Common Rafter Calculator
A common rafter runs at right angles from the exterior wall plate up to the ridge, forming the backbone of any gable roof. This common rafter calculator computes the run, rise, line length (ridge to birdsmouth), total length with overhang, plumb cut angle, seat cut angle, and height above plate (HAP) for any building span and roof pitch. It matches the framing-square and speed-square methods used by carpenters, so the numbers transfer directly to the lumber and cut lines.
What Is a Common Rafter
A common rafter is the "standard" sloped roof framing member that connects the wall's top plate to the ridge board at a 90 degree angle to both walls. Every gable roof has dozens of common rafters, evenly spaced along the building length (usually 16 or 24 inches on center). Hip, valley, and jack rafters are named differently because they run at other angles.
How the Common Rafter Calculator Works
The rafter forms the hypotenuse of a right triangle:
- Run (horizontal leg) = span / 2 minus half the ridge thickness
- Rise (vertical leg) = run x (pitch / 12)
- Line length (hypotenuse) = sqrt(run² + rise²)
- Total rafter length = line length + overhang rafter
The overhang rafter extends the rafter past the wall plate for the eave. Its length uses the same pitch applied to the overhang distance.
Worked Example
24 ft span, 8:12 pitch, 1.5 in (2x) ridge board, 12 in overhang:
- Run = 24/2 - 1.5/24 = 11.9375 ft
- Rise = 11.9375 x 8/12 = 7.9583 ft
- Line length = sqrt(11.9375² + 7.9583²) = 14.3419 ft
- Overhang rafter = sqrt(1.0² + (1.0 x 8/12)²) = 1.2019 ft
- Total rafter length = 15.5438 ft, order 16 ft lumber
Plumb Cut and Seat Cut Angles
The plumb cut (vertical cut at the ridge end and tail end) equals the roof angle from horizontal:
Plumb cut = atan(pitch/12)
For common pitches:
| Pitch | Plumb Cut | Seat Cut |
|---|---|---|
| 3:12 | 14.04° | 75.96° |
| 4:12 | 18.43° | 71.57° |
| 6:12 | 26.57° | 63.43° |
| 8:12 | 33.69° | 56.31° |
| 10:12 | 39.81° | 50.19° |
| 12:12 | 45.00° | 45.00° |
To mark the plumb cut with a framing square, set the tongue at 12 inches and the blade at the pitch rise (e.g., 8 inches for 8:12). The edge of the tongue gives the plumb line.
Height Above Plate (HAP)
HAP is the vertical distance from the wall plate to the top edge of the rafter above the birdsmouth seat cut. It determines how much of the rafter stands "above" the wall.
HAP = rafter_depth / cos(plumb_angle) - seat_cut_depth
For a 2x8 rafter (7.25 in depth) on an 8:12 pitch with a standard 1.5 in seat cut:
HAP = 7.25 / cos(33.69°) - 1.5 = 7.25 / 0.8321 - 1.5 = 8.71 - 1.5 = 7.21 inches
HAP affects soffit and fascia sizing. A larger HAP gives room for a continuous soffit vent; a smaller HAP makes the eave tighter.
Marking the Birdsmouth
- Mark the plumb line at the ridge end of the rafter using a framing square set to the pitch.
- Measure along the rafter edge by the line length distance from that plumb line.
- Mark a second plumb line at that point; this is the outside of the wall plate.
- From that plumb line, measure 1.5 inches horizontally into the rafter; this is the seat cut.
- Mark the seat cut perpendicular to the first plumb line at that 1.5 in depth.
Never cut more than one-third of the rafter depth for the seat cut, or you compromise structural strength.
Common Rafter vs Hip and Jack Rafters
- Common rafters run from wall plate to ridge at 90 degrees to both.
- Hip rafters run from a corner at 45 degrees to the ridge, used in hip roofs.
- Jack rafters are shortened commons that frame into hip or valley rafters.
- Valley rafters run in the opposite direction of hips, at the intersection of two roof sections.
This calculator computes common rafters only. For hip or valley rafters, multiply by 17/12 for hip length per foot of run, and apply different cut angles (33.56° for a 45-degree hip on an 8:12 pitch).