Enter the span and pitch — get the exact rafter length, cut angles and birdsmouth, ready to mark on the board. For gable and shed roofs, common rafters.
A rafter is the hypotenuse of a right triangle. The run is half the building span, the rise comes from the pitch — so the theoretical line length is always the same piece of maths:
Carpenters shortcut it with a pitch multiplier: multiply the run by the factor for your pitch. The calculator then adjusts the line length for the real world — it adds the overhang tail measured along the slope, and deducts half the ridge board thickness so the pair meets at the ridge. Change the job and the tool changes with it: a diagonal roof member needs the hip rafter calculator, and a single-slope roof needs the shed rafter calculator.
| Pitch | Angle | Multiplier | Length per 10 ft of run |
|---|---|---|---|
| 3 / 12 | 14.0° | 1.031 | 10 ft 3 11/16 in |
| 4 / 12 | 18.4° | 1.054 | 10 ft 6½ in |
| 5 / 12 | 22.6° | 1.083 | 10 ft 10 in |
| 6 / 12 | 26.6° | 1.118 | 11 ft 2 3/16 in |
| 8 / 12 | 33.7° | 1.202 | 12 ft 0¼ in |
| 10 / 12 | 39.8° | 1.302 | 13 ft 0 3/16 in |
| 12 / 12 | 45.0° | 1.414 | 14 ft 1 11/16 in |
Run = 24 ÷ 2 = 12 ft. Rise = 6/12 × 12 ft = 6 ft. Line length = √(12² + 6²) = 13 ft 5 in. Add a 12 in overhang on the slope (+13 7/16 in), take off half the 1½ in ridge (−13/16 in).
Run = 10 ft. Rise = 10 × tan 30° = 5 ft 9 5/16 in (a 6.9/12 pitch). Line length = 10 ÷ cos 30° = 11 ft 6 9/16 in, before ridge and overhang adjustments.
Run = 3,600 mm. Rise = 300 × 3.6 = 1,080 mm. Line length = √(3,600² + 1,080²) = 3,758 mm. A 600 mm overhang adds 626 mm measured along the slope, and half of a 38 mm ridge board takes off about 20 mm.
Line length is measured on paper — from the outside of the wall plate to the centre of the ridge. Three adjustments turn it into a cut length: the ridge deduction (half the ridge board's thickness, so two rafters and the board share the same space), the tail (your overhang, which runs longer on the slope than it measures flat), and the birdsmouth — the notch that seats the rafter on the plate.
The birdsmouth has one hard rule: never notch deeper than one-quarter of the board's depth — the IRC end-notch limit, or the rafter is weakened exactly where it carries load. The calculator checks this against your lumber size and reports the HAP — the height above plate left standing over the wall. If you only need the notch worked out, the dedicated birdsmouth calculator goes deeper on seat cuts and heel heights.
A 12 in overhang is 13 7/16 in of board at 6/12. Measuring it flat cuts every tail short.
Skip the deduction and the pair won't close up — the roof gains a gap at the top or a bow at the eaves.
Every formula works on the run — half the span. Double the run and the rafter comes out yards long.
Past ¼ of the board depth — the IRC end-notch limit — the seat cut becomes the weakest point of the whole roof.
Cut one pair, offer it up, check the ridge and eaves — then batch the rest from the pattern rafter.
A “2×8” is 7¼ in deep, not 8. Every HAP and birdsmouth figure here uses actual dimensions.
Every result on this page comes from the method described above, using standard framing geometry and the published data credited below. Found a number that looks wrong? Use Report an Error — every report is read.
Yes. Enter the overhang as a horizontal measurement — the calculator converts it to the longer length along the slope and adds it to the tail.
The span — the full wall-to-wall width. The calculator halves it to get the run. If you already work from the run, double it and enter that as the span.
Half the ridge board's actual thickness, measured along the slope — 13/16 in for a standard 1½ in ridge at 6/12. Enter your ridge thickness and the deduction is automatic.
Line length is the theoretical measure to the ridge centre. Cut length is line length plus the tail, minus the ridge deduction — the board you actually mark and cut.
Yes — switch units at the top of the calculator. Every input and result converts, and the worked examples include a metric roof.
At most one-quarter of the board's actual depth, measured perpendicular to the top edge — the IRC end-notch limit (R502.8.1, applied to rafters by R802.7.1). The calculator warns you if your seat cut goes past it for the lumber size you picked.
Yes — a gable roof's rafters are common rafters, which is exactly what this page calculates. For the diagonal members on a hip roof, use the hip and jack rafter calculators.
The result names the next stock length above your cut length (8, 10, 12, 14, 16, 18 or 20 ft). The offcut is normal — plumb and seat cuts come off the ends.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
Where two roof planes meet — valley length and its cut angles.
First jack length and the common difference for your spacing.
Single-slope rafters between two different wall heights.
Seat cut, heel height and HAP, checked against the IRC one-quarter limit.
Plumb, seat and cheek angles — plus the saw settings to cut them.
Convert pitch, rise/run, degrees and percent, both ways.
How far a board can span — IRC tables by species, grade and load.
The lumber size a span actually needs. The inverse of the span tool.
Two pitches, one roof — upper and lower rafter lengths.
The full pitch × run table, printable for the workshop wall.
Figure any rafter by hand — formula and framing-square methods.