Rafter Calculator

Three cuts on one rafter, and which one the tape reads from

A common rafter carries three cuts: plumb at the ridge, a birdsmouth over the wall plate, a tail cut at the eave. The length a framer marks is not the length of the board — it is the line length, read along the top edge from the ridge plumb line to the heel plumb line, 13 ft 4 3/16 in here. The tail adds 1 ft 1 7/16 in, so the board is 14 ft 5 9/16 in.

Every length here is a run times the slope factor, 1.118034 at 6 in 12 — the one thing this sheet borrows. Where that factor comes from, and how a pitch, an angle and a grade are one fact written three ways, is the roof pitch calculator; bring the rise per 12 back here and this sheet cuts and counts. The angles follow the same rise: plumb 26.57°, seat its complement at 63.43°, 18.43° at 4 in 12. A rise of zero gives a factor of exactly 1, still cut, still counted.

The ridge board, and the half inch that makes a cut list wrong

Two rafters do not meet on the centre line. They meet on the faces of a ridge board, and each gives up half its thickness — horizontally, before the slope. Half of 24 ft is 12 ft; with a 1.5 in ridge the run is 11 ft 11 1/4 in.

Along the slope, that three quarters of an inch becomes 0.8385 in of rafter: cut the same roof with no ridge board and the line length is 13 ft 5 in, not 13 ft 4 3/16 in. Small, until it is the difference between a rafter that seats on the plate and one that rides over it at every pair. Set the field to zero for a shed, for rafters on a strap, or for a ridge beam they hang from.

Height above plate: the number that decides whether the birdsmouth fits

The seat is as wide as the plate, 3.5 in on a milled 2x4. The heel is the plumb face behind it, deeper than the plate is wide because the cut crosses a sloping board: plate width × rise ÷ 12 = 1 3/4 in here, 3 1/2 in at 12 in 12, 2 3/4 in on a 2x6 plate.

What is left above the notch is the height above plate. A 2x8 measured plumb through its depth is 8 1/8 in; less the heel, 6 3/8 in stands above the plate. A 2x12 gives 10 13/16 in; the same 2x8 on a 2x6 plate drops to 5 3/8 in; a 2x6 over a 2x6 plate at 12 in 12 leaves 2 1/4 in. The sheet prints the number and does not judge it: how much may be notched away is a code question.

Counting rafters is a floor plus one

Lay 40 ft of wall out at 16 in o.c. and 480 ÷ 16 gives 30 bays, which takes 31 rafters: one at each mark, plus the one closing the last bay. Two slopes, 62 rafters. The plus one is not a rounding — 37.5 ft gives 28 whole bays and a short one, and still needs 29 a slope, 58 in all.

Stock is the shortest listed length the total fits inside: 16 ft for a rafter of 14 ft 5 9/16 in, 14 ft once the overhang goes, 20 ft at 12 in 12 — and at 24 in o.c. the same building takes 42 of them. No cutting allowance is added: the waste is a decision you take with the yard.

Hips run at 16.9706, not 17

A hip turns a square corner, so its plan run is a diagonal: for every 12 of run on the commons a hip travels √(12² + 12²) = 16.9706 in. The framing-square shorthand rounds that to 17 — 0.17 % long over the whole member. This sheet keeps the root.

Switch the 24 × 40 building to a hip: the ridge shortens by the span to 16 ft, the commons drop to 26, the four hips run 18 ft with 1 ft 6 in of tail, and 8 jacks a side step down by 1 ft 5 7/8 in each — one spacing of run taken along the slope. A valley is the same geometry read inwards. Square the building to 30 × 30 and no ridge is left: the roof is a pyramid, and the sheet prints 4 king commons, not a gable count.

What this sheet will not print

No span table. Whether a rafter of a given depth, species and grade may span a given distance under load is set by the code your jurisdiction has adopted and by the design values the mill publishes, both carrying a revision date; stripped of both, that table is the kind of number that fails an inspection. The same goes for the deepest seat a birdsmouth may be cut to, for any permitted spacing and for a “standard” overhang. This sheet does the geometry on the numbers you work to.

Slope factor   F  =  sqrt( rise^2 + 12^2 ) / 12
Half run       h  =  span x 12 / 2
Run to ridge   R  =  h - ridge thickness / 2
Line length    L  =  R x F
Tail           T  =  overhang x F
Total             =  L + T
Plumb cut      P  =  atan( rise / 12 )        degrees
Seat cut          =  90 - P
Heel           H  =  plate width x rise / 12
Height a/plate    =  depth x F - H
Hip unit run      =  sqrt( 12^2 + 12^2 )  =  16.9706
Rafters/slope     =  floor( length x 12 / spacing ) + 1

Frequently asked

Roof rafter calculator with birdsmouth?

Two cuts and one number. The seat is as wide as the plate, 3.5 in here; the heel is the plumb face behind it, plate width × rise ÷ 12 = 1 3/4 in. What matters is what is left: a rafter 8 1/8 in deep measured plumb, less the heel, stands 6 3/8 in above the plate. All three figures are yours to change.

Shed roof rafter calculator?

One slope, no ridge board — and this sheet frames two slopes off the span you type. So set the ridge thickness to zero, type twice the run, and halve the count. A shed running 8 ft at 3 in 12 with an 18 in overhang is typed as a 16 ft span: line length 8 ft 2 15/16 in, 9 ft 9 1/2 in over the tail, 14.04° plumb, 10 ft stock. Over 24 ft of wall at 24 in o.c. it prints 26: 13 rafters.

How many rafters do I need?

Divide the length by the spacing, drop the fraction, add one, double it for the second slope. 40 ft at 16 in o.c. is 480 ÷ 16 = 30 bays, 31 a slope, 62 in all; at 24 in o.c. 42, at 12 in o.c. 82, and 80 ft of wall 122. Gable-end studs and rafters doubled beside a chimney are extra.

Limits of this sheet

S-203 frames one symmetric roof at one pitch, on a rectangular building, with square hip corners: dormers, unequal pitches and rafter ties are not modelled. The milled dimensions it opens with are defaults — measure your stock and type what you measured.

Sheet S-203 prepared by TakeoffMetric Editorial; no author, credential or field measurement is claimed.