Calculating the size and angles of roof truss dimensions is a simple and fairly practical application of trigonometry. It is also a routine calculation needed in the building trades. Both the dimensions of the roof and the angle of the roof are important.
Get the width of the structure you want to roof by measuring across the tops of the walls. Divide this number by 2. These are the "base boards" of your roof truss.
Obtain the height of the gable by finding the difference in height between the top of the roof and the top of the structure. This is the "gable post" of your roof truss.
Square the result obtained in Step 1. Add it to the square of the result obtained in Step 2. Take the square root of the sum. For example, if you have a 4.2 m (14 foot) wide structure, with a 1.2 m (4 foot) gable, half of the width will be 2.1 m (7 feet). Multiply multiply 2.1 by 2.1 to get 4.41 and 1.2 by 1.2 to obtain 1.44. Adding 4.41 ans 1.44 gives 5.85, and the square root of 5.85 is 2.42 (8.06 feet). This is the minimum length of the outer board of your roof truss.
Take half of the width of the board you're using as the gable post and deduct it from the bottom chord dimension obtained in Step 1. For example, if you use 5 by 15 cm (2 by 6 inch) boards, the width of the board is 4.3 cm (1 3/4 inches), and half of that width is 2.15 cm (7/8 inch). Each of your base boards is going to be 2 m 7.8 cm (6 feet 11 1/8 inches) long. The place where the gable post and the baseboards are joined will be a right angle of 90 degrees.
- The Resources section has an excellent roof truss calculator that does more than just calculate the dimensions, but allows you to adjust pitch angles and asses the needs for compressive stresses based on climate.