Rafter Angle Calculator
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
For a symmetrical gable, the plumb cut angle is 90° minus the roof angle, and the seat cut equals the roof angle. A 6:12 roof sits at 26.57°, so the plumb cut is 63.43° and the seat cut is 26.57°. Set a speed square to the pitch number — 6 on the Common scale — for the same layout.
Your measurements
Enter the values you know — results update live.
Outside-to-outside width of the building at the wall plates.
Enter 6 for a 6:12 roof.
Analysis
Live results from your measurements.
Birdsmouth depth (1.5 in) is within the IRC one-third limit (2.42 in).
Show the working
- Run after ridge deduction:
24 ÷ 2 − 0.125 ÷ 2= 11.938 ft - Rise:
11.938 × (6 ÷ 12)= 5.969 ft - Roof angle:
arctan(6 ÷ 12)= 26.57° - Plumb cut:
90° − 26.57°= 63.43° - Seat cut:
26.57°= 26.57° - Speed square:
Common scale = 6= 6:12 - Line length:
√(11.938² + 5.969²)= 13.347 ft - Total length:
13.347 + 1.677= 15.024 ft
What this calculator does
A rafter has only a few angles, but they have to be right or the whole roof frame is wrong. The plumb cut at the ridge is vertical when the rafter is in place, so its angle measured from the rafter edge is 90° minus the roof angle. The seat cut that lands on the wall plate is horizontal, so it equals the roof angle. A speed square makes this instant: set the Common scale to the pitch number and the fence gives you the plumb cut without any arithmetic. The birdsmouth is the notch that lets the rafter sit flat on the wall plate while keeping the heel above the plate; its depth is limited to one third of the rafter depth under the IRC so the rafter does not weaken at the bearing point.
How to use it
- Measure the building span from outside face to outside face of the wall plates.
- Halve the span and subtract half the ridge board thickness to get the true run.
- Multiply the run by the pitch ratio to get the rise.
- Take the arctangent of pitch ÷ 12 for the roof angle in degrees.
- Set the plumb cut to 90° minus the roof angle and the seat cut to the roof angle.
- Lay out the birdsmouth so the seat depth and heel stand do not exceed one third of the rafter depth.
The formula
Roof angle
angle = arctan(pitch / 12)
The angle in degrees for an X:12 pitch. A 6:12 roof is arctan(0.5) = 26.57°.
Plumb cut angle
plumb cut = 90° − roof angle
The plumb cut is perpendicular to the seat cut and vertical when installed.
Seat cut angle
seat cut = roof angle
The seat cut is horizontal when the rafter is in place, so it matches the roof angle measured from the rafter edge.
Birdsmouth depth limit
max depth = rafter depth / 3
IRC R802.7 limits the birdsmouth notch to one third of the rafter depth at the plate.
Worked example
A 28 ft span at 8:12 with a 1.5 in ridge board, 2 ft overhang, and a 2×8 rafter (7.25 in deep).
- Run: 28 ÷ 2 − 0.0625 = 13.9375 ft
- Rise: 13.9375 × 0.6667 = 9.2917 ft
- Roof angle: arctan(8 ÷ 12) = 33.69°
- Plumb cut: 90° − 33.69° = 56.31°
- Seat cut: 33.69°
- Birdsmouth max: 7.25 ÷ 3 = 2.42 in
Set the speed square to 8 on the Common scale for the plumb cut, set the seat cut to 33.69°, and keep the birdsmouth under 2.42 in deep.
Reference chart
| Pitch | Roof angle | Plumb cut | Seat cut | Speed square |
|---|---|---|---|---|
| 3:12 | 14.04 | 75.96 | 14.04 | 3:12 |
| 4:12 | 18.43 | 71.57 | 18.43 | 4:12 |
| 5:12 | 22.62 | 67.38 | 22.62 | 5:12 |
| 6:12 | 26.57 | 63.43 | 26.57 | 6:12 |
| 7:12 | 30.26 | 59.74 | 30.26 | 7:12 |
| 8:12 | 33.69 | 56.31 | 33.69 | 8:12 |
| 9:12 | 36.87 | 53.13 | 36.87 | 9:12 |
| 10:12 | 39.81 | 50.19 | 39.81 | 10:12 |
| 12:12 | 45 | 45 | 45 | 12:12 |
Rafter depth and maximum birdsmouth depth
| Nominal size | Actual depth | Max birdsmouth depth |
|---|---|---|
| 2×6 | 5.5 in | 1.83 in |
| 2×8 | 7.25 in | 2.42 in |
| 2×10 | 9.25 in | 3.08 in |
| 2×12 | 11.25 in | 3.75 in |
Common mistakes
- Cutting the plumb cut at the roof angle instead of 90° minus the roof angle.
- Forgetting the ridge board deduction, which makes every rafter about 3/4 in too long.
- Birdsmouth cut deeper than one third of the rafter depth, weakening the bearing point.
- Using the speed square degree scale when the Common scale already matches the pitch.
- Measuring the seat cut from the top edge instead of the bottom edge of the rafter.
- Ignoring heel stand, which can leave the rafter end unsupported below the plate.
Assumptions and limits
- A symmetrical gable with both plates at the same height.
- The ridge board thickness is deducted equally from both sides.
- Overhang is measured as a horizontal projection and converted to slope length.
- Birdsmouth depth check uses the conservative one-third rule; local code may use one fourth.
Frequently asked questions
What angle do I cut a rafter for a 6/12 roof?
The plumb cut is 63.43° from the rafter edge, and the seat cut is 26.57°. On a speed square, set the Common scale to 6 for the plumb cut layout.
What is the difference between plumb cut and seat cut?
The plumb cut is the vertical cut at the ridge or birdsmouth heel. The seat cut is the horizontal cut that rests on the wall plate. They are always complementary: plumb cut = 90° − roof angle, seat cut = roof angle.
How deep can a birdsmouth be?
The IRC limits the birdsmouth seat cut to one fourth of the rafter depth in some jurisdictions, but the common conservative rule is one third. On a 2×8 (7.25 in deep), one third is 2.42 in.
What is heel stand on a rafter?
Heel stand is the vertical height of the rafter heel above the top of the wall plate after the birdsmouth is cut. It keeps the rafter supported and prevents the tail from splitting.
How do I use a speed square for roof pitch?
Place the fence on the rafter edge and pivot the square until the Common scale reads the pitch number — 6 for a 6:12 roof. Scribe along the square body for the plumb cut; flip it to lay out the seat cut.
Do I subtract the ridge board for the seat cut?
No. The ridge deduction only affects the rafter length. The seat cut angle is the same regardless of ridge thickness.
Related guides
- Roof Pitch to Degrees: Full Conversion Chart and FormulaThe complete pitch-to-degree conversion table, the trigonometry behind it, and why 6:12 is 26.57° rather than the 30° people expect.
- Roof Angle Calculator Guide: Degrees, Pitch and Percent ExplainedPitch, angle and percent are three languages for the same slope. Here is the trigonometry that connects them, a full conversion chart, and how to measure a roof's real angle with tools you already own.
- Rafter Length and Cuts: The Complete Layout and Calculation GuideRafter math has three layers most guides skip: the difference between line length and true length, the half-ridge deduction, and the geometry of the birdsmouth. Get all three right and the framing square step-off method will put you within a sixteenth of an inch every time.
- Hip Roof Pitch and Area: Hip Rafters, Jacks and the 17-Inch RuleHip roofs replace gable ends with sloped triangular planes, which means every hip rafter, jack rafter and area figure runs through a compound-angle formula rather than the simple gable triangle. Here is that math laid out with worked numbers.
- Roof Height and Ridge Calculation: Rise, Peak Height and Zoning LimitsRidge height is not just a rise calculation — it depends on where you measure from, how the ridge board and heel height shift the number, and whether your jurisdiction measures height to the ridge or to the mean of the roof. Here is the full worked math.
- Roof Overhang and Eaves: How Far Should a Roof Overhang, and WhyAn overhang is one of the cheapest design levers on a house, protecting walls, shading windows and shaping how the roof reads from the street. Get the horizontal-vs-slope math, the shading geometry and the wind limits right, and it works quietly for decades.
Last updated 2026-08-05. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.