The Common Rafter

Concept one

Span and run are not the same number

The span is the full width the roof crosses, outside of plate to outside of plate. A common rafter never travels the span. It travels half of it, because the other half belongs to the rafter coming up from the opposite wall. That half is the run.

Everything after this is built on the run. The most expensive mistake on a roof is using the span where the run belongs, and it produces a rafter twice as long as the one you needed, on every rafter, before anybody notices. Measure the span, halve it, write the run on the board, and work from the number you wrote.

Concept two

Pitch is a ratio, not an angle

Pitch is written as rise over twelve. Six in twelve means the roof climbs six inches for every twelve inches you travel in toward the ridge. It is not degrees. It is not a percentage. It is a ratio.

That matters because a ratio can be laid straight onto a board and an angle cannot. Hold a framing square with twelve on the body and the pitch number on the tongue, scribe along the tongue, and you have drawn the plumb cut without knowing a single degree. The square is that ratio made out of steel.

Concept three

Rise is run times the pitch

Rise is how far the rafter climbs from the plate to the ridge. Take the run in feet, multiply by the pitch, divide by twelve. A twenty-four foot span at six in twelve: the run is twelve feet, and the rise is twelve times six divided by twelve, which is six feet.

Rise is the number you check headroom against, the number that decides whether the gable end clears the power line, and the number that tells you whether the assembled truss will go through the shop door. It is also the upright leg of the triangle you are about to use.

Concept four

The rafter is the hypotenuse, and there is a shortcut

Run flat, rise up, rafter across the top. That is a right triangle, and the rafter is its hypotenuse: the square root of run squared plus rise squared.

There is a faster road that working framers use. For any given pitch the rafter gains the same length for every single foot of run, and that amount is the square root of twelve squared plus the pitch squared, in inches. At six in twelve it is 13.416 inches of rafter for every foot of run. Multiply by the run in feet and you have the line length, no square root required at the top of a ladder.

That column of numbers is stamped on the face of every framing square ever made. Both roads arrive at the same answer. The second one you can do standing up.

Concept five

Line length is not the board you cut

Line length is the theoretical rafter, ridge to seat. The board is longer, because of the overhang, and shorter at the peak, because half the thickness of the ridge board gets taken off the plumb cut.

The overhang matters more than people expect. It adds along the slope, not along the ground. A twelve inch overhang on a six in twelve roof adds 13.416 inches of board, not twelve. Get that wrong on a hundred rafters and you have bought the wrong lumber.

Buy for the long number. Cut to the short one.