Rafter Length Calculator

How Rafter Length Is Calculated

A common rafter is the hypotenuse of a right triangle. The run is the level distance from the outside of the wall to the center of the ridge, and the rise is how high the roof climbs over that run. The pitch, rise per 12 inches of run, sets the multiplier between them.

On a gable roof, the run is half the span. If the rafters land on a ridge board, each rafter stops at the face of the board, not the center, so take half the ridge thickness off the run first. Forgetting that deduction makes the rafters too long, pushes the peak up and the walls out.

The result is the line length: from the long point of the ridge plumb cut to the heel of the birdsmouth, where the rafter meets the outside of the wall. The overhang tail is added on top of that to get the total board length.

Laying Out the Birdsmouth

The birdsmouth is the notch that seats the rafter on the wall plate: a level seat cut and a plumb heel cut. The IRC sets both ends of its size.

• Bearing: rafters need at least 1-1/2" of bearing on wood or metal (R802.6).
• Notch depth: notches at the end of a sawn rafter may not exceed one-fourth of its depth (R802.7.1). On a 2x12, that is 2-13/16".
• Seat width: the seat should be no wider than the top plate, so the heel, not the toe, carries the load.
• Steep roofs: as the pitch rises, a full-width seat cuts deeper into the rafter. On a 12/12 roof, a 2x12 seat cut is limited to about 4".
• Height above plate: the plumb height from the top of the plate to the top of the rafter, which sets where the roof plane lands and how much room there is for insulation at the eaves.

Rafter Formulas

All lengths in inches. The rafter factor is the same multiplier used on the roof pitch calculator.

Rise

Pitch, inches of rise per 12 inches of run

Ridge

Ridge board thickness (1-1/2" for a 2x)

Overhang

Level overhang past the wall

Seat

Level length of the seat cut

θ

Roof angle, the arctangent of rise ÷ 12

Depth

Actual rafter depth (7-1/4" for a 2x8)

Notch depth is measured square to the rafter’s edge, which is how the IRC one-fourth limit is applied.

Worked Example: 24 ft Gable, 6/12, 2x8 Rafters

A 24 ft span with a 6/12 pitch, a 2x ridge board, 12" of level overhang, 2x8 rafters and a 3-1/2" seat cut on 2x4 walls.

1. Run: 288 ÷ 2 − 1.5 ÷ 2 = 143.25".
2. Rafter factor at 6/12: 1.118. Line length: 143.25 × 1.118 = 160.16", or 13' 4-3/16".
3. Overhang along the slope: 12 × 1.118 = 13-7/16". Total length: 14' 5-9/16", so buy 16 ft stock.
4. Birdsmouth: heel cut 1-3/4", notch depth 1-9/16" against a 1-13/16" limit for a 2x8. Height above plate: 6-3/8".

Result: cut each rafter at 13' 4-3/16" from the ridge plumb cut to the heel, with a 3-1/2" seat and a 1-3/4" heel.

Worked Example: Why the Ridge Deduction Matters

A garden shed 8 ft wide with a 5/12 roof and a 2x ridge board.

1. Run with the deduction: 48 − 0.75 = 47.25", or 3' 11-1/4".
2. At 5/12 the rafter factor is exactly 13 ÷ 12, so the line length is 47.25 × 13 ÷ 12 = 51-3/16".
3. Without the deduction, the run is 48" and the rafter is 52".

Result: skipping the deduction makes each rafter 13/16" too long, enough to lift the ridge and push the walls.

Worked Example: Overnotching on a Steep Roof

A 12/12 roof with 2x12 rafters on 2x6 walls, cut for full bearing with a 5-1/2" seat.

1. Notch limit: 11.25 ÷ 4 = 2-13/16".
2. A 5-1/2" seat at 45° cuts 5.5 × 0.707 = 3-7/8" deep, over the limit.
3. Longest seat that stays within the limit: 2.8125 ÷ 0.707 = 4".

Result: shorten the seat to about 3" (a 2-1/8" notch) and still have more than the 1-1/2" of bearing the IRC requires.

Common Rafter Length Chart

Line length from the ridge plumb cut to the birdsmouth heel, with a 1-1/2" ridge board and no overhang. Add the overhang and extra for the tail cut.

Field Tips

Practical advice from framers in JLC and on the Fine Homebuilding forum, checked against the IRC.

1. 1

   Always deduct for the ridge

   Take half the ridge thickness off the level run before you multiply, 3/4" for a 2x ridge. The rafter stops at the face of the ridge, not its center; skipping the deduction makes an 8 ft wide 5/12 shed rafter 13/16" too long.

2. 2

   Measure span to the framing, not the sheathing

   Line length ends at the outside of the wall framing. If the birdsmouth heel lands on the outside of the sheathing instead, every rafter comes up short.

3. 3

   Don’t overnotch big rafters

   The one-fourth notch limit applies even when the rafter is bigger than it needs to be. 2x10 and 2x12 grades allow larger knots, so overnotching them can void the grade stamp.

4. 4

   Use a consistent seat cut

   One veteran framer gang-cuts rafters and sets the saw for a 3" seat on 2x10 and 2x12 rafters most of the time. A 2-1/2" to 3-1/2" seat avoids weakening the rafter better than matching the plate width on steep roofs.

5. 5

   Keep the seat on the plate

   On a low-pitch roof the notch limit allows a seat wider than the plate. Don’t use it: a seat that overhangs the plate puts the load on the toe of the rafter and invites splitting.

Sources: JLC: Sizing the birdsmouth, Fine Homebuilding forum: Roof rafters