Sometimes it’s necessary to cut a shed roof type rafter when you only know the height of the knee-wall or the difference between the two walls and the run.
Difference in height in inches divided by run in feet = pitch
Conversely pitch times run in feet = Height difference
So in the above example if the height difference is 36″ and the run is 12′ then 36/12 =3. The pitch is 3 in 12 ( 3/12). Now you can lay out our rafter using 3 as the rise and 12′ as the total run. Of course conversely if you multiply the pitch by the run in feet you get the height in inches
Let’s try another example. Height difference = 40″, Total run 12′ 4″.
Convert feet to its decimal equivalent by diving by 12. ex. 4″/12 = .33′ total run 12.33′
40/12.33 = 3.24 or about a 3 1/4 in 12 pitch.
Once you know the pitch and the total run you can lay the rafter out using a framing square or you can use a calculators trigonometric functions to figure the length.
Note that the birds mouth cut on the rafter will have to be the same depth at the top and the bottom of the rafter.
By Ray Thornburg , original article 11-15-2011
