Rafter Calculator
Accurately cutting rafters is one of the most critical tasks in roof framing. This rafter calculator uses the Pythagorean theorem to find the exact rafter length from your horizontal run and vertical rise, and adds your desired overhang for the full bird's mouth-to-tail cut length.
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Formula
Rafter = √(Run² + Rise²); With Overhang = Rafter + Overhang
Run is the horizontal distance from wall plate to ridge (half the building width for a symmetric gable). Rise is the vertical height from plate to ridge. The Pythagorean theorem gives the hypotenuse (rafter length). Add overhang for the full tail length. Pitch equals rise divided by run, expressed as rise per 12 inches of run.
How to use the Rafter Calculator
- 1
Enter your horizontal run (ft)
Value should be in ft.
- 2
Enter your vertical rise (ft)
Value should be in ft.
- 3
Enter your overhang (ft)
Value should be in ft.
- 4
Read your results instantly
Results update in real time as you type.
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Common Rafter vs. Hip Rafter
A common rafter runs perpendicular from the wall plate to the ridge. A hip rafter runs at 45 degrees from a corner to the ridge — it spans a longer diagonal distance and requires a different calculation. This calculator handles common rafters. Hip and valley rafters use the rafter factor multiplied by a 17-inch unit run (instead of 12) to account for the diagonal. Consult a framing reference or engineer for hip rafter sizing.
Rafter Sizing and Span Tables
Rafter length determines required lumber size. Short rafters (under 12 feet) can often use 2×6 lumber. Longer spans require 2×8, 2×10, or 2×12 depending on load, spacing, and wood species. The American Wood Council publishes span tables that specify the maximum span for each lumber size, species, and rafter spacing. Always verify your rafter size against local code span tables before framing.
Tips & Insights
Account for Ridge Board Thickness
At the ridge, subtract half the ridge board thickness from the rise measurement (typically 3/4 inch for a 1x ridge or 13/16 inch for a 2x ridge) to get the plumb cut angle correct.
Use a Framing Calculator
For production rafter cutting, a dedicated construction calculator (like the Calculated Industries Construction Master) computes rise, run, rafter length, and angles simultaneously. These tools pay for themselves on a single framing project.
Mark the Bird's Mouth Carefully
The bird's mouth is the notch cut into the rafter that sits on the wall plate. The seat cut depth should not exceed one-third of the rafter's depth, or you risk weakening the rafter at its most critical load point.
Worked Examples
Standard Gable Rafter
Rafter: 15.65 ft; with 2-ft overhang: 17.65 ft. Pitch: 6:12 (standard residential).
Steep Roof Rafter
Rafter: 15 ft exactly; with 1.5-ft overhang: 16.5 ft. A 9:12 pitch requires safety precautions.
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Frequently Asked Questions
How do I find rafter length?
Use the Pythagorean theorem: rafter length = √(run² + rise²). Run is horizontal, rise is vertical. Add overhang length separately as it adds directly to the rafter tail.
What is the run of a rafter?
The run is the horizontal distance from the outside of the wall plate to the center of the ridge board. For a symmetric gable roof, the run equals half the building width.
What size lumber for rafters?
This depends on span, spacing, load, and species. As a rough guide: 2×6 for spans up to 12 ft, 2×8 up to 16 ft, 2×10 up to 20 ft, 2×12 up to 24 ft at 16-inch spacing. Always verify against code span tables.
What is a bird's mouth cut on a rafter?
A bird's mouth is an L-shaped notch cut near the lower end of the rafter where it rests on the wall's top plate. The horizontal cut (seat cut) sits on the plate; the vertical cut (plumb cut) aligns with the outside of the wall.
How many rafters do I need?
Divide the ridge length by the rafter spacing (16 or 24 inches), add 1, and multiply by 2 (for both sides of a gable roof). Add extra for gable end framing and any hips or valleys.
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