Understanding your result
The headline is the total rafter length from the long point of the plumb cut to the end of the tail, with the two parts (to the building line and the tail) and the board to buy. The stats show the theoretical line length, the rise, the plumb cut angle and the height above the plate. The breakdown walks the rafter from ridge to tail, cut by cut, and ends with the birdsmouth check and the stock size.
The number to remember on site is the shortened length to the building line: that is what you measure along the top edge of the board from the plumb cut to lay out the birdsmouth. The HAP is the number that keeps every rafter at the same height, and it is what the ridge height calculator adds to the rise to put the ridge where it belongs.
The hip and valley rafter calculator uses the same run and pitch for the diagonal members, and the truss count calculator is the alternative when the roof is trussed rather than stick-framed.
How we calculate this
The ridge shortening is the step most often skipped. The run is measured to the centre of the ridge, but the rafter stops at the face of the ridge board, half its thickness short, and that half-thickness is measured horizontally, so it is shortened along the rafter by half the thickness times the pitch factor: ⅞ inch for a 1½-inch ridge at 6/12. Small, but it is the difference between a ridge that sits where the plans say and one that creeps.
The birdsmouth check converts the horizontal seat cut into the depth of material removed perpendicular to the rafter, which is what the code’s quarter-depth limit refers to. A wider wall plate needs a wider seat, which on a steep roof can fail the check; the fix is a deeper rafter or a seat that does not cover the whole plate. The guide to rafter maths draws every cut and shows the framing-square layout.
The assumptions behind the numbers
| Assumption | Default | Where it comes from |
|---|---|---|
| Span | 24 ft, so a 12 ft run | A typical small-house span; enter yours |
| Ridge board | 1½ in (nominal 2× lumber) | Dimensional lumber; LVL ridges are 1¾ in |
| Overhang | 12 in horizontal | Common US eave overhang |
| Rafter depth | 7¼ in (2×8) | Actual size of nominal lumber (2×6 = 5½, 2×10 = 9¼, 2×12 = 11¼) |
| Seat cut | 3½ in | The width of a 2×4 wall plate; 5½ in for a 2×6 wall |
| Notch limit | ¼ of the depth at a bearing | IRC R802.7.1.1 |
| Stock lengths | 8 to 24 ft in 2 ft steps | Dimensional lumber as sold; longer rafters are LVL or spliced |
Assumptions last reviewed October 7, 2026.
The calculator does not size the rafter (that is the IRC span table R802.4 or an engineer), does not handle a ridge beam that the rafters sit on rather than butt against, and does not lay out the cuts on an asymmetrical roof with two different runs, which must be run twice. The guide to roof pitch covers where the angles come from if the pitch is given in degrees.
Two worked examples
A 24-foot span at 6/12 with 2×8 rafters
Span 24 feet, pitch 6/12, 1½-inch ridge board, 12-inch overhang, 2×8 rafters on a 2×4 wall (3½-inch seat).
- Run: 24 ÷ 2 = 12 ft; rise: 12 × 6 ÷ 12 = 6 ft
- Line length: 12 × 1.118 = 13.42 ft (13 ft 5 in)
- Shortened: (12 − 0.0625) × 1.118 = 13.35 ft (13 ft 4 in)
- Tail: 1 × 1.118 = 1.12 ft (1 ft 1 in)
- Total: 14 ft 6 in; buy a 16-ft board
- Plumb cut 26.6°, seat cut 63.4°; HAP: 7.25 ÷ cos 26.6° − 3.5 × tan 26.6° = 8.11 − 1.75 = 6.36 in
- Notch: 3.5 × sin 26.6° = 1.57 in of 7.25 in, within the quarter-depth limit
Fourteen and a half feet from a 16-foot board leaves 18 inches of offcut, enough to check the end for splits before cutting the pattern rafter.
A steep 12/12 roof with a wide seat on a 2×6
Run 10 feet, pitch 12/12, 1½-inch ridge, 12-inch overhang, 2×6 rafters on a 2×6 wall (5½-inch seat).
- Line length: 10 × 1.4142 = 14.14 ft; shortened: 14.05 ft; tail: 1.41 ft
- Total: 15 ft 6 in; buy a 16-ft board
- Plumb cut 45°, seat cut 45°; HAP: 5.5 ÷ cos 45° − 5.5 × tan 45° = 7.78 − 5.5 = 2.28 in
- Notch: 5.5 × sin 45° = 3.89 in of 5.5 in, over the quarter-depth limit of 1.38 in
The rafter fits the board, but the birdsmouth takes 70 percent of the rafter away at the wall. The fix is a 3½-inch seat that does not reach the inner edge of the plate (notch 2.47 in, still over) or, properly, a 2×10 with a short seat. The calculator flags it; the span table or an engineer settles it.
Where to find your inputs
Span. Outside of wall to outside of wall across the building, from the plans or a tape at the top plate. Use run mode if the ridge is off-centre, with each side’s run measured to the ridge centreline.
Pitch. From the plans or a level on an existing rafter; the pitch calculator converts degrees.
Ridge thickness. 1½ inches for 2× lumber, 1¾ for LVL, 0 if the rafters meet at a ridge line with no board, or if they sit on a structural ridge beam (then the run is to the beam’s centre and the plumb cut is a bearing cut).
Rafter size and seat. The lumber you are checking and the width of the wall’s top plate. The seat should not extend past the inside face of the plate.
Common mistakes
- Forgetting the ridge shortening. Half the ridge thickness along the slope, at every rafter. Skip it and the ridge rises and the rafters’ tails come up short at the fascia.
- Adding the overhang horizontally. The tail runs along the slope; a 12-inch horizontal overhang is 13.4 inches of rafter at 6/12.
- Different HAP on different rafters. Every birdsmouth must leave the same height above the plate. Cut one pattern and trace it.
- A seat wider than the plate. The seat should stop at the inside face of the plate; a wider seat deepens the notch for nothing.
- Trusting the length for the size. Length is geometry; size is structure. Check the span table.
- Buying to the line length. The board must cover the tail too. Fourteen and a half feet is a 16-foot board, not a 14.
Questions people ask
- How do I calculate rafter length?
- Multiply the run (half the span on a symmetrical roof) by the pitch factor, √(1 + (rise ÷ 12)²), for the line length from the ridge centre to the outside of the wall; subtract half the ridge board thickness times the factor; add the overhang times the factor for the tail. A 12-foot run at 6/12 gives 12 × 1.118 = 13.42 feet, 13.35 feet after a 1½-inch ridge, and 14.46 feet (14 ft 6 in) with a 1-foot overhang.
- What length of rafter do I need for a 24-foot span?
- At 6/12 with a 1-foot overhang and a 1½-inch ridge board, 14 feet 6 inches, so a 16-foot board. At 4/12 it is 13 feet 8 inches; at 8/12, 15 feet 7 inches; at 12/12, 18 feet 4 inches, which needs a 20-foot board. The overhang and the ridge board are included in those figures.
- What are the plumb cut and seat cut angles?
- The plumb cut at the ridge is cut at the pitch angle from square: 26.6 degrees for 6/12, 33.7 for 8/12, 45 for 12/12. The seat cut of the birdsmouth is the complement, 90 minus the pitch angle, so 63.4 degrees at 6/12. On a framing square the same cuts are laid out with the rise on the tongue and 12 on the blade.
- How deep can a birdsmouth be?
- The International Residential Code (R802.7.1.1) limits notches at the ends of a rafter to one quarter of its depth. For a 2×8 (7¼ inches deep) that is 1.81 inches measured perpendicular to the rafter; a 3½-inch seat on a 6/12 roof removes 1.57 inches and passes, while a 5½-inch seat on a 12/12 roof removes 3.9 inches and fails on anything smaller than a 2×12 with a reduced seat.
- What is the height above plate?
- HAP is the vertical distance from the top of the wall plate to the top edge of the rafter at the birdsmouth. It is the rafter's plumb depth (depth ÷ cos of the pitch angle) minus the heel cut (seat length × tan of the angle): 6.36 inches for a 2×8 with a 3½-inch seat at 6/12. Every rafter on the roof must have the same HAP or the roof plane will not be flat, and it sets the ridge height.
- Does the calculator tell me if a 2×8 is strong enough?
- No. It reports geometry: length, angles and the notch check. Whether a 2×8 can span your run at your spacing under your snow load is in the rafter span tables of the IRC (R802.4) or on the plans, and anything unusual is a question for an engineer. Treat the size here as the one you are checking, not a recommendation.