" for a 6/12 roof, so a 12 ft common run gives a 216" hip before the ridge deduction and overhang. Valleys use the same numbers.
What is the common difference for jack rafters?
It is how much each jack rafter grows from one to the next: the spacing × the slope factor. At 16" on center on a 6/12 roof that is 16 × 1.118 = 17.89" (1' 5 7/8"). The calculator lists every jack length for the spacing you choose and the cheek cut where it meets the hip.