Rafter Calculator
Common rafter length from span or run and pitch, with the ridge-board deduction, plumb and seat cut angles, birdsmouth heel height, overhang and rafter count.
Rafter Calculator: with the default inputs, rafter length (ridge cut to tail cut) is 14.837 ft.
For a symmetrical gable the run is half the span. Use Run directly for a shed roof or an off-centre ridge.
Outside face of wall to outside face of wall, across the building.
Run mode only. Outside face of the wall to the centre of the ridge, measured horizontally.
A 6:12 roof rises 6 in for every 12 in of run. Measuring in degrees instead? Convert it with the roof pitch calculator.
Soffit projection measured level, from the outside face of the wall to the end of the tail — not along the slope. Enter 0 for a flush eave.
1.5 in for a nominal 2× ridge board, 1.75 in for a 1¾ in LVL. Half of it comes off the run. Enter 0 if the rafters meet each other or hang from a structural ridge beam on hangers.
Used for the birdsmouth check and the stock length, not for structural sizing.
Measured along the rafter between the two plumb cuts — the number you mark on the board.
- Same length as feet and inches
- 14 ft 10 1/16 in
- Line length (ridge to birdsmouth)
- 13.347 ftRidge plumb cut to the heel (plumb) cut of the birdsmouth, after the ridge deduction.
- Tail length (birdsmouth to tail)
- 17.89 in
- Buy this length
- 16 ftNext standard board long enough to hold the whole rafter including the angled ends.
- Plumb cut angle
- 26.57 degDegrees off square — the mitre-saw setting for the ridge cut. It is the roof angle itself: 26.57° for a 6:12.
- Seat (level) cut angle
- 63.43 degDegrees off square for the level cut of the birdsmouth. Always 90° minus the plumb cut.
- Birdsmouth heel height
- 1.75 inDepth of the plumb leg of the notch: plate width × pitch ÷ 12.
- Height above plate (HAP)
- 6.356 inRafter left above the seat cut, measured plumb. Keep this equal on every rafter or the ridge wanders.
- Total rise (plate to ridge centre)
- 72 in
- Pitch multiplier
- 1.11803Rafter length per unit of run: √(12² + pitch²) ÷ 12.
- Rafters needed (both sides)
- 62Rounded up, with one at each end of each side. Add extras for gable overhangs or a doubled rafter beside a skylight.
- Total rafter stock
- 992 ftRafter count × the stock length.
Assumptions
- Common rafters on a symmetrical gable; hips, valleys and jack rafters use a different multiplier and compound cuts.
- Lengths are measured between plumb cuts, so they are the same along the top edge and the bottom edge. A tail cut square to the rafter instead of plumb is shorter by about the rafter depth × slope.
- The ridge deduction is half the ridge thickness taken off the run horizontally.
- Nominal lumber depths are the dressed dry sizes from NIST PS 20 (a 2×8 is 7¼ in).
- Rafter counts round up and place one at each end of each side; they do not include gable-end outriggers, doubled rafters at openings, or ridge stock.
| Pitch | Angle | Multiplier | Rise (in) | Rafter length |
|---|---|---|---|---|
| 1:12 | 4.76 | 1.00347 | 12 | 13 ft 3 13/16 in |
| 2:12 | 9.46 | 1.01379 | 24 | 13 ft 5 7/16 in |
| 3:12 | 14.04 | 1.03078 | 36 | 13 ft 8 1/8 in |
| 4:12 | 18.43 | 1.05409 | 48 | 13 ft 11 7/8 in |
| 5:12 | 22.62 | 1.08333 | 60 | 14 ft 4 1/2 in |
| 6:12 | 26.57 | 1.11803 | 72 | 14 ft 10 1/16 in |
| 7:12 | 30.26 | 1.1577 | 84 | 15 ft 4 3/8 in |
| 8:12 | 33.69 | 1.20185 | 96 | 15 ft 11 3/8 in |
| 9:12 | 36.87 | 1.25 | 108 | 16 ft 7 1/16 in |
| 10:12 | 39.81 | 1.30171 | 120 | 17 ft 3 5/16 in |
| 12:12 | 45 | 1.41421 | 144 | 18 ft 9 3/16 in |
Rafter length here includes your overhang and ridge deduction. This is the table stamped on a framing square, worked out for your run.
How this is worked out
The formula
Run = span ÷ 2 (symmetrical gable) Effective run = run − ridge thickness ÷ 2 Pitch multiplier = √(12² + pitch²) ÷ 12 Line length = effective run × multiplier Tail length = horizontal overhang × multiplier Rafter length = line length + tail length Roof angle = arctan(pitch ÷ 12) Plumb cut = roof angle (degrees off square) Seat cut = 90° − roof angle Birdsmouth heel height = plate width × pitch ÷ 12 Height above plate = rafter depth ÷ cos(angle) − heel height
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Start from
- For a symmetrical gable the run is half the span. Use Run directly for a shed roof or an off-centre ridge.Span (building width, outside to outside) · Run (measured, one rafter)
- Span
- Outside face of wall to outside face of wall, across the building.in ft, in, m, cm · 0 or more · defaults to 24
- Run
- Run mode only. Outside face of the wall to the centre of the ridge, measured horizontally.in ft, in, m, cm · 0 or more · defaults to 12
- Pitch (rise per 12 in of run)
- A 6:12 roof rises 6 in for every 12 in of run. Measuring in degrees instead? Convert it with the roof pitch calculator.from 0 to 36 · defaults to 6
- Overhang (horizontal)
- Soffit projection measured level, from the outside face of the wall to the end of the tail — not along the slope. Enter 0 for a flush eave.in in, ft, cm, mm, m · 0 or more · defaults to 16
- Ridge board thickness
- 1.5 in for a nominal 2× ridge board, 1.75 in for a 1¾ in LVL. Half of it comes off the run. Enter 0 if the rafters meet each other or hang from a structural ridge beam on hangers.in in, mm, cm · from 0 to 24 · defaults to 1.5
- Rafter size
- Used for the birdsmouth check and the stock length, not for structural sizing.2x6 (5.5 in actual depth) · 2x8 (7.25 in actual depth) · 2x10 (9.25 in actual depth) · 2x12 (11.25 in actual depth)
- Wall plate width (seat cut)(under More options)
- 3.5 in on a 2×4 wall, 5.5 in on a 2×6 wall. This is the level leg of the birdsmouth.in in, mm, cm · from 0 to 24 · defaults to 3.5
- Building length (along the ridge)(under More options)
- Ridge-to-ridge length of the roof. Leave 0 to skip the rafter count.in ft, in, m, cm · 0 or more · defaults to 40
- Rafter spacing(under More options)
- Choose one of 4 options.12 in on centre · 16 in on centre · 19.2 in on centre · 24 in on centre
What you get back
- Rafter length (ridge cut to tail cut)main answer
- Measured along the rafter between the two plumb cuts — the number you mark on the board.
- Same length as feet and inches
- Line length (ridge to birdsmouth)
- Ridge plumb cut to the heel (plumb) cut of the birdsmouth, after the ridge deduction.
- Tail length (birdsmouth to tail)
- Buy this length
- Next standard board long enough to hold the whole rafter including the angled ends.
- Plumb cut angle
- Degrees off square — the mitre-saw setting for the ridge cut. It is the roof angle itself: 26.57° for a 6:12.
- Seat (level) cut angle
- Degrees off square for the level cut of the birdsmouth. Always 90° minus the plumb cut.
- Birdsmouth heel height
- Depth of the plumb leg of the notch: plate width × pitch ÷ 12.
- Height above plate (HAP)
- Rafter left above the seat cut, measured plumb. Keep this equal on every rafter or the ridge wanders.
- Total rise (plate to ridge centre)
- Pitch multiplier
- Rafter length per unit of run: √(12² + pitch²) ÷ 12.
- Rafters needed (both sides)
- Rounded up, with one at each end of each side. Add extras for gable overhangs or a doubled rafter beside a skylight.
- Total rafter stock
- Rafter count × the stock length.
What this assumes
- Common rafters on a symmetrical gable; hips, valleys and jack rafters use a different multiplier and compound cuts.
- Lengths are measured between plumb cuts, so they are the same along the top edge and the bottom edge. A tail cut square to the rafter instead of plumb is shorter by about the rafter depth × slope.
- The ridge deduction is half the ridge thickness taken off the run horizontally.
- Nominal lumber depths are the dressed dry sizes from NIST PS 20 (a 2×8 is 7¼ in).
- Rafter counts round up and place one at each end of each side; they do not include gable-end outriggers, doubled rafters at openings, or ridge stock.
About this calculator
A common rafter runs square from the ridge to the wall plate, and its length is pure right-triangle geometry once you know two things: the run and the pitch. The run is half the span for a symmetrical gable. The pitch gives you the multiplier — the length of rafter per unit of run — and everything else follows from it.
The ridge deduction is the bit people forget
Rafters do not meet at the centreline of the building; they meet the two faces of the ridge board. So half the ridge thickness comes off the run before you multiply. With a nominal 2× ridge that is ¾ in, which shortens each rafter by about ⅞ in on a 6:12 roof. Forget it on both sides and your roof is 1½ in wide at the peak, the birdsmouths do not sit down, and the whole thing fights you. If the rafters hang off a structural ridge beam on hangers, or butt each other with a gusset, set the ridge thickness to 0.
Reading the cuts
- Plumb cut is the vertical cut at the ridge. The angle shown is degrees off square, which is what you dial into a mitre saw. On a framing square you put the pitch on the tongue and 12 on the blade and mark along the tongue.
- Seat cut is the level cut of the birdsmouth. It is always 90° minus the plumb cut, and it is the same setting as the level cut on the tail.
- Heel height is the plumb leg of the birdsmouth notch: plate width × pitch ÷ 12. On a 2×4 wall at 6:12 that is exactly 1¾ in.
- HAP (height above plate) is what is left of the rafter above the seat. Cut one rafter, check the HAP, and use it as the pattern for every other one — that is what keeps the ridge straight.
Overhang and stock length
Enter the overhang measured level, not along the slope; the calculator converts it. Buy this length is the next standard board that will hold the whole rafter including the angled ends — two parallel plumb cuts turn the board into a parallelogram, so the stock has to be longer than the rafter itself by the rafter's depth times the slope.
Use Solve for if you have the length and want the pitch or the run that produces it, and More options for the plate width, the building length and the rafter spacing if you want a count as well.
What this does not do
This is the common rafter only. Hips, valleys and jack rafters run at 45° in plan, so their multiplier is built on 17 in of common run rather than 12, and their cuts are compound. Span tables — what size rafter you actually need for the load — are a separate question entirely; check the IRC rafter span tables or an engineer.
Frequently asked questions
▸How long is a rafter for a 24 ft span at 6:12?
Run is 12 ft (144 in). Take ¾ in off for half a 1½ in ridge board and you have 143¼ in of effective run. The 6:12 multiplier is 1.11803, so the line length is about 160⅛ in — 13 ft 4⅛ in — plus the sloped tail for your overhang.
▸What angle do I set the saw to for the plumb cut?
The roof angle itself, measured off square: 26.57° for 6:12, 18.43° for 4:12, 39.81° for 10:12. The seat cut of the birdsmouth is 90° minus that.
▸How much do I take off for the ridge board?
Half its actual thickness, measured horizontally along the run — ¾ in for a nominal 2× ridge, ⅞ in for a 1¾ in LVL. Each rafter loses that from its run before the multiplier is applied.
▸How deep should the birdsmouth be?
Deep enough to sit flat on the plate and no deeper. The seat is the plate width and the heel is plate width × pitch ÷ 12. IRC R802.7.1 limits a notch at the end of a rafter to a quarter of its depth, and the calculator warns when yours exceeds that.
▸Does this work for hip or valley rafters?
No. A hip or valley runs diagonally, so its run per foot of common run is 16.97 in (usually called 17), and its cheek cuts are compound. This calculator handles common rafters only.
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