Rafter Calculator
Calculate common, hip, and valley rafter lengths, pitch angle, and birdsmouth cuts.
Need to calculate lumber for your rafters? Try our Board Foot Calculator for accurate lumber estimates.
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How It Works
Common rafter length = √(Rise² + Run²). Hip/Valley rafter uses diagonal run = √(Run² + Run²), then length = √(Rise² + DiagRun²). Pitch angle = atan(Rise / Run).
Understanding Rafter Calculations
Rafter calculations are fundamental to roof framing. Accurately determining rafter length, pitch angle, and birdsmouth cuts ensures a structurally sound roof that meets building codes and distributes loads properly.
Rafter Calculation Formulas
The core formula for a common rafter uses the Pythagorean theorem:
For hip and valley rafters, the diagonal run replaces the straight run:
The pitch angle is calculated as:
The birdsmouth seat cut depth (horizontal cut at the wall) equals the wall thickness. The vertical heel stand equals the wall thickness × tan(pitch angle).
How to Calculate Rafter Dimensions
Engineering Applications
- Residential framing: Calculate precise common rafter lengths for gable roofs of any pitch.
- Hip roof construction: Determine hip rafter lengths for roofs with sloping ends.
- Valley rafters: Calculate valley rafter dimensions where two roof planes meet at an internal corner.
- Birdsmouth cuts: Get seat cut and heel stand dimensions for proper wall bearing.
- Material estimation: Combine with board foot calculations to estimate total lumber needed.
Frequently Asked Questions
How do you calculate the length of a common rafter?
Use the Pythagorean theorem: Rafter Length = √(Rise² + Run²). For example, with a 6-inch rise per 12-inch run and a 12-foot run, the rafter length = √(6² + 144²) = √(36 + 20736) = 144.1 inches ≈ 12 ft 0.1 in. Add the overhang to get the total rafter length.
What degree is a 6/12 pitch roof?
A 6/12 pitch means 6 inches of rise per 12 inches of run. The angle = atan(6/12) = atan(0.5) = 26.57°. This is one of the most common roof pitches for residential construction — steep enough to shed water and snow effectively while remaining walkable.
What is a birdsmouth cut on a rafter?
A birdsmouth (or bird's-mouth) cut is a notch at the bottom of a rafter where it sits on the top plate of the wall. It consists of a horizontal seat cut (matching the wall thickness) and a vertical heel cut. The seat cut transfers the roof load to the wall, while the heel cut provides a plumb bearing surface.
How is a hip rafter calculated differently from a common rafter?
A hip rafter runs diagonally from the ridge to the outside corner of the building. Its run is longer than a common rafter's because it spans the diagonal: Diagonal Run = Common Run × √2. With the same rise but a longer run, the hip rafter is longer and at a different angle than common rafters. It also typically requires a double or wider birdsmouth.
What is the standard roof pitch range?
Standard residential roof pitches range from 4/12 to 9/12 (18.4° to 36.9°). Low-slope roofs are 2/12 to 4/12 and require special waterproofing. Steep-slope roofs above 9/12 are harder to walk on but shed snow and water better. A 6/12 or 7/12 pitch is the most common for single-family homes.