Rafter Length Calculator

Span, run and rise: the three words that drive the math

Rafter math trips people because three words sound interchangeable and are not. The span is the full width of the building from outside wall to outside wall. The run is half the span, measured from the wall to the center of the ridge, and it is the number every rafter formula uses. The rise is how far the roof climbs vertically over that run.

A rafter is just the hypotenuse of a right triangle: the run is the flat leg, the rise is the vertical leg, and the rafter is the sloped one. So the whole calculation reduces to the Pythagorean theorem you met in school:

rafter length = square root of (run x run + rise x rise)

That is it. The only practical work is getting run and rise right. Run always comes from half the span, and rise comes from the roof pitch. If a building is 24 ft wide, the run is 12 ft, never 24 ft, and forgetting the division is the single most common way a first rafter comes out twice as long as the roof.

What the pitch notation 6/12 means

American roofs are called out in rise-per-run notation. A 6/12 pitch means the roof rises 6 in for every 12 in of horizontal run, and 12/12 means 12 in of rise over 12 in of run, a 45 degree roof. The second number is always the 12 in run reference, which is why framers call the scale a 12-based pitch square.

The pitch length factor in the last column is the shortcut most framers use on site. It is the length of rafter per foot of run, so once you know it, the square root disappears: rafter length = run x pitch factor. The American Wood Council's span and framing publications are the reference pros use once length is settled and the question becomes lumber size and spacing.

Worked example: a 24 ft building at 6/12

Take the most common small-building setup: a 24 ft wide structure with a 6/12 roof.

• Run: 24 / 2 = 12 ft
• Rise: 12 x 6/12 = 6 ft
• Length: square root of 12 x 12 + 6 x 6 = square root of 180 = 13.42 ft

That 13.42 ft is 13 ft plus 0.42 x 12 = 5.0 in, so the cut list entry is 13 ft 5 in. Framers write it as 13-5-0 on the stick, where the last number is sixteenths of an inch.

Steepen the same building to 12/12 and the run stays 12 ft while the rise grows to 12 ft, giving a length of square root of 12 x 12 + 12 x 12 = square root of 288 = 16.97 ft, nearly 17 ft. Same footprint, over 3.5 ft more rafter per side, which is exactly why steep roofs cost more in lumber and labor even when the floor area is identical.

Step by step with the pitch factor shortcut

On a roof, nobody wants square roots. The pitch factor does the same job with one multiplication, and the calculator above shows it next to the length so you can check either way.

• Find the run: 24 / 2 = 12 ft
• Find the pitch factor for 6/12: square root of 1 + 0.5 x 0.5 = 1.118
• Multiply: 12 x 1.118 = 13.42 ft
• Add the horizontal overhang times the factor: 1 x 1.118 = 1.12 ft, so a 1 ft eave overhang makes the total 13.42 + 1.12 = 14.54 ft

The two methods agree to the inch, and the factor approach scales better when you are laying out a whole roof, because you set the saw once and repeat. Tables of pitch factors are printed on the framing squares sold at any lumberyard, and the numbers here match the standard 12-based squares.

One caution: pitch factors assume the overhang is measured horizontally at the eave. If you measure along the slope from the wall instead, no factor is needed, just add the distance directly to the rafter length.

Common rafter lengths by span, quick table

For planning lumber orders, this table lists common rafter lengths at the three pitches people build most. Read it as wall to ridge, before any overhang.

The table also shows the planning reality of spans past 24 ft: at a 12/12 pitch, a 32 ft building needs rafters pushing 23 ft, which crosses into engineered lumber or truss territory for most builders. Length is only half the check, though. Rafter depth and spacing must carry the roof load, so once the length is known, match it against span tables for your snow and wind zone rather than copying a neighbor's shed.

Spacing and count: how many rafters to buy

Length answers one question; the lumber order needs a count too. Rafters install in pairs at 16 in or 24 in on center along the building length, and the count follows directly from that spacing.

Round the count up, then add 10% for crowned boards you set aside, doubled rafters at stair openings and skylights, and the first pair you will inevitably recut. A 32 ft building at 24 in spacing takes 16 pairs, or 32 rafters, so ordering 36 boards is the normal move.

Birdsmouth and seat cuts: where the math meets the wall

The length above is the plan length from wall plate to the ridge centerline. Real rafters also carry two cuts. The plumb cut at the top sits against the ridge board, angled to match the pitch. The birdsmouth is the triangular notch near the bottom, made of a level seat cut that rests flat on the wall plate and a vertical heel cut that hugs its side.

The birdsmouth does not change the plan length, but it removes depth from the board, so leave at least 2 in of uncut depth above the notch. A 2x6 rafter at a 6/12 pitch has little room for a full seat, which is one reason shallow-pitched sheds often step up to a 2x8. Lay out the notch by hooking the framing square at the pitch numbers, 6 and 12 for this example, and sliding it down the board until the seat width matches the plate.

The ridge board itself eats a little run. A 1 1/2 in thick ridge shortens each rafter's horizontal reach by 3/4 in per side, so on a careful layout each rafter is cut 3/4 in short of the calculated run. Many framers fold that into the plumb cut and check the first pair on the ground before cutting a bundle.

Overhangs, fascia and buying the right boards

Eave overhangs are measured horizontally at the wall line, so their rafter contribution is the horizontal distance times the pitch factor. On the 24 ft example, a 1 ft overhang adds 1 x 1.118 = 1.12 ft, making the tail length 14.54 ft, while a 2 ft overhang adds 2 x 1.118 = 2.24 ft for 15.66 ft. The factor grows with the pitch, which is why a steep 12/12 roof with wide eaves needs surprisingly long boards.

Buy rafters a little long and cut to the mark. Dimensional lumber lengths run in 2 ft steps, so a 13.42 ft rafter means a 14 ft board, and the 14.54 ft total means a 16 ft board once the tail is included. Count pairs before ordering: rafters go in pairs at 16 in or 24 in on center, so a 32 ft long building at 24 in spacing takes 32 x 12 / 24 = 16 pairs, or 32 rafters. Add 10% for crowns you reject, doubled headers at openings, and the mistakes every first roof makes.

Finally, remember the calculator measures geometry, not structure. A length that fits can still be undersized for snow load, and the Forest Products Laboratory's wood handbook research is the underlying reference for how species and grade change capacity. When in doubt, size up one dimension and sleep well.

This page covers common rafter geometry for planning. Structural sizing must follow your local building code and span tables for your load zone.