Rafter calculator: length, overhang, birdsmouth and cut angles
This rafter calculator works out the cut list for a common rafter from the span, the roof pitch and the eave overhang: the line length from the ridge to the birdsmouth, the tail length, the total length and the stock length to buy, with the ridge board reduction already taken off. It also sizes the birdsmouth — seat cut, heel cut and height above plate (HAP) — and gives the plumb and seat cut angles for a speed square or saw.
Tick “hip” for the length and angles of a regular hip or valley rafter. It works in feet and inches (to the nearest 1/16″, and it accepts entries like 24′ 6″ or 7 1/4) and in millimetres, for gable roofs and single-slope shed roofs, and a scaled side view shows the rafter on its wall plate.
How to use the Rafter Calculator
- Choose feet & inches or millimetres, and a gable/hip or shed roof.
- Enter the span between the outside faces of the walls and the pitch — rise per 12 or degrees.
- Enter the level overhang, the ridge board thickness, the rafter’s actual depth and the seat cut length (usually the wall plate width).
- Optionally add the building length and spacing for a rafter count, and tick hip for hip and valley rafters.
- Read the total and line lengths, the cut angles and the birdsmouth, then copy the cut list.
Rafter Calculator features
Ridge reduction built in
Half the ridge board thickness is taken off the run before the multiplier, so the length is ready to mark.
Overhang and tail
The tail is the level overhang × the pitch multiplier, added to the line length for the stock length.
Birdsmouth and HAP
Heel = seat × rise/12; HAP = depth ÷ cos(angle) − heel; a warning shows when the notch exceeds ¼ of the depth.
Cut angles
Plumb cut at the roof angle, seat cut at 90° minus it, plus the speed-square setting.
Hip and valley rafters
Regular hips run 16.97 per 12 of common run; length, angle and 45° cheek cuts.
Feet-inches or mm
Results to 1/16″ or to the millimetre, with US even-foot or metric 0.3 m stock lengths.
How rafter length is calculated
Worked example: a 24 ft span at 6/12 with a 1½″ ridge and a 12″ overhang. Run = 144″ − ¾″ = 143¼″; line length = 143.25 × 1.118 = 160.16″ = 13′ 4 3/16″; tail = 13.42″; total 14′ 5 9/16″, so buy 16 ft boards. With a 2×8 (7¼″) and a 3½″ seat, the heel is 1¾″, the notch is 22% of the depth and the HAP is 6 3/8″. Every rafter in the roof uses the same HAP, which keeps the roof plane flat.
- Run = span ÷ 2 for a gable (the full span for a shed roof), less half the ridge board thickness.
- Pitch multiplier = √(1 + (rise ÷ 12)²). For 6/12 it is 1.1180.
- Line length = run × multiplier, measured along the top edge from the ridge plumb cut to the heel of the birdsmouth.
- Tail = level overhang × multiplier; total = line length + tail.
Birdsmouth, plumb and seat cuts
The plumb cut at the ridge and the heel cut of the birdsmouth are both vertical, at the roof angle from square across the board (26.6° for 6/12). The seat cut is level, at 90° minus that angle. On a speed square, pivot to the rise per 12 on the COMMON scale and draw along the edge for the plumb line.
Keep the birdsmouth shallow: the International Residential Code limits notches at the ends of sawn-lumber rafters to one quarter of the depth (R802.7.1 in recent editions), and the ridge board must be at least as deep as the plumb cut. The seat may bear on less than the full plate width if the notch would otherwise be too deep — check the minimum bearing your code requires.
What this rafter calculator does not do
It is geometry, not structural design. It does not choose the rafter size, spacing or span for snow, wind and dead loads, and it does not design ridge beams, collar ties or ceiling joists. Use the span tables in your building code (IRC tables R802.4.1 in the US, NCC and AS 1684 in Australia, TRADA span tables in the UK) or ask an engineer. Measure the actual building before cutting a full set, and cut one pattern rafter to test-fit first.
Rafter Calculator FAQ
How do I calculate rafter length with an overhang?
Multiply the run (half the span, less half the ridge thickness) by the pitch multiplier for the line length, multiply the level overhang by the same multiplier for the tail, and add them. 24 ft at 6/12 with a 12″ overhang gives 13′ 4 3/16″ + 1′ 1 7/16″ = 14′ 5 9/16″.
How deep should a birdsmouth cut be?
No more than a quarter of the rafter’s depth at the end under the IRC for sawn lumber; many framers aim shallower. The seat is usually the wall plate width, and the heel height is the seat × rise ÷ 12.
How do I work out rafters for a shed roof?
Choose Shed: the run is the full span between the two walls and there is no ridge reduction. A 10 ft shed at 2/12 with a 12″ overhang needs 11′ 1 13/16″ rafters, cut from 12 ft stock.
What is the angle of the plumb cut?
The roof angle itself from square: 18.4° for 4/12, 26.6° for 6/12, 33.7° for 8/12 and 45° for 12/12. The seat cut is 90° minus that.
How long is a hip rafter?
For a regular hip (equal pitches), the hip runs 16.97″ for every 12″ of common run, so its length is the common run × √(2 + (rise/12)²), less the ridge reduction. The rafter calculator gives it with the 45° cheek cuts.
What size rafters do I need?
That depends on span, spacing, timber grade and loads — read it from your local code’s rafter span tables or have an engineer size it. This calculator only gives lengths and cuts.