Rafter Length & Pitch Guide

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How Rafter Length and Pitch Math Works

On a centered gable the building span is the full width, outside of wall to outside of wall. Each common rafter only travels half of that: the run. Rise is measured from the top of the plate up to the top of the ridge. Pitch is rise divided by run, then scaled to 12 inches of run so a framer can say “6-in-12” instead of “0.5”.

That line length is plate-to-ridge along the rafter — the measuring line. Add the tail for a level overhang: tail = overhang ÷ cos(pitch). Total stock ridge-to-fascia is line length plus tail. The calculator prints both so you do not add the overhang twice or forget it.

A ridge board eats run. A 1.5" ridge in the middle shortens each common rafter by 0.75" of run. Subtract that before you cut or the pair will be long and the ridge will sit high. The calculator does not guess your ridge; you do.

This is the same right triangle as a stair stringer — rise, run, hypotenuse — but the units and the cuts are roof cuts. Stairs get an IRC rise/run flag. Rafters get a pitch angle and a birdsmouth. Do not mix the two layouts on one square without resetting the gauges.

Common Pitches (Quick Check, Not a Substitute)

Use the calculator for the job in front of you. This table is the shop-wall check for standard X/12 roofs: angle, rise per foot of run, and the length-per-foot-of-run number you see on rafter tables.

Length per foot of run times run in feet is the theoretical line length. 6/12 at 12 ft of run: 13.416" × 12 = 161.00" — same as the example. Odd spans and non-even pitches belong in the calculator, not in this table.

How to Mark Plumb Cuts from the Calculator

The plumb cut is vertical when the rafter is in the roof. On the board it is the pitch angle relative to the rafter edge. The calculator's pitch angle and “plumb cut / birdsmouth heel” are the same number. That is what you set on a Speed Square or on the saw bevel for the ridge.

1. Lock the numbers. Run the Rafter Length & Roof Pitch Calculator. Write pitch X/12, pitch angle, line length, tail, and total stock on the 2x. PDF the cheat sheet if you want it on the sawhorse.
2. Crown up. Sight the stock. Crown toward the sky so the eave does not sag. Cut the straightest piece as the pattern pair.
3. Square at 12 and pitch. Body on 12, tongue on the pitch number (6 for a 6/12). That setting is both the plumb line and the seat line — they are complementary.
4. Ridge plumb first. Tick the plumb cut at the top. Measure line length down the top edge (or along the measuring line if you drop for a birdsmouth). Do not measure along the bottom edge and expect the same number after the birdsmouth is cut.
5. Fascia plumb. The tail plumb cut is the same angle as the ridge. Measure total stock or add tail to the plate line. Cut a square overhang; do not “eyeball” the fascia and then wonder why the rafter is short.

If the angle on the saw does not match the calculator within about a tenth of a degree, the pair will gap at the ridge or the seat will not sit. That is a troubleshooting problem, not a “tap it in” problem.

How to Mark the Birdsmouth

A birdsmouth is two cuts: a heel (plumb, against the outside of the plate) and a seat (level, on top of the plate). The heel uses the same plumb angle as the ridge. The seat uses 90° minus pitch — the calculator's seat/level cut.

1. From the ridge plumb, measure line length to the building line (outside of the plate). That is where the heel lands.
2. From that heel line, mark the seat into the rafter, level, equal to the plate width you will actually sit on (typically 3.5" on a 2x4 wall, 5.5" on a 2x6). Do not seat the full width if remaining rafter depth would drop below what the span and loading need.
3. Cut the heel and the seat as two stops. Do not let a circular saw blow through the crotch. Remaining wood above the seat is the rafter's beam. Overcutting it is the roof version of killing a stringer throat.

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