Roof Truss Ratios

Why Ratios?

• Establishing the ratio of a roof truss is a way to help calculate costs. Once you know the ratio of the slope of a roof to its run, or width of the bottom line of the triangle, you can estimate costs of materials for both sides of the roof. This allows you to treat the entire roof as a single piece, without having to get specific angles and rafter lengths.

What a Ratio Is

• The ratio of a truss is the relationship between its rise, or vertical height at the peak above the line between two walls, and the run, the distance between the peak and the outer wall. Those figures determine the pitch, or how much the roof slopes up from wall to peak. A 12/12 roof, for instance, will rise 12 inches for every foot of run, a 5/12 will rise 5 inches per foot.

Ratio Calculation

• To find the ratio, multiply the rise by the run. For a 12/12 roof, for example, add 12 squared (144) plus 12 squared (144), which is a total of 288. Use the square root key on a pocket calculator to get the square root of 288, which is 16.97 in this example. Divide that by 12 to get a ratio of 1.142. Use the same equation on a 5/12 roof, with a rise of 5 inches per foot, with a 12-foot run. You add 5 squared (25) plus 12 squared (144), which equals 169 -- the square root of 169 is 13, which is the slope. Multiply 13 by 12, find the square root, divide that by 12 and get a ratio of 1.08.

Using the Ratio

• The ratio will determine the true length of any roof element by essentially treating the roof as a flat rectangle. A house plan will show the basic dimensions of the roof, length and width of walls, in a rectangle. Add those figures and multiply that number by the slope ratio to arrive at the total square footage, which will determine the size of rafter boards, roof decking and other materials.