Most trades people and home handypersons have a framing square (also called a steel square, rafter square or carpenter square) in their woodworking tool kits. If you don't already have one here's a handy link to a good framing square. (buy it)
However, not many people really know how to use the many scales and tables a framing square has. This article covers only the rafter tables. The other tables on the framing square are covered easily and fully in a very good book I highly recommend called Modern Carpentry by Willis H. Wagner. (more info)
The framing square is made up of two legs joined at the heel to form a right angle. The longer leg of the framing square, called the body, is 2" x 24" and the shorter one, called the tongue, is 1 1/2" x 16". If you hold the body of the framing square in your left hand with the tongue pointing to your right you are looking at the face of the framing square, which usually has the brand name on the heel. The back of the framing square is the reverse side. Along the edges of the body and tongue on both sides are the graduations of the framing square. These consist of the following fractions of an inch: eighths, tenths, twelfths, sixteenths and thirty-seconds.
The pitch of a roof can be expressed in three ways (each example has the same pitch):
A carpenter uses the first method, a building code uses the second and a mathematician uses the third.
A carpenter with his framing square in hand will refer to the roof pitch as 4.5 and 12, 5 and 12, 6 and 12, etc. I prefer a pitch of 5 and 12 for an average roof because it is the easiest pitch to calculate.
If you measure the hypotenuse on your framing square between 5" on the inside of the tongue and 12" on the inside of the body you will get a measurement of exactly 13". This tells you that for every 12" of run on your rafter you get 13" of length along the board. That is the same as gaining 1" of rafter length to each foot of run. See how easy that is? For a 26 foot span or 13 foot run of the rafter its length increases by 13". So the length of the rafter from the center of the ridge board to the face of the outside wall will be 14'-1".
Look on the face of the body of your framing square. On some framing squares this is the rafter table. Look under the 5" mark on the top and on the first line of the table. The length of the common rafter per foot of run is 13.0". For a pitch of 7 and 12, look under the 7. See, it's 13.89. So for a 13 foot run the rafter length, from the center of the ridge board to the outside face of the wall would be 13 times 1.89 or 24.57 inches longer than 13 feet, which comes to 15'-0 9/16" or 15.05 feet.
You can also step the framing square down the rafter the number of feet in the total run (half the span). It's just like moving the framing square for each tread and rise on a stair stringer, except going down the rafter. With a 7-12 pitch you would hold the framing square with the 7" mark on the tongue and 12" on the body on the top of the rafter edge with the heel of the framing square below the rafter. Scribe along the side of the tongue where the 7 intersects the rafter and mark the 12, then put the 7 on this new mark and mark a new 12 position on down the rafter. Do this the number of runs or in this case 13 times. Both lengths of rafters should be the same—15.05 feet or 15'-0 9/16", in our example.
Remember, this measurement is from the center of the ridge board to the outside of the wall. You would have to subtract from the rafter half the thickness of the ridge board, which is 3/4" for a 2" ridge board (really 1 1/2" wide) or 3/8" for a 1" ridge board (really 3/4" wide). Determine this length by making a parallel line 3/4" or 3/8" inside the first line, not by measuring along the top of the rafter by 3/4" or 3/8".
The mark on the rafter corresponding to the outside wall point should be scribed along the tongue of the framing square as was the top cut on the rafter. This cut is called the plumb cut since it is plumb or vertical when the rafter is installed.
Now we come to the outside wall of the building and we have to add to the length of the rafter to account for the overhang of the roof, which can be 12", 24" or whatever. From the outside wall line on the rafter, figure your overhang, say 24". So for our example, step down two more steps with the framing square, then subtract 1 1/2" for the rafter trim board parallel to this line. A handy tip is to use the width of the tongue of the framing square, which is 1 1/2", to reduce the length of the overhang by the thickness of the trim board.
Back to the outside wall line, place the outside of the tongue of the framing square alongside this outside wall line, with the body of the framing square pointing away from the wall and the heel below the top of the rafter, then move the tongue of the framing square up and down this line until you read 3 1/2" at the intersection of the bottom of the rafter. Scribe along the framing square at this point. Below this line forms the seat cut or bird's mouth. It drops the rafter down an inch or inch and a half to prevent the wall from spreading out from the roof load. That is also why the ceiling joists are nailed to the rafters at the top of the plate line.
Mark this rafter PAT (not for the neighbour's husband or wife), it's for "pattern" and make a copy of this rafter. Then take both rafters up on the roof and put a short ridge board between them. With the rafters pulled tight against the outside wall they should fit perfectly. Once you're sure the pattern is exactly right you can use it to cut the rest of the rafters.
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