Line length, tail length and why they are measured separately
A common rafter has two distinct parts and they are laid out from different reference points. The line length runs from the ridge plumb cut down to the heel of the birdsmouth — the point where the rafter's top edge crosses the outside face of the wall plate. The tail continues past that point to carry the overhang. Framers set the line length first because it fixes where the rafter bears; the tail is often left long and cut to a chalk line once the rafters are up, so the fascia runs dead straight regardless of small variations in the wall.
Both lengths come from the same idea. Along a roof plane, every horizontal foot of travel corresponds to √(x² + 144)/12 feet of rafter, where x is the rise per 12 inches of run. That ratio is the slope factor. Multiply the horizontal run by it and you get line length; multiply the horizontal overhang by it and you get tail length. Nothing else in rafter layout is as consequential as remembering that the run and the overhang are both horizontal measurements.
The one adjustment is the ridge. Rafters meet a ridge board rather than a mathematical point, so each rafter stops half a ridge thickness short of the centreline. A nominal 2x ridge is 1.5 in thick, so you deduct 0.75 in from the run — measured horizontally, not along the rafter. Forget it and every rafter is long by about 0.84 in at 6:12, which pushes the ridge up and the walls out.
The three cuts, and the angles that make them
The ridge plumb cut is vertical when the rafter is in place. Because the rafter itself is tilted by the roof angle θ = arctan(x/12), a vertical line crosses the rafter's edge at θ off square — which is exactly what you dial into a mitre saw. At 6:12 that is 26.57°. On a framing square you get the same cut by holding 12 on the blade and 6 on the tongue and marking along the tongue.
The seat cut is horizontal, so it is the complement: 90° − θ, or 63.43° at 6:12. Together with the heel plumb cut it forms the birdsmouth, the notch that sits the rafter down onto the plate. The depth of that notch is a code question rather than a geometry question — the birdsmouth calculator sizes the seat so enough of the rafter's depth is left above the notch to carry the load.
The tail cut is usually plumb, so it takes the same angle as the ridge cut, and a level cut is added where a soffit returns to the wall. If you are cutting the tails before the rafters go up, remember that the overall length you cut to is the line length plus the tail length, both measured along the top edge.
Stepping off with a framing square gives the same answer without any of this arithmetic: you walk the square down the stock once per foot of run, then step off the fractional part. The calculator is faster and it does not accumulate the small error that each step of the square introduces, but knowing the square method tells you immediately when a number looks wrong.
Worked example: a 24 ft span at 6:12 with a 12 in overhang
A garage measures 24 ft across the plates. The roof is a 6:12 gable on a 2x ridge board, with 12 in eaves and rafters at 16 in on centre along a 40 ft length.
- Total run. 24 ÷ 2 = 12 ft.
- Ridge deduction. The ridge is 1.5 in thick, so deduct half of it: 0.75 in = 0.0625 ft. Run becomes 11.9375 ft.
- Slope factor. √(6² + 144) ÷ 12 = √180 ÷ 12 = 13.41641 ÷ 12 = 1.118034.
- Line length. 11.9375 × 1.118034 = 13.3465 ft. In inches that is 160.16 in, so 13 ft 4-3/16 in on the tape.
- Tail length. 1 ft of horizontal overhang × 1.118034 = 1.118 ft, or 13-7/16 in.
- Overall cut length. 13.3465 + 1.118 = 14.4646 ft — 14 ft 5-9/16 in. A 16 ft stick covers it with enough left for the plumb cuts.
- Total rise. 12 ft of run × 6/12 = 6 ft from the top of the plate to the top of the roof at the ridge centreline.
- Cut angles. Plumb cut arctan(6/12) = 26.57°; seat cut 63.43°.
- Count. 40 ft × 12 = 480 in; 480 ÷ 16 = 30 bays, so 31 rafters per side and 62 in total.
Cut one rafter, carry it up, and test-fit it at both ends of the building before you cut the other 61. That single check catches a wrong pitch, a missed ridge deduction and an out-of-square building in one go.
What the numbers tell you before you cut
The stock length decides your waste. Dimension lumber comes in even lengths to 20 ft and occasionally 24 ft. An overall length of 14.46 ft takes a 16 ft stick and leaves 16 − 14.46 = 1.54 ft of drop per rafter; at 62 rafters that is 95 ft of offcut, which is worth a second look at the overhang or at ordering precut stock. If the overall length lands just over a stock size, shortening the tail by an inch or two often drops you a size.
Line length does not tell you the rafter is strong enough. Size comes from the span tables in IRC section R802, which key on the horizontal span, the species and grade, the spacing, the ground snow load and whether a ceiling is attached. A 2x6 that works at 16 in on centre may not work at 24 in. Check the table for your case, or use an engineered design.
The count assumes an even layout with a rafter at each end. Real roofs add rafters at openings, doubled rafters at chimneys and skylights, and gable-end studs or a ladder framed rake. Treat the count as a starting order and add for those.
The rise tells you whether the roof clears. Six feet of rise on a 24 ft garage means the ridge sits 6 ft above the plate, before you add the ridge board depth. Check that against your height limit and against any dormer, wall or window the roof has to pass.
Rafter length per foot of run, by pitch
| Pitch | Line length per ft of run | Plumb cut | Seat cut | Line length for a 12 ft run |
|---|---|---|---|---|
| 1:12 | 12.0416 in | 4.76° | 85.24° | 12' 0-1/2" |
| 2:12 | 12.1655 in | 9.46° | 80.54° | 12' 2" |
| 3:12 | 12.3693 in | 14.04° | 75.96° | 12' 4-7/16" |
| 4:12 | 12.6491 in | 18.43° | 71.57° | 12' 7-13/16" |
| 5:12 | 13.0000 in | 22.62° | 67.38° | 13' 0" |
| 6:12 | 13.4164 in | 26.57° | 63.43° | 13' 5" |
| 7:12 | 13.8924 in | 30.26° | 59.74° | 13' 10-11/16" |
| 8:12 | 14.4222 in | 33.69° | 56.31° | 14' 5-1/16" |
| 9:12 | 15.0000 in | 36.87° | 53.13° | 15' 0" |
| 10:12 | 15.6205 in | 39.81° | 50.19° | 15' 7-7/16" |
| 11:12 | 16.2788 in | 42.51° | 47.49° | 16' 3-3/8" |
| 12:12 | 16.9706 in | 45.00° | 45.00° | 16' 11-5/8" |
Line length per foot of run is √(x²+144), the number stamped on the first line of a framing square's rafter table. The plumb cut is arctan(x/12) and the seat cut is its complement.
Geometry here, structure in IRC R802
This calculator solves the layout geometry of a common rafter. It does not size the member. Rafter size, species, grade, maximum span and the required birdsmouth bearing come from the International Residential Code, chapter 8, section R802 and its span tables — the 2021 edition is assumed here — or from an engineered design where the roof falls outside those tables. Snow load, dead load and ceiling attachment all change the answer, and your jurisdiction may amend the code.
Mistakes that put every rafter out
- Measuring the overhang along the rafter. The overhang input is horizontal. A tail measured on the slope already carries the slope factor, so entering it here applies that factor a second time. On a 6:12 roof a 13.4 in sloped tail entered as the overhang yields a 15.0 in tail — 1.6 in of error on every rafter.
- Skipping the ridge deduction. Half the ridge thickness, taken off the run horizontally. At 6:12 a 1.5 in ridge shortens each rafter by 0.84 in along its length.
- Deducting the full ridge thickness. Each rafter only meets one face of the ridge, so it is half, not all.
- Using the span where the run belongs. On a symmetric gable the run is half the span. Enter the span and let the calculator halve it, or switch the selector to run.
- Measuring line length along the bottom edge. Line length is measured on the top edge of the rafter, which is the edge the plumb cut lines are struck from.
- Assuming both plates are level and the building is square. Shim the plates or scribe the birdsmouths; a 1/2 in dip at one plate shows up as a wave in the fascia.
- Forgetting that a shed roof has one row of rafters, not two. Set the roof planes selector to one, or you order twice the lumber.
Beyond the common rafter
Common rafters are the simple case: they run square from plate to ridge in the direction of steepest slope. Hip and valley rafters run diagonally and need a different multiplier, √(x² + 288)/12, along with backing or dropping so the sheathing planes meet cleanly — the hip and valley rafter calculator handles those. Jack rafters shorten by a fixed common difference along the hip, which follows from the same slope factor and the spacing.
If you only need the pitch conversions — degrees, percent, slope factor — the roof pitch calculator is the quicker tool. If you are ordering material rather than cutting it, the roof area calculator turns the same span and pitch into sloped area and squares, and the board foot calculator converts the rafter list into board feet for pricing.
Beyond about 16 ft of run, site-cut rafters usually give way to trusses, which move the structural design to the truss manufacturer's engineer. Site cutting still wins where you want a cathedral ceiling, an unusual plan, or a small structure where a truss order is not worth the lead time.