Every rafter line length for pitches from 1/12 to 12/12 across the runs builders actually use. Find your pitch, read across to your run — that is the rafter's line length, before ridge and overhang adjustments.
Line length (before overhang and ridge adjustments) for every common pitch. Find your pitch row, read across to your run.
| Pitch | Angle | Mult. | 8 ft run | 10 ft run | 12 ft run | 14 ft run | 16 ft run | 18 ft run | 20 ft run |
|---|---|---|---|---|---|---|---|---|---|
| 1 / 12 | 4.8° | 1.003 | 8 ft 0 5/16 in | 10 ft 0 7/16 in | 12 ft 0 1/2 in | 14 ft 0 9/16 in | 16 ft 0 11/16 in | 18 ft 0 3/4 in | 20 ft 0 13/16 in |
| 2 / 12 | 9.5° | 1.014 | 8 ft 1 5/16 in | 10 ft 1 5/8 in | 12 ft 2 in | 14 ft 2 5/16 in | 16 ft 2 5/8 in | 18 ft 3 in | 20 ft 3 5/16 in |
| 3 / 12 | 14.0° | 1.031 | 8 ft 2 15/16 in | 10 ft 3 11/16 in | 12 ft 4 7/16 in | 14 ft 5 3/16 in | 16 ft 5 15/16 in | 18 ft 6 5/8 in | 20 ft 7 3/8 in |
| 4 / 12 | 18.4° | 1.054 | 8 ft 5 3/16 in | 10 ft 6 1/2 in | 12 ft 7 13/16 in | 14 ft 9 1/16 in | 16 ft 10 3/8 in | 18 ft 11 11/16 in | 21 ft 1 in |
| 5 / 12 | 22.6° | 1.083 | 8 ft 8 in | 10 ft 10 in | 13 ft 0 in | 15 ft 2 in | 17 ft 4 in | 19 ft 6 in | 21 ft 8 in |
| 6 / 12 | 26.6° | 1.118 | 8 ft 11 5/16 in | 11 ft 2 3/16 in | 13 ft 5 in | 15 ft 7 13/16 in | 17 ft 10 11/16 in | 20 ft 1 1/2 in | 22 ft 4 5/16 in |
| 7 / 12 | 30.3° | 1.158 | 9 ft 3 1/8 in | 11 ft 6 15/16 in | 13 ft 10 11/16 in | 16 ft 2 1/2 in | 18 ft 6 1/4 in | 20 ft 10 1/16 in | 23 ft 1 7/8 in |
| 8 / 12 | 33.7° | 1.202 | 9 ft 7 3/8 in | 12 ft 0 1/4 in | 14 ft 5 1/16 in | 16 ft 9 15/16 in | 19 ft 2 3/4 in | 21 ft 7 5/8 in | 24 ft 0 7/16 in |
| 9 / 12 | 36.9° | 1.250 | 10 ft 0 in | 12 ft 6 in | 15 ft 0 in | 17 ft 6 in | 20 ft 0 in | 22 ft 6 in | 25 ft 0 in |
| 10 / 12 | 39.8° | 1.302 | 10 ft 4 15/16 in | 13 ft 0 3/16 in | 15 ft 7 7/16 in | 18 ft 2 11/16 in | 20 ft 9 15/16 in | 23 ft 5 3/16 in | 26 ft 0 7/16 in |
| 11 / 12 | 42.5° | 1.357 | 10 ft 10 1/4 in | 13 ft 6 13/16 in | 16 ft 3 3/8 in | 18 ft 11 7/8 in | 21 ft 8 7/16 in | 24 ft 5 in | 27 ft 1 9/16 in |
| 12 / 12 | 45.0° | 1.414 | 11 ft 3 3/4 in | 14 ft 1 11/16 in | 16 ft 11 5/8 in | 19 ft 9 9/16 in | 22 ft 7 1/2 in | 25 ft 5 1/2 in | 28 ft 3 7/16 in |
The chart works in two steps. First halve your building span to get the run — a 28 ft span means a 14 ft run, because each rafter covers only half the building. Then find the row for your roof pitch and read across to the column for your run. The number where they meet is the rafter's line length: the distance from the outside face of the wall plate to the centreline of the ridge, measured along the top edge of the board.
Every length in the table is a line length, and that is deliberate. Line length is the one number every rafter on the roof shares, whatever ridge board, overhang or birdsmouth the job calls for. It is also the number the pitch multiplier produces directly, so the chart and the maths always agree.
Turning a line length into a board you can cut takes two more steps: add the overhang tail (measured along the slope, so it comes out longer than the flat overhang) and deduct half the ridge board thickness. The cut-length calculator on our homepage does both adjustments for you once the chart has given you the line length.
A rafter is the sloping side of a right triangle whose base is the run and whose height is the rise. Because the pitch fixes the shape of that triangle, the rafter is always the same multiple of the run: length = run × √(1 + (pitch ÷ 12)²). Framers call that square root the pitch multiplier, and it is the only number you need to rebuild this entire chart for any run, in any unit of measurement.
At 6/12 the multiplier is 1.118, so each foot of run needs 1.118 ft of rafter. At 12/12 — a 45° roof — it is 1.414. The table below lists the multiplier and roof angle for every whole-number pitch; the main chart above is simply these multipliers applied to runs from 8 ft to 20 ft.
| Pitch | Roof angle | Multiplier |
|---|---|---|
| 1/12 | 4.8° | 1.003 |
| 2/12 | 9.5° | 1.014 |
| 3/12 | 14.0° | 1.031 |
| 4/12 | 18.4° | 1.054 |
| 5/12 | 22.6° | 1.083 |
| 6/12 | 26.6° | 1.118 |
| 7/12 | 30.3° | 1.158 |
| 8/12 | 33.7° | 1.202 |
| 9/12 | 36.9° | 1.250 |
| 10/12 | 39.8° | 1.302 |
| 11/12 | 42.5° | 1.357 |
| 12/12 | 45.0° | 1.414 |
A detached garage is 28 ft wide and the roof is pitched at 6/12. Halve the span: the run is 14 ft. Find the 6/12 row and the 14 ft column and the chart reads 15 ft 7 13/16 in. The multiplier confirms it: 14 × 1.118034 = 15.652 ft, and 0.652 ft is 7 13/16 in — the same answer to the nearest sixteenth.
That is still a line length. With a 12 in overhang the tail adds about 13 7/16 in along the slope, and a standard 1½ in ridge board takes back about 13/16 in, giving a cut length of roughly 16 ft 8 in — which is why this rafter gets cut from an 18 ft board, not a 16 ft one. The chart gets you the geometry; the last two adjustments are what make it a board.
Most residential roofs live between 4/12 and 9/12 and most runs between 10 ft and 16 ft. These are the readings that come up again and again on garages, additions and whole-house roofs — all line lengths, before ridge and overhang adjustments:
Three things change a line length into a finished rafter, and none of them belongs in a general chart because all three are choices, not constants. The ridge deduction depends on the ridge board you actually use. The tail depends on your overhang and is always longer than the overhang measures flat. And the birdsmouth — the notch that seats the rafter on the wall plate — is located from the line length, not added to it.
Print the chart for the workshop wall if you work in whole pitches and round runs; reach for the calculators when the job has fractions, an unusual pitch, or a birdsmouth to lay out. Both come from the same multiplier, so they will never disagree.
A chart length is only half the decision: the span checker confirms a board is permitted to span that distance under the IRC tables, and the size calculator finds the smallest board that passes.
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.
No. The chart gives line lengths — plate to ridge centreline — because those are the same for every job. Add your overhang tail and deduct half your ridge board thickness to get the cut length, or let the homepage calculator apply both.
The 13 ft column. A common rafter only crosses half the building, so the run is always half the span on a symmetrical gable roof. Using the full span as the run is the most common chart mistake, and it produces a rafter roughly twice the right slope length.
Use the multiplier method: at 6.5/12 the multiplier is √(1 + (6.5 ÷ 12)²) = 1.137. Multiply your run by 1.137 for the line length. Interpolating halfway between the 6/12 and 7/12 rows gives almost the same answer.
Not quite. First turn the line length into a cut length (add the tail, deduct the ridge), then round up to the next stock length — 8, 10, 12, 14, 16, 18 or 20 ft. A cut length of 14 ft 5 in means buying 16 ft boards.
The multipliers are unit-free, so the method works in millimetres exactly as in feet: multiply the run by the pitch multiplier. The printed chart is in feet and inches because that is how the pitches themselves are defined, but any run in any unit follows the same table of multipliers.
Hip and valley rafters run at 45° across the corner of the building, so their unit run is 16.97 in instead of 12 in and they follow a different multiplier. They have their own calculators, which also handle their cheek cuts and deductions.
The full common rafter: length, angles, birdsmouth and materials.
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.
Figure any rafter by hand — formula and framing-square methods.