How do you calculate common rafter length?

Common rafter length is calculated using the Pythagorean theorem: rafter length = √(run² + rise²), where run = half the building span minus half the ridge board thickness, and rise = run × (pitch ÷ 12). For a 24 ft wide building with a 6:12 pitch and a 1.5 in ridge board, the run is 11.9375 ft, the rise is 5.97 ft, and the common rafter length is approximately 13.34 ft. Always add extra length for the overhang.

What is a bird's mouth cut on a rafter?

A bird's mouth is an L-shaped notch cut into the bottom edge of a rafter where it rests on the wall's top plate. It consists of a seat cut (horizontal) and a plumb cut (vertical). The seat cut width typically matches the top plate width — 3.5 in for a standard 2×4 top plate. The plumb cut depth equals seat width × tan(pitch angle). The bird's mouth allows the rafter to sit flat on the plate and transfers load directly down into the wall.

What is the plumb cut angle on a rafter?

The plumb cut angle is the angle of the cut at the ridge end of the rafter so the cut face is perfectly plumb (vertical). It equals atan(pitch/12) converted to degrees — for a 6:12 pitch, that is about 26.57°. The seat cut at the bird's mouth is the complementary angle: 90° − plumb cut = 63.43° for a 6:12 pitch. Both cuts are made with the same bevel setting on your saw.

How do you account for the ridge board when cutting rafters?

When laying out a rafter, you must deduct half the ridge board thickness from the theoretical rafter run. For a standard 2× ridge board (1.5 in actual thickness), deduct 0.75 in from the run. This is the "shortening allowance." Without this deduction, opposing rafters will push the ridge out of plumb. The calculator handles this automatically — just enter the ridge board thickness in the input.

What lumber size should I use for rafters?

Rafter size depends on span, spacing, pitch, and lumber species. As a rough guide for 16 in on-center spacing: spans up to 10 ft use 2×6, 10–14 ft use 2×8, 14–18 ft use 2×10, and 18–22 ft use 2×12. Always verify with the IRC span tables (Table R802.4.1) or a structural engineer — these are starting points, not substitutes for code compliance. Higher pitches carry snow load differently and may allow smaller sizes.

How do I calculate rafter spacing (on-center)?

Standard rafter spacing is 16 in on-center (OC) for most residential roofs, with 24 in OC used for heavier lumber or lower loads. To find the number of rafters, divide the ridge length by the OC spacing and add 1 for the end rafter (then double for both sides of the roof). For a 30 ft ridge at 16 in OC: 30 ft ÷ 1.333 ft = 22.5, round up to 23, add 1 = 24 rafters per side, 48 total.

What is the difference between rafter run and rafter span?

Span is the full width of the building from outside wall to outside wall (or from the centerlines of the top plates). Run is half the span, minus half the ridge board thickness — it's the horizontal distance from the wall plate to the centerline of the ridge. For a 24 ft span building with a 1.5 in ridge, the run per rafter is 11.9375 ft. This distinction matters because the rafter length is calculated from the run, not the span.

Rafter Calculator — Length & Bird's Mouth

Calculates common rafter length, total length with overhang, plumb cut angle, and bird's mouth dimensions for any roof pitch.

What Is a Rafter? Roof Framing Fundamentals

This rafter calculator computes common rafter length, count, board feet, and lumber cost from roof span and pitch. A rafter is a structural member in a roof frame that runs from the ridge board (at the peak) down to the top plate of the wall, supporting the roof deck (sheathing), underlayment, and roofing material. Rafters are the primary load-carrying members of a traditional stick-framed roof — they resist the weight of snow, wind uplift, and the roofing material itself, and transfer those loads down through the wall framing to the foundation.

Key rafter components and terminology:

Common rafter — runs perpendicular from ridge to wall plate; the rafter calculated by this tool; most residential roofs use common rafters at 16" or 24" on-center spacing
Hip rafter — runs diagonally from the ridge to a corner of the building in a hip roof; longer than common rafters; requires a different calculation using a hip/valley factor of 17 instead of 12
Valley rafter — runs from the ridge down into a valley where two roof planes meet; the opposite of a hip rafter; same hip/valley factor applies
Jack rafter — a short rafter that runs from a hip or valley rafter to the wall plate or ridge; each is a different length, calculated with the common difference formula
Ridge board — the horizontal board at the peak that rafters frame into on both sides; not a structural ridge beam (which carries load) — a ridge board simply provides a nailing surface
Bird's mouth — the L-shaped notch cut into the bottom of a rafter where it bears on the top plate; the seat cut provides a flat bearing surface; the plumb cut is vertical against the plate
Tail — the portion of the rafter that extends past the wall to form the eave overhang; protects siding and windows from rain

IRC Section R802 governs rafter sizing for residential construction. Critical requirements include: rafters must provide at least 1.5 inches of bearing at the wall plate (R802.6), the bird's mouth notch must not exceed one-third the rafter depth (R802.7.1), and ceiling joists or rafter ties must be present to resist outward thrust at the wall plates (R802.3.1).

How to Use This Rafter Calculator

Enter your building span (the full width from outer wall to outer wall), select your roof pitch, and set your eave overhang. The calculator instantly returns the common rafter length from ridge to wall plate, the total rafter length including overhang, the plumb cut angle for the ridge cut, and the bird's mouth dimensions for the wall plate notch. It also accepts a ridge board thickness so the shortening allowance is applied automatically. For the full roof material picture — shingles, underlayment, and bundles — see our roofing calculator.

How to Calculate Common Rafter Length

Rafter length is calculated with the Pythagorean theorem. The rafter is the hypotenuse of a right triangle whose legs are the run (horizontal) and rise (vertical).

Find the run: run = (span ÷ 2) − (ridge thickness ÷ 2). For a 24 ft span with a 1.5 in ridge board: run = 12 − 0.0625 = 11.9375 ft.
Find the rise: rise = run × (pitch ÷ 12). For a 6:12 pitch: rise = 11.9375 × 0.5 = 5.97 ft.
Apply Pythagorean theorem: rafter = √(11.9375² + 5.97²) ≈ 13.34 ft.
Add the overhang: overhang_length = overhang_run ÷ cos(pitch_angle). For a 12 in horizontal overhang at 6:12: 1 ÷ cos(26.57°) ≈ 1.12 ft.
Total rafter = 13.34 + 1.12 = 14.46 ft. Order lumber at the next standard length above this.

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Plumb Cut Angle and Seat Cut Angle

The plumb cut at the ridge end of a rafter is the angle at which the rafter is cut so its face is perfectly vertical (plumb). It equals atan(pitch ÷ 12) in degrees. For a 6:12 roof, the plumb cut angle is atan(0.5) ≈ 26.57°.

The seat cut at the bird's mouth is the complementary angle: 90° − plumb cut. For a 6:12 roof, seat cut = 63.43°. Both cuts use the same bevel setting on a speed square or miter saw — just flip the reference. A roof pitch calculator can also help you find the exact angle from rise and run measurements.

Setting Your Speed Square

Hold your speed square against the rafter stock with the pivot point at the edge. Read the pitch number (6 for 6:12) on the "Common" row — that gives you the plumb line. Rotate 90° to get the level (seat) line. Mark both lines at the bird's mouth location, then cut. The depth of the plumb cut at the bird's mouth should not exceed one-third of the rafter depth (IRC R802.7.1).

Bird's Mouth: Seat Cut and Plumb Cut Depth

The bird's mouth is the L-shaped notch where the rafter bears on the top plate. It has two faces:

Seat cut (horizontal face): Must bear fully on the top plate. For a 2×4 top plate, the seat cut is 3.5 in wide. For a 2×6 plate, it can extend to 3.5 in without exceeding the IRC one-third depth rule.
Plumb cut (vertical face): The depth of this cut = seat_horizontal × tan(pitch_angle). For a 3.5 in seat on a 6:12 roof: 3.5 × tan(26.57°) = 3.5 × 0.5 = 1.75 in deep.

Per IRC Section R802.7.1, the notch depth at the bird's mouth must not exceed one-third of the rafter's actual depth. For a 2×8 (7.25 in actual), the maximum notch is 7.25 ÷ 3 = 2.42 in. If your calculated plumb cut depth exceeds this, you need a larger rafter or a different plate width.

Rafter Overhang: How It's Calculated

Overhang is specified as the horizontal distance the eave extends past the wall — typically 12 to 24 inches for residential roofs. The actual length of rafter timber in the overhang is longer than the horizontal measurement because it follows the slope:

overhang_length = overhang_run ÷ cos(pitch_angle)

For a 12 in horizontal overhang on a 6:12 roof: 12 ÷ cos(26.57°) = 12 ÷ 0.8944 ≈ 13.4 in (1.12 ft) of rafter stock. Wider overhangs proportionally increase material. Always include the overhang in your total rafter length when ordering lumber.

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Lumber Sizing and Material Ordering

Once you have the total rafter length (including overhang), round up to the next available dimensional lumber length — 8, 10, 12, 14, 16, 18, or 20 ft. For example, a 14.46 ft total rafter requires 16 ft stock. This leaves a small cutting allowance. Multiply by the total rafter count (both sides of the roof) to get the total linear footage to order. Use our board foot calculator to convert linear footage to board feet if your lumber yard prices by BF.

IRC Rafter Size Guidance

The International Residential Code (IRC Table R802.4.1) provides span tables based on lumber species, grade, rafter spacing, and snow load. As a general starting point for #2 Southern Yellow Pine at 16 in OC with a 20 psf live load: 2×6 spans up to about 11 ft, 2×8 up to 15 ft, 2×10 up to 18 ft, and 2×12 up to 21 ft. Verify with your local jurisdiction — climate and ground snow load vary significantly by region.

Sources & References

National Design Specification (NDS) for Wood Construction — American Wood Council

Rafter Calculator

Common Pitch Reference

Rafter Formula

Min. Rafter Bearing (IRC R802)