Rafter Length Calculator
Calculate rafter length, birdsmouth cut, ridge cut, and tail cut angles for any roof pitch. Supports common, hip, and valley rafters.
Building Dimensions
Roof Configuration
Quick Answer
Rafter length formula: Length = √(Run² + Rise²) + Overhang Length. For a typical 24-foot wide building with a 6/12 pitch and 12" overhang, each common rafter is approximately 13' 5" long. Hip and valley rafters require multiplying by 1.414 to account for the diagonal angle.
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Table of Contents
How to Calculate Rafter Length
Calculating rafter length accurately is essential for proper roof framing. The process involves understanding the relationship between roof pitch, building width, and overhang dimensions.
Step 1: Determine the Run
The run is the horizontal distance from the outside of the wall to the center of the ridge board. Calculate it as: Run = (Building Width ÷ 2) - (Ridge Board Thickness ÷ 2)
Step 2: Calculate the Rise
Using your roof pitch (rise per 12 inches of run), calculate total rise: Rise = Run × (Pitch Rise ÷ 12). For a 6/12 pitch with 144" run: Rise = 144 × (6/12) = 72"
Step 3: Apply Pythagorean Theorem
The rafter line length is the hypotenuse: Rafter Length = √(Run² + Rise²). Add the overhang rafter length to get the total rafter length.
Understanding Roof Pitch
Roof pitch describes the steepness of a roof, expressed as the ratio of vertical rise to horizontal run. A 6/12 pitch means the roof rises 6 inches for every 12 inches of horizontal distance.
| Pitch | Angle | Multiplier | Common Use |
|---|---|---|---|
| 2/12 | 9.46° | 1.014 | Low slope, commercial roofs |
| 4/12 | 18.43° | 1.054 | Minimum for shingles |
| 6/12 | 26.57° | 1.118 | Standard residential |
| 8/12 | 33.69° | 1.202 | Steeper residential |
| 12/12 | 45° | 1.414 | Steep, snow country |
Types of Rafters
Common Rafters
Run perpendicular from the ridge to the wall plate. These are the most frequently used rafters and form the main structure of gable and shed roofs. Calculate using standard run and rise.
Hip Rafters
Run diagonally from the ridge to the outside corners of the building. Multiply common rafter length by 1.414 (√2) to account for the 45° angle from the ridge.
Valley Rafters
Run diagonally in the valley where two roof sections meet. Like hip rafters, use the 1.414 multiplier for length calculations.
Jack Rafters
Shorter rafters that run from the wall plate to a hip or valley rafter. They decrease in length progressively based on their position along the hip or valley.
Birdsmouth Cut Explained
The birdsmouth is a critical notch cut into the rafter where it sits on the wall's top plate. It provides a stable, level seat for the rafter and ensures proper load transfer to the wall structure.
Birdsmouth Components
- Seat Cut (Horizontal): The flat bottom that rests on the top plate. Typically matches the plate width (3.5" for 2x4 walls, 5.5" for 2x6 walls).
- Plumb Cut (Vertical): The vertical cut that sits against the inside edge of the wall. The angle matches the roof pitch angle.
- Heel: The remaining rafter material below the birdsmouth. Must leave at least 2/3 of the rafter depth for structural integrity.
Important Rule
Never cut the birdsmouth deeper than 1/3 of the rafter depth. For a 2x8 rafter (7.25" actual), maximum seat cut depth is approximately 2.4". Cutting too deep compromises structural integrity.
Rafter Cutting Angles
Every rafter requires precise angle cuts for proper fit. Understanding these cuts ensures tight joints and structural integrity.
Ridge Cut (Plumb Cut)
The cut at the top of the rafter where it meets the ridge board. Set your circular saw or miter saw to the roof pitch angle. For a 6/12 pitch, this is approximately 26.57°.
Tail Cut
The cut at the bottom end of the rafter overhang. Can be plumb (matching ridge cut angle), square, or decorative. Choose based on fascia and soffit installation requirements.
Using a Framing Square
Mark pitch and run on the framing square's tongue and blade. For a 6/12 pitch, align 6" on the tongue with 12" on the blade against the rafter edge. The tongue indicates plumb cuts; the blade indicates seat cuts.
Rafter Material Selection
Rafter size depends on span, spacing, load requirements, and local building codes. Always consult span tables and local requirements.
| Rafter Size | Max Span (16" O.C.) | Max Span (24" O.C.) | Common Application |
|---|---|---|---|
| 2×6 | 10' 9" | 8' 10" | Small spans, sheds |
| 2×8 | 14' 2" | 11' 8" | Residential standard |
| 2×10 | 18' 0" | 14' 10" | Larger residential |
| 2×12 | 21' 7" | 17' 9" | Long spans, heavy loads |
* Spans based on #2 grade SPF lumber, 20 PSF live load, 10 PSF dead load. Always verify with local codes and engineering requirements.
Frequently Asked Questions
How do you calculate rafter length?
Rafter length is calculated using the Pythagorean theorem: Rafter Length = √(Run² + Rise²). The run is half the building width minus half the ridge board thickness, and the rise is calculated from the roof pitch. Add the overhang length and a small amount for waste.
What is a birdsmouth cut?
A birdsmouth cut is a notch cut into the rafter where it rests on the top plate of the wall. It consists of two cuts: a seat cut (horizontal) and a plumb cut (vertical), allowing the rafter to sit flat on the wall plate while maintaining the correct angle.
How do you determine roof pitch?
Roof pitch is expressed as rise over run, typically as X/12 (rise per 12 inches of run). For example, a 6/12 pitch means the roof rises 6 inches for every 12 inches of horizontal run, creating a 26.57° angle. Use a pitch gauge or level and tape measure to determine existing roof pitch.
What is the difference between common and hip rafters?
Common rafters run perpendicular from the ridge to the wall plate. Hip rafters run diagonally from the ridge to outside corners of the building, requiring a 1.414 multiplier to account for the 45° angle. Hip rafters also require compound angle cuts.
How much overhang should a rafter have?
Typical rafter overhangs range from 12" to 24" depending on design preferences and local climate. Larger overhangs provide better rain and sun protection but require additional structural consideration. Check local codes for maximum allowed overhang without additional support.
What size rafter do I need?
Rafter size depends on span, spacing, roof load, and lumber grade. Generally, 2×6 rafters work for spans up to 10', 2×8 for up to 14', 2×10 for up to 18', and 2×12 for longer spans. Always consult span tables and local building codes for specific requirements.
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Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
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