How do I calculate rafter length from span and pitch?

Halve the span to get the run, subtract half the ridge thickness, then multiply by √(1 + (pitch ÷ 12)²). For a 24 ft span at 6/12 the run is about 143.25 in and the multiplier is 1.118, giving a rafter body of about 160 in.

What is the plumb cut angle for a 6/12 roof?

26.6 degrees. It is arctan(6 ÷ 12), and it applies to both the ridge cut and the vertical face of the birdsmouth. On a framing square, mark it with the pitch on the tongue and 12 on the blade.

How deep can a birdsmouth be?

Most codes cap the notch at one third of the rafter depth, so a 2x8 rafter with an actual depth of 7.25 in allows about 2.4 in. Steep pitches on a 5.5 in seat exceed that quickly — shorten the seat cut or increase the rafter size.

Does rafter length include the overhang?

The primary result here does. The tail is the horizontal overhang multiplied by the same slope factor, so a 16 in overhang on a 6/12 roof adds about 17.9 in of stock, not 16.

How many rafters do I need?

Divide the building length in inches by the spacing and add one, then double it for both roof slopes. Forty feet at 16 in on centre needs 31 per side, 62 total, before extras for gable ends and openings.

Why subtract half the ridge board?

The rafter stops at the face of the ridge, not at the centreline of the building. On a 1.5 in ridge each rafter loses 0.75 in of run. Skipping this makes the roof sit slightly wide and the ridge slightly high.

Rafter Length Calculator

Enter the building span, the roof pitch as rise per 12, and your overhang to get the common rafter length measured along the top edge. It also returns the plumb cut angle, the birdsmouth heel depth and how many rafters the roof needs.

Building span (outside to outside)(ft)

Roof pitch (rise per 12 in of run)(/12)

6 means 6 in of rise for every 12 in of run.

Overhang (horizontal)(in)

Measured level from the outside of the wall, not along the slope.

Rafter spacing on centre

Building length (along the ridge)(ft)

Ridge board thickness(in)

1.5 in for a 2x ridge. Half of this is deducted from the run.

Common rafter length (with overhang)

14' 10.0"

178.0 in along the top edge

Rafter body (ridge to birdsmouth): 13' 4.2"
Tail length (overhang along slope): 1' 5.9"
Horizontal run per side: 11' 11.3"
Total rise at ridge: 5' 11.6"
Plumb cut angleseat cut is 63.4° — mark with a square at 6.0 and 12: 26.6°
Birdsmouth heel depthon a 3.5 in seat cut: 1.75 in
Rafters required31 per side at 16.0 in o.c.: 62pieces

What this figure includes

This calculates a common rafter on a symmetrical gable roof with a level ridge, measured along the top edge of the stock. It does not size the rafter for load, and it does not cover hips, valleys, jack rafters, unequal pitches, or structural ridge beams. Rafter count assumes a uniform layout and does not add extras for gable-end rafters, doubled rafters at openings, or blocking. Check the birdsmouth against the code limit before cutting.

How this is calculated

The formula

A common rafter is the hypotenuse of a right triangle whose base is the run and whose height is the rise. Everything on this page comes out of that triangle.

Run = (span ÷ 2) − (ridge thickness ÷ 2)

Rise = run × (pitch ÷ 12)

Rafter length = √(run² + rise²)

That square root can be simplified into a single multiplier, the *line length per foot of run*:

Factor = √(1 + (pitch ÷ 12)²)

For a 6/12 roof the factor is 1.1180, so every foot of run needs 1.118 ft of rafter. Framing squares and rafter tables have printed this number for a century — the "length of common rafter per foot of run" row on the blade of a framing square is exactly this figure.

The overhang uses the same factor. Overhang is specified horizontally, so the tail measured along the slope is the horizontal overhang times the factor. Adding the tail to the body gives the total stock length.

A worked example

A 24 ft span on a 6/12 pitch with a 16 in overhang and a 1.5 in ridge board:

Run: (24 × 12 ÷ 2) − (1.5 ÷ 2) = 144 − 0.75 = 143.25 in
Factor: √(1 + 0.25) = 1.1180
Body: 143.25 × 1.1180 = 160.2 in, or 13 ft 4.2 in
Tail: 16 × 1.1180 = 17.9 in
Total: 178.1 in, or 14 ft 10.1 in — so cut from 16 ft stock
Rise: 143.25 × 0.5 = 71.6 in at the ridge
Plumb cut: arctan(6 ÷ 12) = 26.6° from vertical, marked as 6 and 12 on the square

Reading the cuts

The plumb cut at the ridge and the plumb face of the birdsmouth are the same angle, because both are vertical when the rafter is in place. On the framing square you mark it by placing the pitch number on the tongue and 12 on the blade and scribing along the tongue. On a speed square, set the pitch on the common scale. On a mitre saw, set the bevel to the angle this calculator reports.

The seat cut is the complement — 90° minus the plumb angle — and it lands flat on the top plate. Its length is the plate width, normally 3.5 in for a 2x4 wall or 5.5 in for a 2x6 wall.

The birdsmouth heel depth is the vertical dimension of the notch: seat run times pitch over twelve. Most codes limit the notch to one third of the rafter depth. A 3.5 in seat on a 12/12 roof cuts 3.5 in deep, which is already too much for a 2x8 — either shorten the seat, drop the ridge, or move up a size in stock.

Laying out the rafter count

Rafters are laid out at a fixed spacing along the ridge, so the count per side is the building length in inches divided by the spacing, plus one for the closing rafter. Forty feet at 16 in on centre gives 480 ÷ 16 = 30, plus one, so 31 per side and 62 total.

That is the bare count. A real order adds gable-end rafters or a gable ladder, doubled rafters either side of skylights and chimneys, and extras where the layout has to shift around an opening. Add roughly 5% and round up to the next full bundle.

Practical notes

Cut one rafter, carry it up, and test-fit it against the ridge and both plates before cutting the rest. Calculated lengths assume the walls are straight, parallel and level, and walls rarely are. Once one rafter fits, use it as the pattern for every other common rafter and trace rather than re-measure.

Note also that this length is measured along the top edge of the rafter, from the plumb cut at the ridge to the end of the tail. If you measure along the bottom edge or from the outside of the wall, you will get a different number and conclude the calculator is wrong.

Frequently asked questions

How do I calculate rafter length from span and pitch?: Halve the span to get the run, subtract half the ridge thickness, then multiply by √(1 + (pitch ÷ 12)²). For a 24 ft span at 6/12 the run is about 143.25 in and the multiplier is 1.118, giving a rafter body of about 160 in.
What is the plumb cut angle for a 6/12 roof?: 26.6 degrees. It is arctan(6 ÷ 12), and it applies to both the ridge cut and the vertical face of the birdsmouth. On a framing square, mark it with the pitch on the tongue and 12 on the blade.
How deep can a birdsmouth be?: Most codes cap the notch at one third of the rafter depth, so a 2x8 rafter with an actual depth of 7.25 in allows about 2.4 in. Steep pitches on a 5.5 in seat exceed that quickly — shorten the seat cut or increase the rafter size.
Does rafter length include the overhang?: The primary result here does. The tail is the horizontal overhang multiplied by the same slope factor, so a 16 in overhang on a 6/12 roof adds about 17.9 in of stock, not 16.
How many rafters do I need?: Divide the building length in inches by the spacing and add one, then double it for both roof slopes. Forty feet at 16 in on centre needs 31 per side, 62 total, before extras for gable ends and openings.
Why subtract half the ridge board?: The rafter stops at the face of the ridge, not at the centreline of the building. On a 1.5 in ridge each rafter loses 0.75 in of run. Skipping this makes the roof sit slightly wide and the ridge slightly high.