Rafter lengths and cuts
Pitch and span in, rafter out: the line length, the tail, the plumb and seat cuts and the birdsmouth, with the hip and its jacks underneath. Every figure is one you can check against the table on a framing square.
6 means 6 in 12
= 288"
Horizontal, past the wall
= 1.5"
= 3.5"
= 384"
One common rafter, 6:12
Ridge to heel
160 3/16"
160.158"
With the tail
178 1/16"
Buy 16 ft
Run
143 1/4"
Rise
71 5/8"
Slope
26.6°
The birdsmouth, close up
Cutting one common rafter
- Framing square settingsRise on the tongue, 12 on the blade, stepped down the board
- 6" and 12
- Per foot of runThe common rafter line on the square
- 13.4164"
- Plumb cutsRidge, heel and the tail if you cut it plumb
- 26.6° off square
- Seat cut3 1/2" of bearing on the plate
- 63.4° off square
- Heel heightThe plumb part of the birdsmouth
- 1 3/4"
- Height above plateMeasured plumb at the outside of the wall — every rafter matches this
- 6 3/8"
- Rafter at the fasciaPlumb depth at a plumb-cut tail
- 8 1/8"
Against the model code
- Birdsmouth leaves at least two-thirds of the rafter — passesThe seat takes 1.57" square to the rafter, leaving 5.68" of 7.25".
- Something left above the plate — passes6.36" of rafter stands above the plate, measured plumb. Every rafter on the roof has to match this or the sheathing will read the difference.
- At least 2:12 for asphalt shingles — passesThis roof is 6:12, which takes shingles with a single underlayment.
Notch limits and roofing slopes are from the 2021 IRC, and rafter spans themselves are a table this calculator does not have: how far a 2x8 will reach depends on species, grade, spacing, snow load and whether there is a ceiling hanging off it. Ring your building department, and get the span out of their table rather than this page.
If this corner is hipped
- Hip per foot of runOver 17 of run, not 12 — the hip crosses the diagonal
- 18.0000"
- Hip length202 9/16" of run at 19.5°
- 214 7/8"
- Hip plumb cutShallower than the common — the hip lies over a longer run
- 19.5° off square
- Jack rafter differenceEach jack is this much shorter than the last at 16" centres
- 17 7/8"
- Ridge boardA regular hip is short by the span, half at each end
- 8 ft hipped, 32 ft gabled
Jacks down one side, longest first
- Jack 1142 1/4" to the long point, less the hip
- 141 1/16"
- Jack 2124 3/8" to the long point, less the hip
- 123 3/16"
- Jack 3106 1/2" to the long point, less the hip
- 105 5/16"
- Jack 488 5/8" to the long point, less the hip
- 87 7/16"
- Jack 570 11/16" to the long point, less the hip
- 69 1/2"
- Jack 652 13/16" to the long point, less the hip
- 51 5/8"
- Jack 734 15/16" to the long point, less the hip
- 33 3/4"
- Jack 817 1/16" to the long point, less the hip
- 15 7/8"
These are regular hips: the same pitch either side of a square corner, so the hip runs at 45° in plan and both cheek cuts are 45°. An irregular hip — two different pitches meeting, or a corner that is not square — is a different calculation and this is not it.
For the whole roof
- Rafter pairs50 rafters at 16" centres, before the gable ends
- 25
- Stock length178 1/16" of rafter, plus a foot to cut
- 16 ft
Cut one and try it
Lay out the first rafter, cut it, and offer it up to the ridge and the plate before you cut twenty more. A sixteenth of error in the seat cut is invisible on the bench and an inch and a half out by the far end of the building.
Then use that one as the pattern rather than measuring each rafter again. Every rafter traced from the same board is the same length; every rafter measured separately is not.
About cutting rafters
- How long is a rafter for a 6/12 roof?
- 13.4164" of rafter for every foot of run, which is the square root of 12² + 6². Run is not half the building: the rafter stops at the face of the ridge board, so half the ridge thickness comes off first. A 24' wide building with a 1 1/2" ridge has a run of 143 1/4", giving a line length of 160 3/16" from the ridge cut to the heel, before the tail is added.
- Why do hip rafters use 17 instead of 12?
- Because a hip runs the diagonal of the square its run sits in, and the diagonal of a 12" square is 16.97" — which every framing square rounds to 17. So a hip on a 6/12 roof rises 6" over 16.97" of its own run and measures 18" per foot of common run. Its plumb cut is shallower than the common rafter's for the same reason: 19.5° against 26.6°.
- How deep can a birdsmouth be?
- The usual rule is that the seat cut may not take more than a third of the rafter's depth, measured square to the rafter rather than horizontally. That distinction matters on a steep roof: a 3 1/2" seat cut takes 1.57" out of a rafter at 6/12 and 2.47" at 12/12, so the same cut that is fine on a shallow roof is over the limit on a steep one. The IRC's own limit on notches at the end of a bending member (R802.7.1) is a quarter of the depth, and which applies to a birdsmouth is a question for your inspector.
- What is height above plate and why does every rafter need the same one?
- HAP is the depth of rafter left standing above the wall plate, measured plumb at the outside of the wall. It sets how high the roof plane sits, so every common, hip and jack on the roof has to share it — a rafter with a 1/4" deeper birdsmouth than its neighbours drops that corner of the sheathing by a quarter inch, and no amount of shimming at the ridge fixes it.
- Is a ridge board structural?
- Usually not. A conventional ridge board is a spacer that gives the rafters something to bear against; the outward thrust is held by rafter ties or a ceiling joist near the plate, which is why removing ceiling joists to open a room pushes the walls out. A ridge beam, which carries load, is a different member sized by an engineer. If there is nothing tying the bottom of your rafters together, you need one of the two, and this calculator cannot tell you which.