How to Calculate Gable Roof Rafter Angles

Determine the span, run and pitch -- the key figures in calculating angles for gable roof rafters. You must figure three angles or cuts: top or plumb, where two rafters meet at the peak; birdsmouth or bearing point, where the rafter sits on the top of the wall; and tail or end cut, the end of the rafter on the eave or overhang.

Use the run and pitch to calculate the top or plumb cut, with a framing square which has a 1 ½-inch-wide tongue and a 2-inch-wide blade that form a 90-degree angle at the point or heel. Place the heel on the bottom of the wide edge of a rafter board. Align the pitch mark on the tongue, the 5-inch mark for a 5/12 rafter, and the 12-inch mark on the blade at the top of the board to create an angle along the tongue at the end of the board. This is the plumb cut angle.

Look up the length of common rafter per foot of run table on the square's blade. Get the figure under the pitch mark, which shows how long a rafter must be to cover each foot of run; a 5/12 rafter, for instance, would have a length of 13, meaning each rafter must be 13 inches long for every foot between peak and wall. Multiply that figure by the run; a 10-foot run on a 5/12 rafter would be 130 inches, for example.

Measure that distance with a tape measure on the bottom of the rafter from the bottom of the plumb cut to calculate a birdsmouth, a triangular notch that will fit on the wall cap board. Mark that point and draw a vertical line 1 inch up into the board. Measure 3 ½ inches up the bottom of the board. Draw a line to the top of the 1-inch mark. That forms a 1-inch-by-3 ½-inch triangle to sit on the cap.

Add any overhang or eave to the bottom of the birdsmouth, and mark that point. Figure an end cut one of three ways: Mark an angle like the plumb cut, but reversed, by putting the heel of the square at the top of the board. Do a 90-degree angle straight across the width of the board. Make a double angle by marking the 90-degree point, then cutting off the bottom edge with a horizontal line; the double angle will vary with house design.