Construction
Rafter Calculator
Calculate rafter length, bird's mouth cut dimensions, cut angles in degrees-minutes-seconds, and lumber requirements for gable, shed, hip, and lean-to roofs. Includes HAP, jack rafter tables, and imperial fraction output ready for the job site.
Spacing OC
Rafter Size
Tail Cut
Total Length
14' 5-9/16"
173.6"
Cut Angle
26° 33' 54"
26.57°
HAP
2-1/4"
2.24"
Ridge Height
6' 1-7/8"
73.9"
Seat Cut Depth
3-1/2"
Plumb Cut Height
1-3/4"
Bird's Mouth
OK
Rafters / Side
13
Total Rafters
26
Lumber Size
2x8
Buy Length
16'
~7% waste
Tail Cut Angle
26° 33' 54"
26.57°
Overhang Length
1' 1-7/16"
13.42"
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What this does
Computes every dimension you need to cut and install roof rafters: total rafter length (including overhang), plumb cut and seat cut angles in degrees-minutes-seconds format, bird's mouth seat cut depth and plumb cut height, height above plate (HAP), ridge height, rafter count, and suggested lumber sizes. For hip roofs, it also computes hip rafter lengths, cheek cut angles, and a complete jack rafter length table.
Who it is for
DIY homeowners building a shed or garage, semi-professional carpenters and contractors who need quick precise cut dimensions on the job site, and anyone learning roof framing who wants to see the math behind each measurement.
How it works
Enter your building span, roof length, overhang, and roof pitch (in any format: X/12, degrees, or percentage). The calculator instantly computes the rafter factor, all cut angles, bird's mouth dimensions, HAP, and suggested lumber. Change any input and all results update in real time. The imperial fraction output rounds to the nearest 1/16 inch for job-site accuracy.
Limitations
Does not perform structural load calculations or account for snow/wind loads. Lumber sizing suggestions are based on typical span tables and should be verified by a structural engineer for spans over 22 feet. All imperial fractions are rounded to the nearest 1/16 inch.
Key calculations
- Rafter Factor
- The multiplier that converts horizontal run to rafter length along the slope. rafterFactor = √(1 + (pitch/12)²)
- Rafter Length
- Total rafter length including overhang. length = (run + overhang) × rafterFactor
- Cutting Angle
- The plumb cut angle for the rafter top, seat, and tail. angle = arctan(pitch/12)
- Bird's Mouth
- Seat cut depth equals the top plate width. Plumb cut height = seatCutDepth × (pitch/12). Must not exceed rafter depth ÷ 3 per IRC.
- HAP (Height Above Plate)
- The vertical distance from the top plate to the rafter's top edge after the bird's mouth is cut. HAP = (rafterDepth − seatCutDepth) / cos(cuttingAngle)
- Hip Rafter Factor
- The multiplier for hip rafter length, different from common rafter. hipFactor = √(1 + pitch²/288)
- Jack Rafter Step
- The length difference between successive jack rafters. step = spacing × rafterFactor
Reference ranges
- Common Roof Pitches
- 4/12 to 7/12 covers most residential roofs. Low-slope (1/12-3/12) needs special underlayment. Steep (8/12+) handles heavy snow and creates usable attic space.
- Overhang
- Standard overhang is 12-16 inches for gable ends, 12-24 inches for eaves. Larger overhangs protect siding but increase rafter length and cost.
- Rafter Spacing
- 16 inch OC is the standard for most residential construction. 24 inch OC saves materials for light loads. 12 inch OC for heavy snow loads or tile roofing.
- Bird's Mouth Rule
- The plumb cut height of the bird's mouth must not exceed one-third of the rafter depth. A 2x6 rafter (5.5 inch actual) can have a heel cut up to 1.83 inches.
How to use it
- 1.Enter building dimensionsType the total span (wall-to-wall) and roof length (along the ridge). For hip roofs, also enter the perpendicular dimension.
- 2.Set the roof pitchChoose a pitch using the visual selector (1/12 through 12/12) or type a custom value in degrees or percentage.
- 3.Specify overhangEnter the overhang distance beyond the wall. This is required — it directly affects lumber length and material ordering.
- 4.Review cut dimensionsCheck the plumb cut angle (displayed in both decimal degrees and DMS format for your miter saw), bird's mouth seat cut depth, and plumb cut height.
- 5.Note the HAPHAP (Height Above Plate) tells you how high the rafter sits above the wall top plate. Use it to set ridge board height.
- 6.Check lumber suggestionsThe calculator suggests a rafter size and lumber length based on the span and spacing. Order with 5-10% extra for waste.
A bird's mouth is a notch cut into the bottom of a rafter where it sits on the top plate of the wall. It consists of a horizontal seat cut (that rests on the plate) and a vertical plumb cut (that aligns with the wall). The seat cut depth equals the top plate width, and the plumb cut height must not exceed one-third of the rafter's depth per building code.
HAP stands for Height Above Plate. It is the vertical distance from the top of the wall plate to the top edge of the rafter after the bird's mouth is cut. HAP determines how high the ridge board sits relative to the walls, and it's essential for ensuring the ridge lines up correctly across different spans.
Carpenters set miter saws using whole degrees and fractional degree tick marks, which correspond directly to the minutes component of DMS. Displaying 26° 33' instead of 26.565° makes it practical to set the saw blade accurately on the job site.
Overhang is the horizontal distance the rafter extends beyond the exterior wall. It is required because it directly affects the total rafter length and the lumber you need to buy. Measure from the outside face of the wall to where you want the rafter tail to end.
In a hip roof, jack rafters are the progressively shorter common rafters that run from the wall plate to the hip rafter. The calculator generates a complete jack rafter table showing each jack's length (with overhang), so you know exactly what to cut.
The building code (IRC) requires that the plumb cut height of the bird's mouth not exceed one-third of the rafter depth to maintain structural integrity. If you see a warning, try upgrading to a larger rafter size (e.g., 2x6 to 2x8) or reducing the top plate width.
No. The rafter calculator is designed for the imperial (feet-inches-fractions) system used in US and Canadian residential construction. All outputs are in feet, inches, and fractional inches to the nearest 1/16.
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