Rafter length calculator

For a gable roof the calculator takes half the width across the wall plates, subtracts half the ridge board and applies the slope factor, then adds the overhang along the slope. It also tells you how deep to cut the birdsmouth and how high the ridge sits. New to this? Words explained.

The rafter math

A common rafter is the hypotenuse of a right triangle: the level run from the wall to the ridge, and the rise that the pitch creates over that run. The slope factor turns any level distance into the length along the slope, so the same factor works for the main rafter and the overhang.

run = building width ÷ 2 − ½ ridge thickness   (gable)
slope factor = √(1 + (pitch ÷ 12)²)
rafter = (run + overhang) × slope factor
roof angle = atan(pitch ÷ 12)

Example: a 12 ft wide shed with a 6/12 roof and a 1½ in ridge. Run = 72 − ¾ = 71¼ in. The 6/12 slope factor is 1.118, so plate to ridge is 79.66 in; a 12 in overhang adds 13.42 in, for 93.08 in — about 7 ft 9-1/16 in along the top edge.

Two worked examples go further: Rafter length for a 12 ft shed at 4/12 for a backyard shed, and Rafter length for a 24 ft span at 6/12 pitch for a two-car garage.

How long a board to buy

The rafter length is a line length along the top edge — not the length of the board. A plumb-cut tail is vertical, so its bottom corner reaches past the end of the top-edge line by the rafter depth × the pitch (rise ÷ 12). Add that, then about 1 in to square up the factory end:

board needed = rafter length + depth × (pitch ÷ 12)   (plumb-cut tail)
                + 1 in trim → next stock length

In the 12 ft, 6/12 example the 93.08 in line is not an 8 ft rafter. A 2×6 (5½ in deep) adds 2.75 in for the plumb cut — 95.83 in — and the 1 in trim makes 96.83 in, just over 96 in, so buy 10 ft boards. A 2×8 (7¼ in) adds 3.63 in: 96.70 in, 97.70 in with trim. At 12/12 the same building needs a 117.73 in line; a 2×6 adds a full 5.5 in (123.23 in) and 12 ft stock. A tail cut square to the rafter needs no plumb-cut allowance, but it won’t take a flat fascia board.

Birdsmouth, HAP and ridge height

The birdsmouth is a seat cut (level, bearing on the top plate) and a heel cut (plumb, against the outside of the wall). The seat length is usually the plate width — 3½ in on a 2×4 wall. The heel cut height is the seat length × rise ÷ 12, and what is left above it is the height above plate (HAP): the distance, measured plumb at the wall line, from the top of the plate to the top of the rafter. Keep the HAP the same on every rafter and the roof plane stays flat.

plumb depth = rafter depth × slope factor
heel = seat × (pitch ÷ 12)
HAP = plumb depth − heel
top of ridge board above the plates = HAP + run × (pitch ÷ 12)
birdsmouth depth (square to the rafter) = heel ÷ slope factor ≤ ¼ × rafter depth

For a 2×6 at 6/12 with a 3½ in seat: plumb depth 5.5 × 1.118 = 6.15 in, heel 1.75 in, HAP 4.40 in (4-3/8 in). On the 12 ft building the top of the ridge board then sits 4.40 + 71.25 × 0.5 = 40.02 in above the plates. The simple rise on the measuring line (36 in for 6 ft of run) is not where the ridge board goes — the HAP and the ridge deduction move it.

The notch depth matters. The 2021 IRC sends rafter notches to R502.8.1 — “Notches at the ends of the member shall not exceed one-fourth the depth of the member” — and Figure R802.7.1.1 draws the birdsmouth with a D/4 maximum, measured square to the rafter. That 2×6 at 6/12 fails with a full 3½ in seat: the notch is 1.57 in against a 1.38 in limit. Cut a seat of about 3 in (the code minimum bearing on wood is 1½ in, R802.6) or use a 2×8, whose limit is 1.81 in. The calculator runs this check and says which way it goes.

The ridge board itself must be “not less in depth than the cut end of the rafter” (R802.3) — the plumb cut, which is deeper than the rafter. A 2×6 at 6/12 has a 6-1/8 in plumb cut, so the ridge is a 2×8.

Overhangs, fascia, rakes and shed roofs

• Fascia. A plumb tail cut is as tall as the plumb depth (6-1/8 in for a 2×6 at 6/12), so the fascia board must be at least that wide. The bottom of the tail sits the heel height plus overhang × pitch ÷ 12 below the top of the wall — 1.75 + 6 = 7¾ in for a 12 in overhang at 6/12 — which sets the soffit line.
• Notched tails. R802.7.1.1 allows notches on the overhanging part of a rafter only where at least 3½ in of rafter remains and the overhang is no more than 24 in long.
• Rake overhangs. Past the gable ends, the roof is carried by fly (barge) rafters — one at each end of each slope, four on a gable — and the ridge board and sheathing run the rake overhang further at each end.
• Shed roofs. One rafter spans the whole width, so the run is the full building width. With a birdsmouth on both walls, the heel on the high wall sits at the inside face of its plate, so the run between heels is the width minus the high plate’s width, and the high plate must sit that run × pitch ÷ 12 above the low one. Overhangs past both walls simply add to the rafter length.

New to roof framing? Framing basics: rafters, hips and deck joists puts the pieces in order. Hip roofs need two more calculations: the hip and valley rafter calculator (hips run 16.97 in per foot of common run) and the jack rafter calculator for the shortened rafters between the hips and the walls.

Measuring and marking

1. Measure the building width across the outside of the top plates at several points; walls are rarely perfectly parallel.
2. Cut one pattern rafter: mark the ridge plumb cut, measure the line length along the top edge, mark the heel cut at the wall line with the HAP above the seat, then add the tail.
3. Test the pattern at both ends of the building before cutting the rest.
4. Crown every rafter up — sight down each board and put the bow on top.