How do you calculate rafter length?

Take the run (half the span on a gable), subtract half the ridge board thickness, and multiply by the rafter multiplier for your pitch: √(pitch² + 144) ÷ 12. Add the overhang × the same multiplier for the tail. For a 24 ft span at 6/12 with a 1½ in ridge and 1 ft overhang that is 14 ft 5⅝ in.

Why subtract half the ridge board?

Rafter tables and multipliers give the length to the centre line of the ridge, what the US Navy's carpentry manual calls the theoretical length. A ridge board sits between the rafters, so each rafter is shortened by half the board's thickness, ¾ in for a 1½ in board.

What length lumber should I buy for rafters?

The next stock length longer than the full rafter, including the tail and some room for the plumb cut. Mills commonly stock dimension lumber from 8 to 20 ft in 2 ft steps, with some wider sizes to 24 ft. The calculator suggests the shortest length that fits.

What are the plumb cut and seat cut angles?

The plumb cut at the ridge is vertical when the rafter is in place. Measured from the rafter's edge, it is the roof angle (26.6° for 6/12). The seat (level) cut of the birdsmouth is 90° minus that (63.4°). On a framing square, you simply hold 12 and the rise.

Rafter Length Calculator — Cut Length & Angles

What a common rafter length is

A common rafter runs at right angles from the wall plate up to the ridge. Its length is measured along the rafter's measuring line, from the plumb line over the outside of the wall (the plate line) to the face of the ridge board, plus the tail that forms the overhang. Every common rafter on a simple gable roof is the same length, so you cut one pattern rafter and copy it.

The calculator needs four things: the span (outside of wall to outside of wall), thepitch or angle, the level overhang, and the ridge board thickness. If you don't know the pitch, find it with the roof pitch calculator first.

The formula

Run = span ÷ 2 − ridge thickness ÷ 2
Multiplier = √(pitch² + 12²) ÷ 12
Rafter to ridge = run × multiplier
Tail = level overhang × multiplier
Ridge height above plate = run × pitch ÷ 12
Plumb cut = roof angle; seat cut = 90° − roof angle

Worked example: 24 ft span at 6/12

A 24 ft wide garage, 6/12 pitch, 12 inch overhang, 2× ridge board (1½ in actual). These are the calculator's defaults.

Run = 24 ÷ 2 − 1.5 in ÷ 2 = 12 ft − ¾ in = 11.9375 ft.
Multiplier for 6/12 = √(36 + 144) ÷ 12 = 1.118.
Rafter to ridge = 11.9375 × 1.1180 = 13.346 ft = 13 ft 4 1/8 in.
Tail = 1 × 1.1180 = 1 ft 1 3/8 in.
Total = 14 ft 5 5/8 in (14.465 ft), so buy 16 ft boards.
Ridge sits 5 ft 11 5/8 in above the top of the wall plate (to the measuring line). Plumb cut 26.6°, seat cut 63.4°.

Load this example in the calculator

Laying out the pattern rafter

The calculator gives the lengths. Marking them on a board is the same for every common rafter. The US Navy's carpentry manual describes it with a framing square held at 12 on the blade and the unit rise on the tongue:

Pick a straight board and sight along it. Mark the crown (the slight upward bow) and keep it on top.
Near the top end, mark the ridge plumb line: the plumb cut angle from the calculator, or the square at 12 and the rise.
Measure the plate to ridge length along the measuring line from that plumb line and mark a second plumb line. This is the heel, where the rafter crosses the outside of the wall. The ridge allowance is already taken off.
Mark the seat cut of the birdsmouth square to the heel line, at the seat cut angle, so the rafter sits flat on the plate.
From the heel line, measure the tail length and mark the tail plumb cut.
Cut, test the pattern on the ridge and plate at both ends of the building, then use it to mark the rest.

Rafter lengths by span and pitch

Plate line to ridge face, with a 1½ in ridge board and no overhang. Add overhang × multiplier for the tail.

Span	4/12	6/12	8/12	10/12	12/12
12 ft	6 ft 3 1/8 in	6 ft 7 5/8 in	7 ft 1 5/8 in	7 ft 8 3/4 in	8 ft 4 3/4 in
16 ft	8 ft 4 3/8 in	8 ft 10 1/2 in	9 ft 6 1/2 in	10 ft 4 in	11 ft 2 3/4 in
20 ft	10 ft 5 3/4 in	11 ft 1 3/8 in	11 ft 11 3/8 in	12 ft 11 1/4 in	14 ft 0 5/8 in
24 ft	12 ft 7 in	13 ft 4 1/8 in	14 ft 4 1/8 in	15 ft 6 1/2 in	16 ft 10 5/8 in
28 ft	14 ft 8 1/4 in	15 ft 7 in	16 ft 9 in	18 ft 1 3/4 in	19 ft 8 1/2 in
32 ft	16 ft 9 5/8 in	17 ft 9 7/8 in	19 ft 1 7/8 in	20 ft 9 in	22 ft 6 1/2 in

Common mistakes

Using the full span as the run. On a gable each rafter covers half the span.
Measuring the overhang along the slope. Enter it level, as it shows on the plans. The calculator converts it to a sloped tail.
Forgetting the ridge allowance. Without it each rafter is ¾ in too long and the ridge rides high.
Buying exact-length lumber. 13 ft 11 3/8 in of rafter won't come out of a 14 ft board once you square the ends and cut the plumb line. Leave a few inches.
Assuming hips use the same numbers. Hip and valley rafters run diagonally and need the hip/valley factor from the roof pitch chart.

The roofing over these rafters can be estimated with the roofing squares calculator. The minimum pitch for each covering is in the minimum roof pitch guide. The calculator doesn't size rafters for load or span. Use your local code's rafter span tables for that.

Rafter Length Calculator

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