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Estimating · 9 min read

How to Calculate Rafter Lengths (With Overhang)

A step-by-step guide to using the Pythagorean theorem and pitch multipliers to cut rafters that actually fit.

BuildMetric Engineering

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Cutting rafters is one of the most satisfying parts of framing a roof — and one of the most unforgiving. If your math is off by half an inch, the ridge board will be out of level, the fascia won't line up, and the sheathing will show the error.

You do not need a degree in trigonometry to get it right, but you do need to understand the basic geometry of a roof triangle. This guide walks through the exact steps to calculate rafter length, including how to account for the overhang and the width of your ridge board.

01. The Anatomy of a Rafter

Before calculating, let's define the parts of the triangle you are working with. Every roof rafter is the hypotenuse (the long side) of a right-angled triangle.

  • Rise: The vertical distance from the top of the wall plate to the top of the ridge.
  • Total Run: The horizontal distance from the outside edge of the wall plate to the center of the ridge board.
  • Actual Run: The Total Run minus half the thickness of the ridge board.
  • Overhang: The distance the rafter extends past the outside of the wall to create the eaves (soffit).

Because the roof is symmetrical, you typically calculate one side and use that same length for the other side.

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02. The Math (Pythagorean Theorem)

If you know the Rise and the Run, you can calculate the Rafter Length using the Pythagorean theorem: a² + b² = c².

Example Calculation:

Let's say you have a 6:12 pitch and a Total Run of 12 feet.

  1. Rise = (12 ÷ 12) × 6 = 6 feet
  2. Run = 12 feet
  3. c² = (6²) + (12²)
  4. c² = 36 + 144 = 180
  5. c = √180 = 13.416 feet

So, the base rafter length (from the outer edge of the wall to the center of the ridge) is 13.416 feet, or about 13 feet 5 inches.

Note: This calculation assumes the rafter sits perfectly on the outer edge of the wall plate. In reality, we need to account for the overhang and the ridge board (covered in sections 4 and 5).

03. Using Pitch Multipliers

While the Pythagorean theorem works perfectly, calculating square roots on site is tedious. Most framers use a Rafter Multiplier (also called the secant).

The multiplier is a pre-calculated number that allows you to find the rafter length by simply multiplying the Run.

Roof Pitch Multiplier Example (Run = 10 ft)
4:12 1.054 10 × 1.054 = 10.54 ft
6:12 1.118 10 × 1.118 = 11.18 ft
8:12 1.202 10 × 1.202 = 12.02 ft
12:12 1.414 10 × 1.414 = 14.14 ft

To get your total rafter length, simply multiply your Total Run (including overhang) by the multiplier for your pitch.

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04. Accounting for Overhang

The rafter doesn't stop at the wall; it continues to form the eaves. If you calculated your rafter using only the building width, your roof will have no overhang and water will run straight down your walls.

To account for the overhang, you must add the horizontal distance of the overhang to your Total Run before applying the multiplier.

Example Calculation (with overhang):

  • Building width = 24 ft. (Total Run = 12 ft).
  • Desired overhang = 2 ft.
  • Actual Total Run = 12 ft + 2 ft = 14 ft.
  • Multiply by the 6:12 multiplier (1.118):
  • 14 ft × 1.118 = 15.65 ft (total rafter length).

Note: The overhang measurement is usually taken horizontally from the outside of the wall plate. If you measure the overhang along the slope of the roof, you can simply add that length directly to the calculated rafter length.

05. Deducting for Ridge & Birdsmouth

Your calculated rafter length is the distance from the outside edge of the wall to the apex of the roof. However, you cannot cut the rafter to this exact length. Two final deductions are required:

1. Deduct Half the Ridge Board Thickness

The rafter doesn't extend all the way to the opposite side of the building; it stops at the center of the ridge board. If you are using a 2-inch thick ridge board, you must deduct 1 inch (half the thickness) from the total run before calculating.

2. The Birdsmouth Cut

The birdsmouth is the notch cut into the bottom of the rafter so it sits flat on the wall plate. This cut drops the top edge of the rafter down. You must ensure the "Heel" (the vertical distance from the top of the rafter to the top of the wall plate) is consistent. If you cut the birdsmouth too deep, it weakens the rafter. The general rule is that the depth of the notch should not exceed one-third of the rafter's width.

Because the birdsmouth drops the rafter, the calculated length represents the top edge of the rafter. Your measurement line should be run along the top edge, and the birdsmouth cut out from the bottom.

The Bottom Line

Rafter math is straightforward once you break it down into Rise, Run, and Overhang. Always draw a rough triangle, double-check your multiplier, and remember to account for the ridge thickness. It is also highly recommended to cut one "test rafter" first, test-fit it on the roof, and use it as a template for the rest of the roof.

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About the Author

BuildMetric Engineering Team

Technical Writing & Code Review

This guide was written by the BuildMetric editorial team and reviewed by a practising structural engineer. We combine field experience with published standards to explain construction math without the jargon. Every article is versioned and dated.

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Frequently Asked Questions

Rafter Length FAQs

01 How do I calculate the length of a roof rafter?

To calculate rafter length, you can use the Pythagorean theorem (a² + b² = c²) where 'a' is the Rise and 'b' is the Run. Alternatively, multiply the Run by the Rafter Multiplier for your specific pitch (e.g., 1.118 for a 6:12 pitch). Always remember to deduct half the thickness of the ridge board from your total run before calculating.

02 How do you account for the overhang when calculating rafters?

To include the overhang, you must add the horizontal distance of the overhang to your Total Run before applying the pitch multiplier. For example, if your building run is 12 feet and you want a 2-foot overhang, your Actual Total Run is 14 feet. Multiply 14 by your rafter multiplier to get the final length.

03 What is a rafter multiplier?

A rafter multiplier (or pitch multiplier) is a pre-calculated number used to find the diagonal length of a rafter based on the horizontal run. It is equal to the secant of the roof pitch angle. For example, a 4:12 pitch has a multiplier of 1.054, a 6:12 pitch is 1.118, and a 12:12 pitch is 1.414.

04 How much do I deduct for the ridge board?

You must deduct half the thickness of the ridge board from your total horizontal run. For example, if you are using a standard 2-inch thick ridge board, deduct 1 inch from your run. This ensures the rafters meet perfectly at the center of the ridge without overlapping or leaving a gap.

05 What is a birdsmouth cut and how deep should it be?

A birdsmouth cut is a triangular notch cut into the bottom of a rafter so it sits flat on the wall plate. To avoid weakening the rafter, the depth of the birdsmouth cut should never exceed one-third of the rafter's actual width. For a 2x6 rafter (actual width 5.5 inches), the maximum notch depth is about 1.8 inches.

06 Where do I measure a rafter from?

Rafter length is measured along the top edge of the rafter. The measurement starts from the 'plumb cut' (the vertical cut at the top that meets the ridge) and ends at the 'plumb cut' at the tail (the vertical cut that forms the fascia). The birdsmouth is then cut out from the bottom edge.

07 Does a steeper pitch make the rafter longer or shorter?

A steeper pitch makes the rafter longer. As the pitch increases, the rise increases while the run remains the same, making the diagonal rafter longer. For example, a 12-foot run with a 4:12 pitch results in a 12.65-foot rafter, while a 12:12 pitch on the same run results in a 16.97-foot rafter.

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