Enter the total roof span (wall-to-wall width) and the roof pitch angle into the calculator to determine the rafter length per side (from ridge to wall plate, excluding any overhang). This calculator can also evaluate any of the variables when the other two are known.
4/12 Pitch Roof Formula
The following formula is used to calculate the length of a rafter (one side) for a symmetrical gable roof when the total span is known.
R = (S/2) / cos(θ)
Variables:
- R is the length of the rafter (ft or m)
- S is the total span of the roof (wall-to-wall) (ft or m)
- θ is the angle of the roof pitch (degrees or radians)
To calculate the length of the rafter, divide half the span of the roof (the run for one side) by the cosine of the roof pitch angle. For a 4/12 pitch roof, the angle is typically 18.43° (since θ = arctan(4/12)).
What is a 4/12 Pitch Roof?
A 4/12 pitch roof refers to a roof slope that rises by 4 inches for every 12 inches of horizontal run. This is a common pitch for residential homes, as it provides a balance between efficient water runoff and architectural aesthetics. The pitch of a roof can impact its overall style, cost, and suitability for certain climates or weather conditions.
