Common rafter calculator.
Give it the building width and the pitch and it lays out one common rafter: line length, total length with the tail, total rise, how much stock to grab, the plumb-cut speed-square setting, and the birdsmouth seat cut. It draws the whole cut plan so you can carry it to the saw.
This is a common rafter on a gable roof, not a hip or valley. The ridge is assumed centered on the building. Ridge cut and tail cut are both plumb cuts at the same 6 / 12 setting.
Side profile of one common rafter, drawn to your numbers: the plumb cut at the ridge, the birdsmouth seat on the top plate, and the tail out to its plumb cut. Screenshot it and take it to the saw.
Set your speed square to 6 on the common scale (that is 26.57 degrees off level) for every plumb cut. The birdsmouth is a 3.50 in level seat with a plumb heel where the rafter lands on the plate.
Separate from the cut math above. Give the building length and your on-center spacing to ballpark the rafter count for the whole roof.
A ballpark: one row per side plus one for the end. Gable-end walls, openings, and doubled rafters at the ends can change the real count.
The same math you’d do off the rafter table.
The run is half the span less half the ridge, since the ridge sits centered. The total rise is that run times the pitch over 12. A 24 ft wide building at 6/12 gives a 143.25 in run and a 71.6 in rise.
Every 12 in of run carries a set rafter length: the square root of 144 plus the pitch squared, the classic rafter-table number. Multiply that by the run over 12 and you have the line length from ridge to seat.
The overhang rides the same slope, so its rafter length is the overhang times that same table number over 12. Add it to the line length, add a little waste, and round up to the next even foot of stock.
The plumb cut is the pitch on the common scale of your speed square, the roof-slope angle marked off level. Ridge and tail are both plumb cuts. The birdsmouth is a level seat as wide as the plate plus a plumb heel.
This is the free warm-up. PlumbCut reads your whole plan set and prices the entire frame: walls, headers, sheathing, trusses, and the roof. The rafter math is the easy part. Let the AI do the takeoff on your next real job and hand you a customer-ready bid.