How to Calculate Rafter Length: Pitch, Run, and Rise Guide
By The Calcumatix Team Reviewed by Calcumatix Editorial Review 3 min read
Quick Answer
Rafter length equals the square root of (run² + rise²). Rise equals run multiplied by the pitch ratio: for a 5/12 pitch and a 12-foot run, rise = 12 × (5 ÷ 12) = 5 ft. Rafter length = √(12² + 5²) = √(144 + 25) = √169 = 13 ft. Add the overhang by extending the run by the horizontal eave projection before calculating, or calculate it separately and add.
Rafter length is the diagonal distance from the ridge to the wall plate, calculated as the hypotenuse of the right triangle formed by the roof’s run and rise. The run is the horizontal distance from the outside of the wall to the centre of the ridge. The rise is the vertical height from the top of the wall plate to the peak of the ridge. This guide covers the formula, how to find rise from pitch, and how to add the overhang. It does not cover structural sizing, load calculations, or building code requirements.
How Do You Find the Rafter Length Step by Step?
The calculation runs in three steps: find the rise from the pitch and run, apply the Pythagorean theorem, then add the overhang if needed.
- Identify the run (horizontal distance from wall plate to ridge center).
- Calculate the rise using the roof pitch (rise = run × pitch ÷ 12).
- Apply the Pythagorean theorem: Rafter Line Length = √(run² + rise²), then add overhang.
Rafter Length Worked Example
Inputs: 24-ft building width, 5/12 roof pitch, 1.5-inch ridge beam, no overhang.
Step 1: Find the run Run = (24 − 0.125) ÷ 2 = 11.9375 ft
Step 2: Find the rise Rise = 11.9375 × (5 ÷ 12) = 11.9375 × 0.4167 = 4.974 ft (rounded to three decimal places)
Step 3: Apply Pythagorean theorem Run² = 11.9375² = 142.50 (rounded to two decimal places) Rise² = 4.974² = 24.74 (rounded to two decimal places) Sum = 142.50 + 24.74 = 167.24 Rafter line length = √167.24 = 12.93 ft (rounded to two decimal places)
Result: The rafter line length is 12.93 feet. Order lumber in the next standard length above this (typically 14 ft) to allow for birdsmouth cuts and any tail trimming.
Use the rafter calculator to test different pitch and building dimensions.
How Does Roof Pitch Affect Rafter Length?
Roof pitch describes the slope of the roof as a ratio of rise to run per 12 inches of horizontal run. A 5/12 pitch rises 5 inches for every 12 inches of horizontal run. A 12/12 pitch rises 12 inches for every 12 inches of run, which is a 45-degree angle. As pitch increases, rafter length increases relative to run.
| Pitch (rise/12) | Rise for 12 ft run | Rafter length for 12 ft run |
|---|---|---|
| 4/12 | 4 ft | 12.65 ft |
| 5/12 | 5 ft | 13.00 ft |
| 6/12 | 6 ft | 13.42 ft |
| 8/12 | 8 ft | 14.42 ft |
| 12/12 | 12 ft | 16.97 ft |
These values are the rafter line lengths for a clean 12-foot run at each pitch, before ridge deduction or overhang. For actual lumber orders, always work from the specific building dimensions.
How Do You Add the Overhang to Rafter Length?
The overhang (eave projection) extends the rafter beyond the wall plate. To include it, add the horizontal eave projection to the run before calculating:
Extended run = run + eave horizontal projection Extended rise = extended run × (pitch ÷ 12) Total rafter length = √(extended run² + extended rise²)
Overhang Worked Example (Added to Previous)
Inputs: Previous 12-ft run, 5/12 pitch, 18-inch (1.5 ft) horizontal eave projection.
Step 1: Extended run Extended run = 12 + 1.5 = 13.5 ft
Step 2: Extended rise Extended rise = 13.5 × (5 ÷ 12) = 13.5 × 0.4167 = 5.625 ft
Step 3: Rafter length with overhang 13.5² = 182.25 5.625² = 31.64 √(182.25 + 31.64) = √213.89 = 14.63 ft (rounded to two decimal places)
Result: The full rafter length including the 18-inch overhang is 14.63 feet. Order 16-ft lumber.
Sources
- CHBA: Residential Roof Framing Guide, run, rise, and pitch definitions with rafter length calculation.
- Roofing Megastore: How to Calculate Rafter Length, Pythagorean method with illustrated step-by-step.
Find surface area with the roof square footage calculator or see all tools in the construction calculators hub.
Frequently asked questions
What Is the Difference Between Run and Span in Roof Framing?
Span is the full horizontal distance across the building from outside wall to outside wall. Run is half the span (for a symmetrical roof). Rafter length is calculated from the run, not the span. If you are given the span, divide by 2 and subtract half the ridge thickness to find the run. Using the full span instead of the run doubles the rise and produces a rafter that is too long.
Does the Rafter Length Include the Ridge Deduction?
The line length formula (√(run² + rise²)) gives the rafter length from the centre of the ridge to the outside face of the wall. When you calculate the run as (building width − ridge thickness) ÷ 2, the ridge deduction is already built in. If you used the full half-width without subtracting half the ridge thickness, add the deduction step before calculating.
What Tools Do I Need to Cut a Rafter to Length?
Once the rafter length is calculated, mark the plumb cut at the ridge end and the birdsmouth at the wall plate. The birdsmouth notch depth is typically one-third the rafter depth or less, limited by building code. The tail cut at the eave end determines the finished eave line. The Rafter Calculator outputs the line length, pitch angle, and rise for direct use with a framing square or speed square on the job site.
Is This Formula the Same for All Roof Types?
The Pythagorean theorem formula works for any simple sloped rafter. Hip and valley rafters require a different calculation because they run at 45 degrees to the building and use the combined diagonal of the plan view. Compound cuts on hip rafters involve backing angles not covered by this formula. For hip and valley rafter calculations, use a dedicated hip-and-valley calculator.