How do I calculate rafter length from pitch and span?

Run = Span ÷ 2. Rafter Length = Run × Pitch Multiplier. Common multipliers: 6/12 pitch = 1.118, 8/12 = 1.202, 4/12 = 1.054. For a 24-foot span (12-foot run) at 6/12 pitch: 12 × 1.118 = 13.42 feet. Add overhang separately: 2-foot overhang at 6/12 = 2 × 1.118 = 2.24 feet additional.

What is the pitch multiplier method for rafters?

The pitch multiplier is the length of rafter per foot of horizontal run, derived from the Pythagorean theorem. At 6/12 pitch: √(1² + 0.5²) = √1.25 = 1.118. Multiply run by this factor to get rafter line length without drawing or calculating right triangles. Multipliers are published in rafter tables on most framing squares.

How much does ridge board thickness affect rafter length?

The ridge board shortens each rafter's layout line by half the ridge board thickness, measured perpendicular to the plumb cut. For a standard 1.5-inch (2×) ridge board, rafters shorten by approximately 3/4 inch measured horizontally. This is often called the 'ridge reduction' and is important for accurate layout on site.

How many rafters do I need for a 40-foot building?

For 16" on-center spacing: (40 ft ÷ 1.333 ft) + 1 = 30 + 1 = 31 rafters per side, or 62 total for a gable roof. At 24" o.c.: (40 ÷ 2) + 1 = 21 per side, 42 total. Always add one rafter per side because you need a rafter at both ends.

How to Calculate Roof Rafters: Span, Rise, Pitch, and Rafter Length

Calculate common rafter length from roof pitch, span, and ridge board size. Covers the Pythagorean theorem approach, roof pitch rise-per-foot, and how to account for overhang and ridge reduction.

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Understanding Rafter Components

A common rafter runs from the ridge board at the peak to the top plate of the exterior wall. Calculating rafter length requires knowing:

Span: Total horizontal distance across the building (wall-to-wall, exterior)
Run: Half the span = the horizontal distance each rafter covers
Rise: The vertical height from top plate to ridge
Pitch: Rise over run, expressed as "X in 12" (X inches of rise per 12 inches of run)
Rafter length: The diagonal hypotenuse of the right triangle formed by run and rise

Step 1: Determine the Run

Run = (Building Width − Ridge Board Thickness) ÷ 2

For a 24-foot wide building with a 1.5-inch ridge board: Run = (24 ft − 0.125 ft) ÷ 2 = 11.9375 ft (11 ft 11¼ in)

Many builders simplify: Run = Span ÷ 2, then subtract half the ridge board at the seat cut.

Step 2: Calculate the Rise

Rise = Run × (Pitch numerator ÷ 12)

For a 6/12 pitch and 12-foot run: Rise = 12 × (6 ÷ 12) = 12 × 0.5 = 6 feet

For an 8/12 pitch and 12-foot run: Rise = 12 × (8 ÷ 12) = 8 feet

Step 3: Calculate Rafter Length (Pythagorean Theorem)

Rafter Line Length = √(Run² + Rise²)

Example (6/12 pitch, 12-foot run): Line Length = √(12² + 6²) = √(144 + 36) = √180 = 13.42 feet (13 ft 5 in)

Pitch Multiplier Method (Faster)

Each pitch has a constant multiplier: Rafter Length per 12 inches of run

Pitch	Multiplier (per ft of run)
3/12	1.031
4/12	1.054
5/12	1.083
6/12	1.118
7/12	1.158
8/12	1.202
9/12	1.250
10/12	1.302
12/12	1.414

Formula: Rafter Length = Run × Multiplier

For 6/12 pitch, 12-foot run: Rafter Length = 12 × 1.118 = 13.42 ft (same result as above)

Step 4: Add the Overhang

The overhang extends beyond the wall. Calculate overhang rafter length separately:

Overhang Line Length = Overhang Horizontal Run × Pitch Multiplier

For 2-foot overhang at 6/12 pitch: Overhang = 2 × 1.118 = 2.24 feet (2 ft 3 in)

Total rafter from ridge to tail = 13.42 + 2.24 = 15.66 feet

Ridge Board Reduction

At the ridge, each rafter is cut at an angle (plumb cut) and rests against the ridge board. The rafter layout line shortens by half the ridge board thickness, measured perpendicular to the plumb cut.

For a 1.5-inch ridge board (2× lumber): Shortening = (1.5 ÷ 2) ÷ cos(pitch angle)

For practical carpentry, the shortening is typically 3/4 inch measured horizontally from the calculated length.

Standard Rafter Spacing

Common rafter spacing: 16" o.c. or 24" o.c.

Number of rafters per slope = (Roof Length ÷ Spacing) + 1

For 40-foot building, 16" o.c.: (40 ÷ 1.333) + 1 = 31 spaces + 1 = 32 rafters per side (64 total)

Related Guides

Frequently Asked Questions

How do I calculate rafter length from pitch and span?: Run = Span ÷ 2. Rafter Length = Run × Pitch Multiplier. Common multipliers: 6/12 pitch = 1.118, 8/12 = 1.202, 4/12 = 1.054. For a 24-foot span (12-foot run) at 6/12 pitch: 12 × 1.118 = 13.42 feet. Add overhang separately: 2-foot overhang at 6/12 = 2 × 1.118 = 2.24 feet additional.
What is the pitch multiplier method for rafters?: The pitch multiplier is the length of rafter per foot of horizontal run, derived from the Pythagorean theorem. At 6/12 pitch: √(1² + 0.5²) = √1.25 = 1.118. Multiply run by this factor to get rafter line length without drawing or calculating right triangles. Multipliers are published in rafter tables on most framing squares.
How much does ridge board thickness affect rafter length?: The ridge board shortens each rafter's layout line by half the ridge board thickness, measured perpendicular to the plumb cut. For a standard 1.5-inch (2×) ridge board, rafters shorten by approximately 3/4 inch measured horizontally. This is often called the 'ridge reduction' and is important for accurate layout on site.
How many rafters do I need for a 40-foot building?: For 16" on-center spacing: (40 ft ÷ 1.333 ft) + 1 = 30 + 1 = 31 rafters per side, or 62 total for a gable roof. At 24" o.c.: (40 ÷ 2) + 1 = 21 per side, 42 total. Always add one rafter per side because you need a rafter at both ends.

Last updated 7/28/2026