How to calculate angles on roof trusses

Written by brad painting | 13/05/2017
How to calculate angles on roof trusses
A truss adds structural integrity to a roof. (Residential Construction image by Chad McDermott from

A roof truss is the structural support for a roof's sheathing and shingles. You might need the angle of a roof truss for various purposes. A steep-sloped roof will absorb greater wind loads, while a gradual slope will absorb more UV rays. These factors might affect structural loading or energy calculations. You can calculate the angles of a triangular roof truss with some basic measurements and trigonometry.

Measure the length of the truss's base. The base is the horizontal component of the truss parallel to the building's ceiling. You actually want the horizontal distance from the edge of the base to the point directly below the apex, or peak. Let us call this distance "b". For symmetrical trusses, this is simply one half of the total base length.

Measure the height of the truss. Let's call it "h". This is simply the vertical distance from its apex to its base.

Calculate the angle of the truss's lower corner. This is the angle made by the base and one of the sloping edges, technically known as "top chords." You can use the trigonometric function inverse tangent, or "arctan," to find this angle. The tangent of an angle is the opposite edge divided by the adjacent edge. Therefore, using algebra, the base angle equals arctan(h/b). If the truss is symmetrical, the two base angles are equal. If not, repeat the same process you used to find the left-side base angle in order to find the right-side base angle.

Calculate the truss's top angle, at the peak. Use the fact that the sum of angles within a triangle always equals 180 degrees. If you have calculated the two base angles, you can subtract their total from 180 to get the peak angle, i.e., the peak angle equals 180 minus base angle 1 minus base angle 2.

Things you need

  • Scientific calculator
  • Measuring tape

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