Prefabricated trusses have replaced rafters in many roof jobs. The trusses come from a factory and combine angled rafters and joists across the roof. But rafters can provide more attic space and builders still use them in many houses. Figuring rafter angles requires mathematical skills, a good, complete rafter table, or simply a framer's square. That square, also called a carpenter's or roofer's square, will tell you everything you need to know to cut any kind of roof rafter. It combines information from centuries of carpenters in a simple form.
Determine the rafter span, the total width of a roof; the rafter run, the distance each rafter must cover from peak to eave; the roof length, to figure the number of rafters you will need, and the roof pitch, the angle at which it slopes from peak to eave. Use a tape measure to get the length and the span, if the house plan does not provide them, and divide the span by two to get the run. Figure the pitch from a house plan or design. Find the pitch on an existing roof by putting the framer's square on a joist, measuring out 12 inches, then measuring the height to the rafter.
Use the pitch to calculate the first rafter angle, called a top or plumb cut. Most house roofs will be 5/12 or 6/12, meaning a rise of 5 or 6 inches for every foot. Put the point or heel of the framer's square at the bottom of a 2-by-4-inch rafter board, with the thin edge (tongue) to the right. Put the 5-inch mark on the tongue and the 12-inch mark on the wide edge of the square (blade) at the top of the board. That will make an angle at the end of the board along the tongue. That is the plumb cut, which will fit against a ridge board to form the roof peak.
Find the "length of common rafters" line on the table marked on the blade of the square and look up the pitch number (5 for a 5/12 roof). That will show the distance each rafter must cover per foot of run. For a 5/12 it is 13, or 13 inches for every foot of run. For a 12-foot run, it equals 13 feet or 156 inches. Measure that distance down the rafter from the plumb cut, then measure up 1 inch from that spot and make a mark. Measure back 3 1/2 inches and make another mark. Connect those two marks in a triangle, called a bird's-mouth, which will fit over the top cap on the wall.
Figure an additional length for the overhang of the eave and mark a cut angle like the plumb cut, but reversed. Calculate this just like the plumb cut but working on the bottom of the rafter board. Move back to the plumb cut, measure another 3/4 inch down and mark a cut line at the same angle. This will accommodate a 2-inch ridge board, which is actually 1-1/2 inches thick. Cut one pattern rafter, test it on the roof to make sure all the cuts are proper, then use it to cut all other rafters. Determine the number by dividing the roof length by 24 for rafters 24 inches apart, then doubling that number for a rafter on each side.
These are instructions for common rafters, used in gable roofs and in sections of hip roofs, which have slopes on all four sides. Use tables on the framing square to cut hip rafters in similar fashion; these will be longer because they run diagonally from the peak to a corner.