Rafter Calculator

Roof pitch determines virtually every rafter calculation—rise, run, cut angles, and material quantities:

Pitch Notation Explained: Pitch is expressed as X/12, meaning the roof rises X inches for every 12 inches of horizontal run. A 6/12 pitch rises 6 inches per foot of run.

Using Pitch Factor: The pitch factor converts horizontal measurements to slope measurements:

• Rafter length on slope = Horizontal run × Pitch factor
• Example: 12 ft run at 6/12 pitch = 12 × 1.118 = 13.4 ft on slope

Converting Pitch to Degrees:

Angle (degrees) = arctan(pitch ÷ 12) × (180 ÷ π)
Example: 6/12 pitch = arctan(0.5) × 57.3 = 26.6°

Pitch and Climate Considerations:

The birdsmouth is the notch cut where the rafter sits on the wall top plate—proper execution is essential for structural integrity:

Components of the Birdsmouth:

1. Seat Cut (Level Cut):

• Horizontal cut that rests flat on the top plate
• Standard width: 3.5" (width of 2×4 wall plate)
• For 2×6 walls: 5.5" seat cut possible but not required
• Must provide full bearing on plate

2. Plumb Cut (Heel Cut):

• Vertical cut at the back of the birdsmouth
• Height determined by seat cut and pitch
• Creates the "heel" that bears against plate edge

3. Heel Height:

• Vertical distance from top plate to top of rafter
• Affects insulation space at eaves
• Formula: Heel Height = Seat Cut × tan(pitch angle)

The 1/3 Rule (IRC R802.6): Never notch more than 1/3 of the rafter depth:

Birdsmouth Calculation Example (6/12 pitch):

• Seat cut: 3.5" (standard)
• Pitch angle: 26.6°
• Heel height: 3.5" × tan(26.6°) = 3.5" × 0.5 = 1.75"
• This is within limits for 2×6 rafters (max notch 1.83")

When to Raise the Birdsmouth:

• Need more insulation space at eaves (raised heel truss)
• Cathedral ceiling with deeper insulation
• Matching existing roofline
• Energy code compliance (R-38+ at eaves)

Rafter size depends on span, spacing, species, grade, and roof loads. These tables assume #2 or better SPF (Spruce-Pine-Fir):

Rafter Span Table - 16" OC, 20 PSF Live Load + 10 PSF Dead Load:

Rafter Span Table - 24" OC, 20 PSF Live Load + 10 PSF Dead Load:

Heavy Snow Load Areas (30 PSF Live + 15 PSF Dead):

When to Consult Span Tables:

• Snow loads over 30 PSF
• Tile or slate roofing (heavy dead load)
• Spans exceeding table values
• Cathedral ceilings (no attic storage bracing)
• Point loads (dormers, solar panels)

2026 Rafter Lumber Prices:

Accurate rafter cutting ensures proper fit and structural integrity:

Tools Required:

• Framing square or speed square
• Stair gauges (for framing square)
• Circular saw with sharp blade
• Tape measure (25' minimum)
• Pencil
• Calculator or rafter table

Setting Up a Speed Square:

1. Locate the "Common" scale on the square
2. Find your pitch number on that scale
3. Pivot the square so pitch mark aligns with board edge
4. Blade edge shows plumb cut angle
5. Tongue shows level cut angle

Marking the Four Cuts:

1. Ridge Plumb Cut:

• Starting point for rafter layout
• Mark plumb line at ridge end
• Shorten by half ridge board thickness (typically 3/4")

2. Birdsmouth (Two Cuts):

• Measure down from ridge plumb cut = rafter line length
• Mark plumb cut (heel cut)
• Mark level cut (seat cut) = wall plate width
• Double-check notch depth doesn't exceed 1/3 rule

3. Tail Plumb Cut:

• Measure overhang along top edge from birdsmouth
• Mark plumb cut for fascia attachment
• May need level cut for soffit nailer

The Pattern Rafter System:

1. Carefully cut ONE pattern rafter
2. Test-fit on actual building
3. Verify: Ridge fits, birdsmouth seats, overhang correct
4. Make adjustments if needed
5. Use pattern to mark ALL remaining rafters
6. Gang-cut multiples when possible

Common Cutting Errors to Avoid:

The ridge supports opposing rafters at the peak—understanding the difference between ridge boards and ridge beams is essential:

Ridge Board (Most Common):

• Provides alignment for opposing rafters
• NOT structural—ceiling joists or collar ties resist thrust
• Size: Minimum 1×6, typically 2× lumber
• Depth: Equal to or greater than rafter cut depth
• Ridge deduction: Subtract half ridge thickness from each rafter run

Ridge Beam (Structural):

• Carries roof load when no ceiling joists provide thrust resistance
• Required for cathedral ceilings without collar ties
• Must be sized by engineer or span tables
• Much larger than ridge board (LVL or built-up)

When Ridge Beams Are Required:

Ridge Board Sizing:

Ridge Board Length Calculation:

Ridge length = Building length - (2 × gable overhang)
For common gable: Ridge = Building length
For barge rafters: Ridge = Building length - (2 × barge extension)

Ridge Height Calculation:

Ridge height above wall plates = Run × (Pitch ÷ 12)
Example: 12' run at 6/12 = 12 × 0.5 = 6 feet
Total height = Wall height + Ridge height above plates

Accurate material takeoffs prevent costly job-site delays and excess waste:

Rafter Quantity Formula:

Rafters per side = (Building length in inches ÷ Spacing) + 1
Total rafters = Rafters per side × 2
Add 10% for waste and defects

Example - 40' Building at 16" OC:

• Building length: 40 ft = 480 inches
• Rafters per side: (480 ÷ 16) + 1 = 31 rafters
• Total rafters: 31 × 2 = 62 rafters
• With 10% waste: 62 × 1.10 = 69 rafters

Complete Materials List for Typical Roof:

Fastener Requirements (per IRC):

2026 Hardware Costs:

Beyond common rafters, various rafter types handle different roof geometries:

Hip Rafters:

• Run diagonally from corner to ridge
• Longer than common rafters (× 1.414 for 12/12 pitch)
• Require compound angle cuts
• Support jack rafters on both sides

Hip Rafter Length Factor:

Hip factor = √(pitch factor² + 1)
Example at 6/12: √(1.118² + 1) = √2.250 = 1.5
Hip run = Common run × 1.414 (for 45° plan angle)
Hip length = Hip run × Hip factor

Valley Rafters:

• Run diagonally in roof valleys
• Same calculations as hip rafters
• Require different direction compound cuts
• Must handle concentrated water drainage

Jack Rafters:

• Shorter rafters from hip/valley to eave or ridge
• Maintain same pitch as common rafters
• Progressive length change by "common difference"
• Common difference = Spacing × Pitch factor

Jack Rafter Common Difference:

Barge (Fly/Rake) Rafters:

• Extend beyond gable end wall
• Supported by lookouts or outriggers
• No birdsmouth cut
• May be decorative/larger dimension

Cripple Jack Rafters:

• Short rafters between two hip/valley rafters
• Found in complex roof intersections
• Both ends cut at compound angles

Modern energy codes often require raised heel details for full insulation depth at eaves:

Standard vs. Raised Heel:

2026 Energy Code Requirements (IECC):

Achieving Raised Heel with Site-Built Rafters:

1. Raise the birdsmouth - Cut seat higher on rafter
2. Add vertical block - Above standard birdsmouth
3. Use deeper rafters - 2×8 or 2×10 even if 2×6 spans work
4. Install blocking - Between rafters at raised heel

Benefits of Raised Heel:

• Full insulation depth to exterior wall
• Eliminates cold/hot spots at eaves
• Prevents ice dams in cold climates
• Required for energy rebates/credits
• Better moisture management

Cost Impact:

• Additional lumber: $50-150 per roof
• Taller fascia: $25-75
• More insulation: Included (it's going in anyway)
• Energy savings: 5-15% heating/cooling