Rafter length calculator

What a common rafter is

A common rafter runs square off the wall plate straight up to the ridge, at 90° to both. On a plain gable every rafter is a common rafter, so one length cut once and traced as a pattern gives you the whole roof. Hip and valley rafters run at 45° in plan and jacks fill in between them, but every one of those lengths starts from the same two numbers as the common rafter: the run and the pitch. The hip vs gable comparison covers what the extra framing does to area, waste and cost.

How to use the calculator

1. Measure the building span from the outside of one wall plate to the outside of the other. The run is half of it on an equal-pitch gable. If you already have the run (a shed roof, or an addition tying into a wall), switch to Run.
2. Enter the actual ridge thickness: 1.5 in for a 2× ridge board, 0.75 in for 1× stock, more for a doubled or engineered ridge beam. Half of it comes off the run.
3. Pick the pitch. If you do not know it, the roof pitch calculator turns a rise-and-run measurement into one; odd pitches like 7.5/12 go in Custom.
4. Enter the overhang as the horizontal distance from the wall line to the fascia, not a length measured along the slope. That is how plans and fascia lines are dimensioned.
5. Tick the hip or valley box if the roof has them, then read the takeoff and print it.

The rafter length formula, worked

A rafter is the hypotenuse of a right triangle: run along the bottom, rise up the ridge line. You never need the rise to get the length. Multiply the run by the pitch multiplier, √(1 + (rise ÷ 12)²), and you have the line length. The same multiplier converts the horizontal overhang into the tail length. Here is the default on the calculator, a 24 ft span at 6/12:

That 14′ 5 5/8″ piece comes out of a 16 ft board, and the spare length is where the ridge plumb cut and the tail trim come from. Yards usually stock 2× framing lumber in 2 ft steps, so the calculator rounds up to the next even length and tells you when a piece runs past 20 ft, which is a special order or a different member.

Plumb cut and seat cut angles

The plumb cut is the one that stands vertical once the rafter is up: the cut against the ridge, the heel of the birdsmouth, and usually the tail where the fascia goes. Its angle off a square cut equals the roof angle, 26.6° at 6/12. The seat cut is the level cut that sits on the wall plate, and its angle is the complement, 63.4°. On a speed square you skip the degrees and pivot to the pitch number on the common scale. The roof pitch chart lists the angle for every pitch from 1/12 to 12/12.

Hip and valley rafters: the 17-inch unit run

Where two planes of the same pitch meet at an outside corner (a hip) or an inside corner (a valley), the rafter between them runs at 45° in plan. For every 12 in the common rafter travels toward the ridge, the hip travels the diagonal of a 12 × 12 square, 16.97 in. Framers round it to 17. The rise is the same, so a 6/12 main roof has a hip that climbs 6 in every 17 in, a flatter 19.5° plumb cut instead of 26.6°.

In length, that is the common run × √2 for the plan run, then the hypotenuse against the same total rise. On the worked example the hip or valley comes to 17′ 10 7/8″ to the ridge centre, plus 1′ 6″ of tail, so 19′ 4 7/8″ overall: a 20 ft board. Treat it as the theoretical length. The hip's own deduction at the ridge depends on how it lands (against the ridge end or between two common rafters), and it needs side cuts at 45°. Measure those on the deck. The valley types guide covers how the valley is then flashed and shingled.

The birdsmouth and what the code allows

The birdsmouth is the notch that lets the rafter sit flat on the wall plate: a seat cut on the plate and a short plumb cut against its outside face. It is the one notch every stick-framed rafter gets, so it is the one worth getting right. The 2021 International Residential Code sends rafter notches (§R802.7.1) to the joist rules in §R502.8.1, which cap a notch at the end of a member at one-fourth of its depth, and cap any other notch at one-sixth of the depth with none in the middle third of the span.

Two more numbers set the size of the seat. §R802.6 asks for at least 1 1/2 in of bearing on wood or metal and 3 in on masonry or concrete, so the seat cut has to land that much rafter on the plate. And §R802.7.1.1 lets you notch the cantilevered tail as long as at least 3 1/2 in of rafter remains and the cantilever is no longer than 24 in.

Ridge, hip and span rules that touch the length

• Ridge board (§R802.3). At least 1 in nominal thickness and no shallower than the cut end of the rafter. The plumb cut is deeper than the board: a 2×8 rafter (7 1/4 in) at 6/12 cuts about 8.1 in deep at the ridge, so it needs a 2×10 ridge, not a 2×8. Without ceiling joists or rafter ties tying the walls together, the ridge has to be a supported beam, not a board.
• Opposing rafters (§R802.4.2). Framed opposite each other at the ridge, offset no more than 1 1/2 in.
• Hips and valleys (§R802.4.3). At least 2 in nominal thickness, no shallower than the cut end of the rafter, and braced to a bearing partition at the ridge unless designed to carry that load.
• Span tables (§R802.4.1). Rafter spans are measured on the horizontal projection, which is the run, not the length this calculator gives you. Size the lumber against the run, then cut it to the length.

From rafter length to roof area and squares

The rafter length, eave to ridge, is also the slope height of the roof plane. Multiply it by the ridge length plus the rake overhangs and you have one plane of a gable. The worked example on a 40 ft house with 12 in rakes: 14′ 5 5/8″ × 42 ft = 608 sq ft a side, 1,215 sq ft for both, 12.2 squares. Add the 10% waste a simple gable takes and you order against 13.4.

Cut-up roofs are easier on the roof area calculator, which works from plan dimensions and pitch. The roof square calculator adds the waste factor, and what is a roof square explains why the trade counts in hundreds of square feet. From there the shingle bundle calculator turns squares into bundles, starter and ridge cap.