Rafter Length Calculator

About the Rafter Length Calculator

This calculator finds the sloped length of a common roof rafter, from ridge to eave, using the horizontal run it spans, the roof's pitch, and any eave overhang. It applies straightforward right-triangle geometry rather than a lookup table, so it works for any pitch and run combination a builder enters. The result is a framing reference for estimating rafter lumber length before cutting.

How It Works

Enter the horizontal run in feet, typically half the building width for a common ridge-to-eave rafter, the roof pitch in the standard X:12 rise-per-run notation, and the eave overhang in inches. The overhang is converted to feet and added to the run, and that combined horizontal distance is multiplied by a pitch multiplier derived from the Pythagorean theorem to produce the actual sloped rafter length.

pitch multiplier = sqrt(1 + (pitch / 12)^2); rafter length = (run + overhang in feet) x pitch multiplier

Formula & Methodology

The pitch multiplier comes directly from the roof's right triangle: for every 12 inches of horizontal run, the rafter rises by the pitch value, so the sloped hypotenuse per 12 inches of run is sqrt(12^2 + pitch^2) / 12, which simplifies to sqrt(1 + (pitch/12)^2). Multiplying that factor by the total horizontal distance, run plus overhang, gives the sloped rafter length.

Examples

Standard Gable Roof

With the default 12-foot run, 6:12 pitch, and 18-inch overhang, the pitch multiplier is about 1.118, giving a rafter length of roughly 15.09 feet.

Steeper Pitch, Larger Span

For a 14-foot run at a 10:12 pitch with a 12-inch overhang, the pitch multiplier rises to about 1.302, producing a rafter length of approximately 19.53 feet.

Advantages

Converts a pitch notation and run measurement directly into a usable lumber length instead of requiring manual trigonometry on site.
Accounts for eave overhang separately from the structural run, so the total reflects the actual board length needed rather than just the span.
Uses the same X:12 pitch convention found on building plans and cut with a framing square, so inputs match what's already on the drawings.

Common Mistakes

Ordering rafter stock at exactly the calculated length with no allowance for the birdsmouth notch and ridge board offset.
Entering the full building width as the run instead of half the width, which is what a common rafter actually spans.
Mixing up pitch notation, such as entering a rise-per-foot value that isn't referenced to the standard 12-inch run.

Edge Cases to Watch For

The result is the theoretical line length only - it doesn't subtract for ridge board thickness or the birdsmouth seat cut, so the actual board cut will be a bit shorter than the calculated figure.
The formula is built for a straight common rafter with uniform pitch; hip and valley rafters follow different geometry and need their own multipliers.
Add a margin when ordering lumber, since this is a bare geometric measurement rather than a finished cut-list length.

Common Use Cases

DIY builders framing a shed, porch, or small addition roof.
Framing carpenters double-checking a rafter takeoff before cutting stock.
Apprentices and students learning the geometry behind common roof framing.

Frequently asked questions

Where does the pitch multiplier formula come from?

It's the Pythagorean theorem applied to the roof's right triangle: for every 12 inches of horizontal run, the rafter rises by the pitch amount, so the rafter's actual sloped length compared to its horizontal run is the hypotenuse of that triangle - the multiplier √(1 + (pitch/12)²) captures exactly how much longer the sloped rafter is than the flat horizontal distance it spans.