Cut each common rafter 14′ 5 9/16″ long, overhang included. It runs 11′ 11 1/4″ across and rises 5′ 11 5/8″, at 26.57°. The birdsmouth is within the code limit.
Run 11′ 11 1/4″, rise 5′ 11 5/8″, 26.57°.
Buy a 16 ft board. Rafters grow with the tail, so the rise grows too.
Seat 3 1/2″ · plumb 1 3/4″ · notch depth 1 9/16″ of 9 1/4″.
Factor 1.5 × run. Buy a 24 ft board. Theoretical line before cheek cuts.
Type the building span and the pitch. This rafter calculator gives you the common rafter length, the length with overhang, the birdsmouth seat and plumb cuts, and the hip or valley length. Shed roof? Switch it on. Cut one pair, test-fit it on the walls, then batch the rest.
Quick answer A 24′ (7.32 m) span at 6:12 with a 1½ in ridge board has a common rafter run of 11′ 11 1/4″ and a line length of 13′ 4 3/16″ up to the ridge. Add a 12 in overhang and the rafter measures 14′ 5 9/16″, so buy 16 ft stock.
How to figure rafter length for a whole roof: every common rafter on the same slope and span is the same length, so a rafter length calculator only has to work one out. Half the span runs from the outside of one wall to the theoretical centre of the ridge. Take off half the ridge thickness so the rafter stops at the face of the ridge board. From that run the rise follows the pitch, and the line length is the slope distance.
To calculate the length of rafters for a roof with eaves, remember the overhang is a horizontal projection: it gets added to the run, and the whole run is multiplied by the pitch factor. The tail keeps falling on the same slope, so its rise grows with it. It is not the building rise pasted onto a longer run. A hip rafter calculator applies √(2 + (pitch ÷ 12)²) to the run, because a hip or valley on a regular 45° plan corner is longer again.
A shed or lean-to roof has one slope and no ridge. The shed roof rafter calculator treats the run as the full span: the rafter goes from the high wall to the low wall, there is no hip, and the high wall has to stand taller than the low wall by the rise.
For the birdsmouth, open More options and enter the seat cut and the rafter depth. The calculator gives the height above the plate and checks the notch against the quarter-depth limit, so you find out the notch is too deep before you cut it into a rafter.
The pitch cut is the angle of the plumb cut, which is the roof pitch itself. On a speed square, set the pivot on the rafter edge and the pitch number (6 for a 6:12 roof) on the same edge, then scribe along the blade. For the seat cut, mark the plumb line where the rafter crosses the outside of the wall. The seat starts that many inches up from the bottom edge: seat width times pitch ÷ 12. Height above plate is the plumb distance left from there to the top edge.
If you only have a rise and a run, find the pitch first with the roof pitch calculator. Once the rafters are sized, the roofing calculator turns the same span and pitch into roof square feet and shingles, and the feet and inches calculator adds up rafter and overhang lengths.
L = rafter length with tail, S = span, t = ridge thickness, o = horizontal overhang, p = pitch (x in x:12).
run = (span / 2) − (ridge thickness / 2) gable run = span shed / lean-to, no ridge rise = run × (pitch / 12) multiplier = √(1 + (pitch / 12)²) line length = run × multiplier tail length = (run + overhang) × multiplier birdsmouth plumb (inches up for a seat cut) = seat cut × (pitch / 12) height above plate (HAP) = rafter depth × multiplier − plumb notch depth = plumb / multiplier limit = ¼ × rafter depth hip factor = √(2 + (pitch / 12)²) hip length = run × hip factor
Half of 24 ft is 144 in. A 1½ in ridge shortens the run by ¾ in to 143.25 in. Rise is half of that, 71.63 in. The line length is 143.25 × 1.118 = 13′ 4 3/16″. A 12 in overhang adds to the run before the same multiplier: 14′ 5 9/16″. The seat cut of 3½ in on a 2×10 leaves 8 9/16″ height above plate.
A steeper pitch makes the plumb cut taller for the same seat. Here the notch is 1 15/16″ deep against a quarter-depth limit of 1 13/16″ on a 2×8, so the birdsmouth check fails. It would have passed a one-third rule, which is why the check follows IRC R802.7.1. Try a 2×10 or a shallower seat.
A shed rafter runs the whole 144 in, with no ridge to subtract. Rise is 144 × 4 ÷ 12 = 48 in, so the high wall stands 4′ taller than the low wall. The line length is 144 × 1.0541 = 12′ 7 13/16″. A 12 in overhang at the low eave brings the rafter to 13′ 8 7/16″, so buy 16 ft stock.
A 35° roof is 8.40:12. With a 6000 mm span, a 38 mm ridge, a 300 mm overhang and 47×175 mm rafters, the common rafter run is 2981 mm and the line length is 3639 mm. With the tail it is 4005 mm, so buy 14 ft timber.
Need a quick number before you open the calculator? Read it off here. Each cell is the line length along the top edge of a common rafter, with no overhang and the ridge thickness ignored, straight from the calculation above. Add the tail from the calculator for any overhang, because the tail is not just extra run: it keeps falling on the same slope.
| Pitch | 12 ft span | 16 ft span | 20 ft span | 24 ft span |
|---|---|---|---|---|
| 3:12 | 6′ 2 3/16″ | 8′ 2 15/16″ | 10′ 3 11/16″ | 12′ 4 7/16″ |
| 4:12 | 6′ 3 7/8″ | 8′ 5 3/16″ | 10′ 6 1/2″ | 12′ 7 13/16″ |
| 5:12 | 6′ 6″ | 8′ 8″ | 10′ 10″ | 13′ |
| 6:12 | 6′ 8 1/2″ | 8′ 11 5/16″ | 11′ 2 3/16″ | 13′ 5″ |
| 8:12 | 7′ 2 9/16″ | 9′ 7 3/8″ | 12′ 1/4″ | 14′ 5 1/16″ |
| 10:12 | 7′ 9 3/4″ | 10′ 4 15/16″ | 13′ 3/16″ | 15′ 7 7/16″ |
| 12:12 | 8′ 5 13/16″ | 11′ 3 3/4″ | 14′ 1 11/16″ | 16′ 11 5/8″ |
| Pitch | 8 ft wide | 10 ft wide | 12 ft wide | 14 ft wide |
|---|---|---|---|---|
| 2:12 | 8′ 1 5/16″ | 10′ 1 5/8″ | 12′ 2″ | 14′ 2 5/16″ |
| 3:12 | 8′ 2 15/16″ | 10′ 3 11/16″ | 12′ 4 7/16″ | 14′ 5 3/16″ |
| 4:12 | 8′ 5 3/16″ | 10′ 6 1/2″ | 12′ 7 13/16″ | 14′ 9 1/16″ |
| 6:12 | 8′ 11 5/16″ | 11′ 2 3/16″ | 13′ 5″ | 15′ 7 13/16″ |
| 8:12 | 9′ 7 3/8″ | 12′ 1/4″ | 14′ 5 1/16″ | 16′ 9 15/16″ |
| 12:12 | 11′ 3 3/4″ | 14′ 1 11/16″ | 16′ 11 5/8″ | 19′ 9 9/16″ |
Marking a birdsmouth? These are the numbers. The seat cut sits flat on the wall plate, and the plumb cut is how far up the plumb line the seat starts. The last column is the one that saves a rafter: the longest seat you can cut before the notch passes a quarter of the board.
| Pitch | Roof angle off level | Plumb cut off the rafter edge | Plumb cut up from the bottom edge | Height above plate | Longest seat inside the ¼ limit |
|---|---|---|---|---|---|
| 3:12 | 14.04° | 75.96° | 7/8″ | 8 11/16″ | 9 1/2″ |
| 4:12 | 18.43° | 71.57° | 1 3/16″ | 8 9/16″ | 7 5/16″ |
| 5:12 | 22.62° | 67.38° | 1 7/16″ | 8 9/16″ | 6″ |
| 6:12 | 26.57° | 63.43° | 1 3/4″ | 8 9/16″ | 5 1/8″ |
| 7:12 | 30.26° | 59.74° | 2 1/16″ | 8 11/16″ | 4 9/16″ |
| 8:12 | 33.69° | 56.31° | 2 5/16″ | 8 13/16″ | 4 1/8″ |
| 9:12 | 36.87° | 53.13° | 2 5/8″ | 8 15/16″ | 3 13/16″ |
| 10:12 | 39.81° | 50.19° | 2 15/16″ | 9 1/8″ | 3 9/16″ |
| 12:12 | 45° | 45° | 3 1/2″ | 9 9/16″ | 3 1/4″ |
| Seat cut | 4:12 | 6:12 | 8:12 | 12:12 |
|---|---|---|---|---|
| 3 1/2″ | 1 3/16″ | 1 3/4″ | 2 5/16″ | 3 1/2″ |
| 5 1/2″ | 1 13/16″ | 2 3/4″ | 3 11/16″ | 5 1/2″ |
Rafter size comes from span tables, not from this length. IRC roof framing is in IRC 2021 Chapter 8, Roof-Ceiling Construction, and the wood design values behind it are explained for residential wood by the American Wood Council. A ridge board is not a structural ridge beam; if the ridge supports the rafters, it is designed as a beam.
IRC R802.7.1 limits a notch at the end of a sawn rafter to one quarter of its depth. The birdsmouth check uses that limit. Hip and valley lengths assume a regular 45° plan corner; irregular hips, where the pitches differ, need a different run. All lengths are theoretical line lengths before shortening for cheek cuts.
In the UK, rafter sizes and spans come from the span tables for the timber grade you buy (for example the TRADA tables) and from the roof design. This page gives the geometry only.
Section numbers refer to IRC 2021 section numbers; England Approved Document K. Local amendments are common, so confirm with your building authority.
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For a common rafter, take half the building span, subtract half the ridge thickness, and call that the run. Rise is the run times pitch over 12. The line length to the ridge is the run times √(1 + (pitch ÷ 12)²). Add the horizontal overhang to the run before multiplying if you want the tail. The board to buy is that length plus one rafter depth, rounded up to the next stock length.
The notch that lets the rafter sit on the wall plate. The seat cut is the horizontal flat, usually the plate width. The plumb cut is the vertical face. Height above plate is what is left of the rafter above the notch. IRC R802.7.1 limits a notch at the end of a rafter to one quarter of its depth.
Mark the plumb line where the rafter crosses the outside of the wall, then measure up it from the bottom edge by the seat width times pitch ÷ 12. A 3½ inch seat on a 6:12 roof is 1¾ inches up, and on a 12:12 roof it is 3½. The level seat starts there, and the plumb distance from there to the top edge is the height above plate.
The angle where the rafter meets the ridge or the wall, which equals the roof pitch. On a speed square, put the pivot on the rafter edge, the pitch number on the same edge, and scribe along the blade. A 6:12 pitch cut is 26.6 degrees off level, or 63.4 degrees off the rafter edge.
On a regular hip, where the corner is 45 degrees in plan, the hip run is the common run times √2 and the length is the common run times √(2 + (pitch ÷ 12)²). Do not just multiply the common rafter by √2: at 6:12 that overstates the hip by about 5%. This is the theoretical line before cheek cuts and jack rafters.
The theoretical apex is the centre of the ridge, but the common rafter stops at the face of the ridge board. So its horizontal run is shorter by half the ridge thickness. A 1½ inch ridge shortens the run by ¾ inch.
This rafter calculator with overhang finds the common rafter from the run and the pitch, then adds the tail: the horizontal overhang times the same multiplier. The overhang adds rise as well as run, because the tail keeps falling on the same slope. Hold the rise constant and the tail comes out too short, by about 2.6 inches on a 24 ft span at 6:12 with a 12 inch overhang.
Choose Shed / lean-to. A shed rafter runs from the high wall to the low wall, so the level run is the full building width and there is no ridge board. The line length is the width times √(1 + (pitch ÷ 12)²). Add the overhang to the run before multiplying to get the tail. The high wall has to be taller than the low wall by the width times pitch ÷ 12.