How do I calculate rafter length?

Rafter length = Run × Pitch Multiplier. The run is half the building width (for a gable roof). The pitch multiplier equals √(1 + (Rise/Run)²). For a 12-ft run at 6/12 pitch: multiplier = √(1.25) = 1.118, so rafter = 12 × 1.118 = 13.42 ft. Add tail length for the overhang.

What is a birdsmouth cut on a rafter?

A birdsmouth (or bird's mouth) is a notch cut into the bottom of a rafter where it sits on the top plate of the wall. It consists of a plumb cut (vertical) and a seat cut (horizontal). The seat cut depth should not exceed 1/3 of the rafter's depth to maintain structural integrity.

How many rafters do I need?

Rafter count = (Ridge Length / Spacing) + 1, then multiply by 2 for both sides of a gable roof. Standard spacing is 16 inches on center (OC) or 24 inches OC. A 40-ft ridge with 16-inch spacing: (40 × 12 / 16) + 1 = 31 per side × 2 = 62 rafters total.

What size lumber do I need for rafters?

Rafter size depends on span, spacing, lumber species, and load. Common sizes: 2×6 for spans up to 12 ft, 2×8 for 12–16 ft, 2×10 for 16–20 ft, and 2×12 for 20–26 ft at 24-inch OC. Always verify with span tables in your local building code (IRC Table R802.4).

What is the difference between a rafter and a truss?

Rafters are individual dimensional lumber pieces cut and installed on-site. Trusses are engineered prefabricated assemblies. Trusses are stronger for long spans and faster to install, but leave no usable attic space. Rafters allow a finished attic but require larger lumber and more labor.

Rafter Calculator

Get exact rafter length, birdsmouth cut dimensions, tail overhang, rafter count, and total board feet — everything you need to frame a roof from scratch.

Roof Framing Inputs

Building Span (ft)?

Roof Pitch?

Rafter Overhang (ft)?

Rafter Spacing?

Building Length (ft)?

Ridge Board Thickness (in)?

Common Rafter Length

14.465 ft

Rafter to Plate13.347 ft

Tail (Overhang)1.118 ft

Run (half span)12.000 ft

Rise (total)6.000 ft

Rafters (each side)31

Total Rafters62

Ridge Board Length40.000 ft

Pitch Angle26.6°

Birdsmouth Cut Dimensions

Plumb cut angle (from vertical)26.6°

Seat cut angle (from horizontal)63.4°

Seat cut width (horizontal)3.5" (standard plate)

Plumb cut depth (vertical)1.75"

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How to Use This Calculator

Enter these values to get complete rafter dimensions:

Building Width — The outside-to-outside dimension of the building perpendicular to the ridge. The rafter run = half this width minus ridge board thickness (usually ½ inch).
Roof Pitch — Rise over 12 inches of run (e.g., 6/12). This determines the rafter angle and plumb cut.
Overhang / Eave — How far the rafter extends beyond the wall plate (horizontal measurement). Typical eaves are 12–24 inches.
Rafter Spacing — Distance from center to center, typically 16" OC or 24" OC
Ridge Length — The length of your building parallel to the ridge, for calculating total rafter count

Outputs include: rafter length (plumb to birdsmouth), tail length, total rafter length, plumb cut angle, seat cut depth, and total rafter count with board feet.

The Formula

Run = (Building Width / 2) - (Ridge Thickness / 2)
Pitch Multiplier = √(1 + (Rise/Run)²) = √(1 + (pitch/12)²)
Rafter Length = Run × Pitch Multiplier
Tail Length = Overhang × Pitch Multiplier
Total Rafter = Rafter Length + Tail Length

Plumb Cut Angle = arctan(Rise/12) degrees
Seat Cut Depth = (Plate Width × 12) / Rafter Depth (max 1/3 depth)

Rafter Count = ((Ridge Length × 12) / Spacing) + 1, × 2 sides

Example: 28 ft Wide House, 6/12 Pitch, 18-inch Overhang

Example: Gable Roof, 28 ft span, 6/12 pitch, 1.5 ft overhang, 16-inch OC, 40 ft long

Run28/2 - 0.5/2 = 13.75 ft

Pitch Multiplier√(1 + 0.25) = 1.118

Rafter Length13.75 × 1.118 = 15.37 ft

Tail Length1.5 × 1.118 = 1.68 ft

Total Rafter17.05 ft (cut from 18-ft lumber)

Plumb Cut Angle26.57° from vertical

Rafters per Side(40 × 12 / 16) + 1 = 31

Total Rafters62 pieces

Order 64 pieces of 2×8×18 lumber (2 extra for waste/mistakes). At 16-inch OC spacing with a 6/12 pitch, 2×8 framing is typically adequate for this span with standard live and dead loads.

Frequently Asked Questions

Rafter length = Run × Pitch Multiplier. Run = half the building width minus half the ridge thickness. For 6/12 pitch, multiplier = 1.118. So a 14-ft run: 14 × 1.118 = 15.65 ft. Add tail length separately (overhang × multiplier).

The seat cut (horizontal cut) of the birdsmouth must not exceed 1/3 of the rafter's total depth. For a 2×8 (actual 7.25 inches), max seat depth = 7.25 / 3 = 2.42 inches. Deeper cuts weaken the rafter at its most critical load point.

Opposing rafters must be nailed together at the ridge — either to a ridge board (structural or non-structural) or face-nailed together. IRC requires collar ties or ridge beams to resist outward thrust at the walls. Toenailing is the traditional method; hurricane clips are superior.

For a 6/12 pitch, the plumb cut angle is 26.57° from vertical (or 63.43° from horizontal). Set your circular saw blade to 26.57°. The tail plumb cut (at the eave) uses the same angle. This calculator shows all cut angles.

Refer to IRC span tables. As a rough guide at 16-inch OC: 2×6 spans up to 12 ft, 2×8 up to 16 ft, 2×10 up to 20 ft, 2×12 up to 24 ft (for standard residential loads with Douglas Fir No. 2). Verify with your local code official or engineer.

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Sources & References

The formulas, code requirements, and reference data used in this calculator are sourced from the following authoritative organizations and publications. Local codes vary — always verify with your jurisdiction's building department.

International Residential Code (IRC) 2024 — Chapter 9: Roof Assemblies — ICC
NRCA Roofing Manual (Steep-Slope & Low-Slope) — National Roofing Contractors Association
Asphalt Shingle Installation Manual — ARMA (Asphalt Roofing Manufacturers Association)
ASCE 7-22 — Minimum Design Loads & Associated Criteria — American Society of Civil Engineers
AWC Span Tables for Joists & Rafters — American Wood Council
IRC Chapter 8 — Roof-Ceiling Construction — ICC

Disclaimer: Calculator results are estimates intended for planning and educational purposes only. They do not replace professional engineering analysis, building permit review, or contractor estimates. Always consult a licensed roofing contractor or structural engineer for final specifications.