How to cut rafters
The order you work a common rafter: run from the span, rise from the pitch, line length, the ridge deduction, the tail, then the birdsmouth. Plus how to read the rafter table stamped on a framing square. Worked from one real 20 ft span.
Updated
Skip the arithmetic
The rafter length calculator runs every step below from your span and pitch, and prints the birdsmouth and saw angles.
The short version
To cut a common rafter, take half the span as the run, multiply the run by the pitch (rise per 12 in) to get the rise, and take the line length as the square root of the rise squared plus the run squared. Deduct half the ridge thickness measured along the slope, add the overhang tail, then cut the birdsmouth: a seat the width of the wall plate and a plumb cut equal to the seat times the tangent of the roof angle. Mark the plumb cut at the ridge, the birdsmouth at the plate, and the plumb cut again at the tail.
Step by step, worked from a 20 ft span at 8/12
A 240 in span, 8/12 pitch, 2x8 rafters, a 12 in overhang over a 1-1/2 in ridge. Every number in the table is computed by the same code the app runs, not typed in.
- 01
Halve the span for the run
The run is half the total span, measured from the outside of the wall to the center of the ridge. A 20 ft span gives a 10 ft run. Everything downstream hangs off the run and the pitch, so get the span right first.
- 02
Get the rise from the pitch
Pitch is the rise per 12 in of run. At 8/12 the rafter climbs 8 in for every 12 in it runs, so a 120 in run rises 80 in. You read the pitch straight off the framing square instead of estimating an angle.
- 03
Take the line length as the hypotenuse
Line length is the diagonal of the run-and-rise triangle: the square root of the rise squared plus the run squared. That is the distance from the ridge centerline to the outside of the wall, measured along the top of the rafter.
- 04
Deduct half the ridge, along the slope
Line length runs to the ridge centerline, but the board stops at the face of the ridge. Deduct half the ridge thickness divided by the cosine of the roof angle, because the cut is on the slope, not level. Skip the cosine and every rafter lands short at the peak.
- 05
Add the overhang tail
The overhang is a second triangle at the same pitch. A 12 in level overhang at 8/12 is more than 12 in of board, because the tail runs down the slope. Add it to the line length for the full board length before you notch anything.
- 06
Cut the birdsmouth last
The seat cut is the width of the wall plate, 3-1/2 in on a 2x4 wall. The plumb cut follows from it: the seat times the tangent of the roof angle. What is left of the board above the seat is the HAP, and that number has to be identical on every common rafter or the ridge will not sit level.
For a 20 ft span at 8/12
| Run | 10 ft |
| Rise | 6 ft 8 in |
| Line length | 12 ft 1/4 in |
| Plumb cut angle | 33.69° |
| Seat cut angle | 56.31° |
| Ridge deduction | 7/8 in |
| Overhang tail | 14-7/16 in |
| Birdsmouth seat | 3-1/2 in |
| Birdsmouth plumb | 2-5/16 in |
| HAP | 6-3/8 in |
How to read a rafter table
The rafter table stamped on a framing square gives the length of common rafter per foot of run, the length-per-foot column below. It is the rafter factor times twelve: at 8/12 the factor is 1.2019, so the square reads 14.42 inches of rafter for every foot of run. Read the row for your pitch, multiply by your run in feet, and you have the line length without a calculator. Most pitches do not land on a clean fraction, because most are not Pythagorean triples, which is why the factor runs to four decimals.
| Pitch | Angle | Length per foot of run | Factor |
|---|---|---|---|
| 3/12 | 14.04° | 12.37 | 1.0308 |
| 4/12 | 18.43° | 12.65 | 1.0541 |
| 6/12 | 26.57° | 13.42 | 1.1180 |
| 8/12 | 33.69° | 14.42 | 1.2019 |
| 10/12 | 39.81° | 15.62 | 1.3017 |
| 12/12 | 45.00° | 16.97 | 1.4142 |
To use it: run in feet times the length per foot equals the line length. A 10 ft run at 8/12 is about 12 ft of rafter before the ridge deduction and the tail.
The one code rule this triggers
Rafter sizing is a span-table question tied to species, grade, spacing, and load, so this page does not size the stock. There is one rule the geometry sets off: the ridge board has to be at least as deep as the rafter's plumb-cut depth, which is the rafter depth divided by the cosine of the roof angle (IRC R802.3). At a steeper pitch a 2x8 rafter can need a 2x10 ridge, which the app flags when it prints the cut plan.
Common questions
- How do you calculate rafter length by hand?
- Take half the span as the run, multiply the run by the pitch over 12 for the rise, and take the square root of the rise squared plus the run squared. That is the line length. Then deduct half the ridge along the slope and add the overhang tail for the board length.
- How do I read the rafter table on my framing square?
- The top row of figures on the square is the length of common rafter per foot of run, indexed under the inch mark that matches your pitch. Find your rise (say 8), read the number under it, and multiply by the run in feet. It is the same factor as the table on this page.
- What is the birdsmouth and where does it go?
- The birdsmouth is the notch that lets the rafter sit on the wall plate. It has a level seat cut the width of the plate and a plumb cut that meets it. Cut it after you mark the plumb cut at the ridge, and keep the HAP identical on every rafter so the roof plane stays true.
- Do hips, valleys, and jacks use the same math?
- No. Hips and valleys run on a longer unit length and need backing angles and drop, and jacks step down in a common difference. This page is common rafters only; the app's hip and valley calculator handles the rest.
Cut it from a plan, not a guess
The app runs this math from your span and pitch, checks the ridge depth, and prints a cut plan with the birdsmouth and every saw angle marked on the board.
See also