Roof pitch calculator

The whole geometry hangs on one number, the pitch factor 1/cos(angle): plan area times the factor is the true sloping area, whatever the roof type, as long as every plane shares the pitch. Rafter lengths are geometric and deliberately exclude ridge board thickness and the birdsmouth cut, so a carpenter cuts them longer. Material minimum pitches, load limits, and structural rafter sizing are out of scope: check your local code for those.