Rafter Calculator

How rafter length and roof angle are calculated

A common rafter forms the hypotenuse of a right triangle whose two legs are the horizontal run (half the building width for a gable roof, plus any overhang) and the total rise (how much the roof climbs over that run). Once run and rise are known, the rafter length follows directly from the Pythagorean theorem: Length = √(run² + rise²).

Roof pitch is expressed as rise per 12 inches of run (a "6/12" pitch rises 6 inches for every 12 inches of horizontal run). Total rise for a given run is therefore rise = run × (pitch ÷ 12), and the roof angle in degrees is angle = arctan(pitch ÷ 12).

This calculator adds the overhang as its own small right triangle (using the same pitch) and adds its length to the main span length to give a full ridge-to-tail rafter length. Actual cut length in the field will be shortened slightly at the ridge for the ridge board thickness and adjusted for the birdsmouth notch at the wall plate — this figure gives the working line length to start from.

Where these numbers come from

The formula and default values in this calculator are based on:

• Right-triangle roof framing method (run, rise, and pitch expressed as rise-per-12) is the standard approach used in carpentry framing squares and framing reference tables such as those published by the American Wood Council and traditional rafter-square manuals.

These are planning estimates. Check your local building code, product specifications, and a licensed contractor before you buy materials or build.