Rafter Calculator

A rafter calculator turns four measurements, span, pitch, ridge thickness and overhang, into the numbers you mark on the board: the cut length, the plumb and seat angles and the birdsmouth. This one also picks the stock length to buy, checks the ridge board and the birdsmouth against the 2021 International Residential Code (IRC), and counts rafters for the length of the building.

Neighboring tools cover the steps before and after. The Roof Pitch Calculator finds the pitch of an existing roof from a rise-and-run measurement, the Roofing Calculator turns the finished roof into squares of shingles, and the Board Feet Calculator prices the lumber list. Use this page when the roof is still a set of boards to cut.

How a common rafter is laid out, and the formulas

Framers measure a common rafter along a measuring line that starts at the building line, the outside face of the wall at the top of the plate, and runs parallel to the rafter edge to the center of the ridge. Level, that line covers the run, half the span; vertically it climbs the rise. Its length, the theoretical line length, is the hypotenuse. Half the ridge board comes off at the top and the overhang tail goes on at the bottom. Both are measured level, so both are multiplied by the slope factor first:

The board line matters at the lumber yard. The ridge and tail cuts are parallel plumb cuts, and their angled ends shift the board by the rafter depth times the unit rise. For a 2x8 at 6/12 that offset is 3-5/8 in, which is why a rafter that looks as if it fits a board often does not.

Worked example: a 24 ft garage at 6/12 with 2x8 rafters

Take a garage 24 ft wide and 40 ft long with a 6/12 roof, 2x8 rafters at 16 in on center, a single 2x ridge board (1-1/2 in thick), 2x4 walls with a 3-1/2 in top plate and a 12 in eave overhang. These are the calculator's default inputs.

• Run and rise: 24 ft ÷ 2 = 12 ft (144 in); 144 × 6 ÷ 12 = 72 in, or 6 ft.
• Slope factor: √(1 + 0.5²) = 1.11803, so the line length is 144 × 1.11803 = 13 ft 5 in.
• Rafter length: (144 − 0.75 + 12) × 1.11803 = 155.25 × 1.11803 = 173.57 in, or 14 ft 5-9/16 in. The ridge took off 13/16 in and the overhang added 13-7/16 in.
• Board: 7-1/4 × 6 ÷ 12 = 3-5/8 in for the plumb cuts, so the shortest board is 14 ft 9-3/16 in and the stock length is 16 ft, with 14-13/16 in to spare.
• Count: 480 in ÷ 16 = 30 spaces, so 31 rafters per side and 62 rafters: 992 linear ft, or 1,322.67 board feet of 2x8.

The birdsmouth has a 3-1/2 in seat and a 1-3/4 in heel. Measured square to the edge the notch is 1-9/16 in deep, about 22% of the 7-1/4 in depth, which leaves 5-11/16 in of rafter, well above the 3-1/2 in the IRC asks for. The plumb cut is 8-1/8 in long, so a 2x8 ridge is too shallow and a 2x10 is the smallest ridge that meets R802.3. The rafter tops meet the ridge 6 ft 6 in above the top plate, not 6 ft, because the top edge of each rafter sits 6-3/8 in above the plate at the wall line.

Second example: a 28 ft house at 8/12 with 2x10 rafters

Now a house 28 ft wide and 36 ft long with an 8/12 roof, 2x10 rafters at 24 in on center, a 1-1/2 in ridge, 2x6 walls (5-1/2 in plate) and a 16 in overhang. The run is 14 ft (168 in) and the rise 9 ft 4 in (112 in). The slope factor is √(1 + (8 ÷ 12)²) = 1.20185, so the rafter is (168 − 0.75 + 16) × 1.20185 = 220.24 in, or 18 ft 4-1/4 in.

The 8/12 plumb cuts shift the board ends by 9-1/4 × 8 ÷ 12 = 6-3/16 in, so the shortest board is 18 ft 10-3/8 in and the stock length is 20 ft. With the full 5-1/2 in seat the heel is 3-11/16 in and the notch takes 3-1/16 in, about a third of the depth, yet 6-3/16 in of rafter remains, so the 3-1/2 in rule is met. The plumb cut is 11-1/8 in, just under the 11-1/4 in depth of a 2x12, which makes a 2x12 the ridge. At 24 in on center the 36 ft length gives 18 spaces, 19 rafters per side and 38 rafters: 760 linear ft, or 1,266.67 board feet.

Plumb cut, seat cut and birdsmouth by pitch

The ridge cut, the heel of the birdsmouth and usually the tail are plumb cuts, vertical once installed; the seat is a level cut. With a framing square, hold the unit rise on the tongue and 12 on the blade along the top edge: the tongue gives the plumb line and the blade the seat. On a saw, the plumb cut is the roof angle measured from a square cut and the seat cut is its complement. The table lists both for 2/12 to 12/12, with the framing square's length per foot of run and the birdsmouth heel on 2x4 and 2x6 walls:

Two code limits govern the birdsmouth. IRC R802.6 requires at least 1-1/2 in of bearing on wood or metal, and R802.7.1.1 requires at least 3-1/2 in of rafter left above the notch on a rafter whose overhang is 24 in or less. Steep roofs on 2x6 walls are where that bites: a 2x6 rafter at 12/12 with a full 5-1/2 in seat is notched 3-7/8 in deep and keeps only 1-5/8 in. Cutting the seat back to 2-13/16 in leaves 3-1/2 in and still bears well over 1-1/2 in.

Ridge depth and rafter span in the IRC

A ridge board must be at least 1 in nominal thickness and at least as deep as the cut end of the rafter (R802.3). On a sloped rafter the cut end is the plumb cut, the rafter depth times the slope factor, so the ridge almost always has to be one size deeper than the rafters. The table shows the plumb cut and the smallest dimensional ridge for each case; a 2x14 is 13-1/4 in deep under NIST PS 20-25, and anything deeper calls for an engineered member:

Span is the one question geometry cannot answer. The IRC sizes rafters with Tables R802.4.1(1) through R802.4.1(8): allowable spans by species and grade, rafter size and spacing, dead load, and either a 20 psf roof live load or a 30, 50 or 70 psf ground snow load, with and without a ceiling attached. Spans are measured on the horizontal projection, so you look up the run, not the sloped length. Raised ceiling joists or rafter ties reduce the span through Table R802.4.1(9), and other species, grades or loads go to the American Wood Council's span tables.

What changes the result

Span and pitch drive almost everything. The cut length grows in proportion to the run and with the pitch through the slope factor, which climbs from 1.05409 at 4/12 to 1.41421 at 12/12. Rafter depth leaves the cut length alone but changes the board, the birdsmouth and the ridge. The table shows the cut length and the board to buy for 2x10 rafters with a 1-1/2 in ridge and a 12 in overhang:

These are lengths only; whether a 2x10 can carry the load over those runs is a question for the span tables. Watch the tight cells: the 24 ft span at 4/12 leaves about 1-1/4 in on a 14 ft board, and the 32 ft span at 12/12 needs a board longer than 24 ft.

Three framing scenarios

• Garden shed, 10 ft span at 4/12: 2x6 rafters with a 1x ridge and a 6 in overhang are 5 ft 9-3/16 in long and come out of 8 ft boards. Their plumb cut is 5-13/16 in, deeper than a 2x6, so even a small shed needs a ridge board 7-1/4 in deep, a 1x8 or a 2x8. A 12 ft shed at 24 in on center takes 14 rafters.
• Porch roof, 12 ft span at 3/12 with a 2x ridge and no overhang: the rafters stop at the wall line, so the birdsmouth is an end notch under R502.8.1 and may take up to one-fourth of the depth. A 3-1/2 in seat notches a 2x6 only 7/8 in, about 15% of its depth, and each rafter is 6 ft 1-7/16 in.
• Steep cabin, 16 ft span at 12/12: 2x6 rafters with a 12 in overhang are 12 ft 7-11/16 in long but need 14 ft boards, because the plumb cuts add 5-1/2 in. On 2x6 walls the seat has to shrink to 2-13/16 in to keep 3-1/2 in of rafter above the notch.

How to use this calculator

1. Enter the span from the outside of one wall to the outside of the other, in feet and inches.
2. Enter the slope as a pitch or an angle; 6, 6/12 and 26.57 degrees describe the same roof.
3. Pick the rafter size. It leaves the cut length alone but sets the plumb cut, the board length and the birdsmouth checks.
4. Enter the ridge, overhang and seat: 1-1/2 in for a single 2x ridge or 0 for gusset plates, the level overhang past the wall, and the plate width the rafter bears on.
5. Add the building length and spacing to count rafters, then read the cut length, the breakdown, the birdsmouth, the IRC checks and the table of other pitches.

Who this calculator is for

Framers use it to cut a pattern rafter without stepping off a framing square. Homeowners planning a shed, garage or porch use it to build a lumber list before the trip to the yard. Estimators get rafter counts and board feet, and plan reviewers can confirm that a ridge board and birdsmouth make sense before they turn to the span tables.

Key terms

• Span: the building width, outside of wall to outside of wall. Run: half of it for a gable rafter.
• Rise and unit rise: the total height the rafter climbs, and the rise per 12 in of run, the "6" in 6/12.
• Slope factor: sloped length per unit of run, √(1 + (pitch ÷ 12)²).
• Line length: the theoretical length from the building line to the ridge center, before ridge and overhang.
• Plumb cut and seat cut: the vertical and level cuts; the seat and the heel together form the birdsmouth.
• Height above plate: the rafter depth left above the seat, measured plumb at the wall line.
• Ridge board and ridge beam: a board only connects opposing rafters; a beam carries load and is engineered.

Tips for cutting rafters

• Cut one pattern rafter, test it at the ridge and at the wall on both sides of the building, then trace the rest from it.
• Sight each board and set the crown, the convex edge, up so the roof load works against the bow.
• Measure along the top edge or the measuring line; between parallel plumb cuts both give the same length.
• Stop the saw at the inside corner of the birdsmouth and finish with a handsaw so you do not overcut into the rafter.
• Order a few spare boards for split ends and rejects; the lumber list here has none.

Limitations

The calculator handles common rafters on a symmetrical gable with both slopes at the same pitch. Hip, valley and jack rafters, shed roofs on a ledger, unequal pitches and trusses need different geometry. It does not size rafters for load, check span, snow drift, wind uplift or connections, and it does not know your local amendments. Section numbers are from the 2021 IRC; if your jurisdiction uses the 2018 or 2024 edition, check the matching sections there.

Related calculators

• To find the pitch of an existing roof with a level and tape, use the Roof Pitch Calculator.
• To order shingles and underlayment for the finished roof, use the Roofing Calculator.
• To convert the rafter list into board feet for pricing, use the Board Feet Calculator.
• For stair stringers, which use the same rise and run layout, use the Stair Calculator.

Sources

• International Code Council, 2021 International Residential Code, Chapter 8: R802.3 (ridge), R802.4.1 with Tables R802.4.1(1) to R802.4.1(9) (rafter size and spans), R802.6 (bearing), R802.7.1 and R802.7.1.1 (notches and cantilevered rafters), with the notch limits of R502.8.1.
• NIST, Voluntary Product Standard PS 20-25, American Softwood Lumber Standard (January 2025): Table 3 dressed sizes (2x8 = 1-1/2 × 7-1/4 in) and section 5.3 on standard lengths and trimming.
• Geometry: run, rise, slope factor, cut angles and the birdsmouth follow from right-triangle relationships and need no outside data. Every figure on this page was computed with the same functions the calculator uses.