CarpentryInstant Tool
Rafter Calculator
Calculate common rafter length, total rise, plumb cuts, and birdsmouth cuts
Rafter Length Estimator
Calculate common rafter length, total rise, cut angles, and overhang
How Rafter Calculator Works
Rafter Length = Square Root of Run Squared plus Rise Squared plus Overhang LengthDetermines common rafter framing length based on building span, half-span horizontal run minus half ridge thickness, and roof pitch rise. Pythagorean geometry calculates line length and overhang tail.
Variable Breakdown
Span
Building SpanTotal exterior wall to exterior wall width in feet
Pitch
Roof PitchInches of vertical rise per 12 inches of horizontal run
Overhang
Eave OverhangHorizontal eave projection beyond exterior wall
Ridge
Ridge ThicknessThickness of center ridge board usually 1.5 inches
Example Calculation
24 Foot Span Building with 6 in 12 Pitch
A builder frames a gable roof with a 24-foot building span, 6 in 12 pitch, 1.5-inch ridge board, and 16-inch overhang.
- Half span run equals 12 feet minus 0.75 inch ridge half thickness which equals 11.94 feet
- Total rise equals 11.94 multiplied by 6 divided by 12 which equals 5.97 feet or 5 ft 11.6 in
- Rafter line length equals square root of 11.94 squared plus 5.97 squared which equals 13.35 feet
- Overhang rafter tail equals 16 divided by 12 divided by cosine 26.6 degrees which equals 1.49 feet
- Total rafter board length equals 13.35 plus 1.49 which equals 14.84 feet or 14 ft 10 in
Result:14 ft 10 in Cut Length
Common Roof Pitch Angles and Length Multipliers
| Pitch | Angle Degrees | Length Multiplier | Plumb Cut Angle |
|---|---|---|---|
| 3 in 12 | 14.0 degrees | 1.031 | 14.0 degrees |
| 4 in 12 | 18.4 degrees | 1.054 | 18.4 degrees |
| 5 in 12 | 22.6 degrees | 1.083 | 22.6 degrees |
| 6 in 12 | 26.6 degrees | 1.118 | 26.6 degrees |
| 7 in 12 | 30.3 degrees | 1.158 | 30.3 degrees |
| 8 in 12 | 33.7 degrees | 1.202 | 33.7 degrees |
| 9 in 12 | 36.9 degrees | 1.250 | 36.9 degrees |
| 10 in 12 | 39.8 degrees | 1.302 | 39.8 degrees |
| 12 in 12 | 45.0 degrees | 1.414 | 45.0 degrees |
Frequently Asked Questions
How is rafter length calculated from pitch and span?
Calculate run as half the building span minus half the ridge thickness. Multiply run by pitch over 12 to find rise. Use the Pythagorean theorem to calculate the hypotenuse rafter length.
What is a birdsmouth cut on a rafter?
A birdsmouth cut is an L-shaped notch cut into a rafter where it rests on the wall top plate, consisting of a horizontal seat cut and a vertical plumb cut.
What lumber size is standard for roof rafters?
Common residential rafter lumber sizes include 2x6, 2x8, 2x10, and 2x12, depending on rafter span, spacing 16 or 24 inches on center, and local snow load codes.
How do you adjust rafter length for a ridge board?
Deduct half the thickness of the ridge board typically 0.75 inches for standard 2x lumber from the rafter run before calculating rafter length.
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