📐 Framing Geometry Tool

Rafter Length Calculator

Calculate precise common rafter line lengths, ridge board deductions, eave overhang tails, and saw cut angles formatted in standard feet, inches, and fractions.

Span Presets:

Framing & Rafter Dimensions

feet

*Total width of the building from the outside of exterior wall framing.

inches (1.5" = 2x lumber)
inches

*Horizontal distance from exterior wall sheathing to fascia board line.

⚠️ Mathematical Geometry Reference Only

This tool calculates geometric cut lengths and angles. It does NOT specify allowable spans, lumber species, member grades (2x6 vs 2x8), or structural load-bearing capacity. Verify all framing sizing against IRC Table R802.5.1 or structural engineering plans.

Common Rafter Geometry6:12 Pitch • 26.5651° Angle
Rafter Line Length (Ridge to Wall Plate)
13' 4-3/16"
13.346531 ft decimal • from ridge cut to birdsmouth plumb line
Eave Overhang Tail
1' 1-7/16"
1.118034 ft
Total Rafter Length
14' 5-9/16"
14.464565 ft
Saw Cut Angles & Dimensions
Plumb Cut (Ridge & Heel):63.4349°from top edge (90° − θ)
Seat Cut (Horizontal Plate):26.5651°level seat angle (θ)
Run, Rise & Length Breakdown
Half-Span (Span ÷ 2):12 ft
Ridge Deduction (Half of 1.5"):−0.0625 ft (0.75")
Effective Run to Wall Plate:11.9375 ft
Line Rise to Wall Plate:5.96875 ft
Eave / Overhang Extension (Horizontal):+1 ft (12")
Total Horizontal Run:12.9375 ft
Total Vertical Rise:6.46875 ft
Pitch Multiplier:1.118034
• Roof Pitch & Angle Trigonometry Hub →• Complete Roof Pitch Reference Chart →• Estimate Shingles & Materials Takeoff →

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Common Rafter Trigonometry & Formulas

In roof framing, a common rafter extends perpendicularly from the exterior wall top plate up to the central ridge board. Calculating its cut length requires three core right-triangle formulas:

1. Effective Line RunLine Run = (Total Span ÷ 2) − (Ridge Board Thickness ÷ 2)

For a 24 ft span with a 1.5" (0.125 ft) ridge board: Half-span is 12.0 ft, minus 0.0625 ft ridge half-thickness = 11.9375 ft effective run.

2. Sloped Line LengthLine Length = Line Run × √(1 + (Rise ÷ 12)²)

At a 6/12 pitch (multiplier 1.118034), an 11.9375 ft run yields an exact line length of 13.3465 ft (13' 4-3/16").

Understanding Birdsmouth Cuts & Saw Angles

A common rafter requires three distinct cuts:

  • Ridge Plumb Cut: A vertical cut at the apex that butts flush against the ridge board. The plumb angle from the rafter top edge equals 90° − Pitch Angle.
  • Birdsmouth Heel (Plumb) Cut: A vertical notch cut that aligns with the exterior face of the wall stud sheathing.
  • Birdsmouth Seat (Horizontal) Cut: A level horizontal notch cut that rests flat on the top wall plate (typically 3.5 inches for 2x4 framing or 5.5 inches for 2x6 framing). Per IRC Section R802.5.2, the bearing notch depth must never exceed one-third of the rafter depth.
  • Eave Overhang Tail Cut: Plumb or square cut at the bottom end of the rafter tail to receive the sub-fascia board.

Frequently Asked Questions

How do I calculate common rafter length?

To calculate common rafter line length: (1) Find half the building span (total width ÷ 2), (2) Subtract half the thickness of the ridge board to find the effective horizontal run, (3) Multiply this effective run by the pitch multiplier √(1 + (Rise/12)²). This gives the exact line length from the top plumb cut to the birdsmouth heel.

Does ridge-board thickness affect rafter run?

Yes. In standard dimensional framing using a nominal 2x ridge board (actual thickness 1.5 inches), each opposing common rafter must be shortened by half the ridge thickness (0.75 inches, or 0.0625 feet) along the horizontal run. Failing to deduct ridge thickness will cause the rafters to push the exterior walls out of plumb.

Does the eave overhang affect rafter length?

Yes. The total board length of a rafter equals the Line Length (ridge to wall plate) plus the Overhang Tail Length. The sloped overhang tail length is calculated as the horizontal overhang distance multiplied by the pitch multiplier (e.g., a 12-inch horizontal overhang at 6/12 pitch adds 12 × 1.1180 = 13.42 inches of sloped tail).

What is the angle for a plumb cut on a rafter?

The plumb cut angle (measured relative to the top edge of the rafter) equals 90 degrees minus the roof pitch angle. For example, a 6/12 roof has a pitch angle of 26.57 degrees, making the plumb cut angle 63.43 degrees (or simply setting your speed square to 6 on the common scale).

Does this calculator size structural rafters?

No. This tool is strictly a mathematical geometry calculator for cut lengths and angles. Sizing the structural member (e.g., choosing 2x6, 2x8, or 2x10 lumber) depends on ground snow loads, dead loads, lumber species and grade, and rafter spacing. Consult IRC Table R802.5.1 or a licensed structural engineer for member sizing.