Rafter Length Calculator (Angle & Pitch)

Calculate Rafter Length from Roof Angle or Pitch

Rafter Length Formula

Formula

\[ L = V + \frac{R}{2}\cdot\sqrt{1 + \left(\frac{P}{12}\right)^2} \] \[ L = V + \frac{R}{2\cos(A)} \]

Where:

\(L\) — total rafter length, including overhang (ft)
\(V\) — rafter overhang, measured along the slope (ft)
\(R\) — roof span, the full horizontal width covered by the roof (ft)
\(P\) — roof pitch, expressed as rise per 12 inches of run (e.g., 6 means 6/12)
\(A\) — roof pitch angle in degrees

The first formula uses the pitch ratio, the second uses the roof angle. Both give the length of one rafter from the ridge to the wall plate, plus the overhang.

Rafter Length – Calculation Example

Example: a gable roof spans 20 ft (\(R = 20\)), has a 6/12 pitch (\(P = 6\)), and each rafter extends 1 ft beyond the wall (\(V = 1\)).

\[ L = 1 + \frac{20}{2}\cdot\sqrt{1 + \left(\frac{6}{12}\right)^2} = 1 + 10\cdot\sqrt{1.25} = 1 + 11.1803 \approx 12.18 \text{ ft} \]

Result: the rafter length is approximately 12.18 ft (about 12 ft 2\u2044 in). Using the angle method with the same roof: a 6/12 pitch corresponds to an angle of about 26.57°, and \(L = 1 + \frac{20}{2\cos(26.57^\circ)} \approx 12.18\) ft — the same answer.

How to Use the Rafter Length Calculator

In the Rafter length using dropdown, choose Pitch if you know the pitch ratio (e.g., 6/12) or Angle if you know the roof slope in degrees.
Enter the Overhang in feet — the part of the rafter that extends past the wall, measured along the slope. Enter 0 if the rafter ends at the wall plate.
Enter the Roof span in feet — the total horizontal distance the roof covers. For a standard gable roof, the rafter covers half the span.
If you chose Pitch, enter the rise per 12 inches of run (e.g., enter 6 for a 6/12 roof). If you chose Angle, enter the slope angle in degrees instead.
Read the Rafter length in feet, measured from the ridge to the tail of the rafter, including the overhang.

What Is Rafter Length and Why It Matters

A rafter is the sloped structural member that runs from the ridge of the roof down to the top plate of the wall, supporting the roof deck, underlayment, and covering. The rafter length is the distance along that slope — the actual board length you need to cut, not the horizontal run. Because the rafter is the hypotenuse of a right triangle formed by the run (half the span) and the rise, it is always longer than the run.

Both formulas come from that right triangle. With the pitch method, a pitch of \(P\) means the roof rises \(P\) inches for every 12 inches of run, so the slope factor per unit of run is \(\sqrt{1 + (P/12)^2}\). With the angle method, the run is the side adjacent to the angle and the rafter is the hypotenuse, so \(L = \text{run}/\cos(A)\). Carpenters often know this factor as the "rafter multiplier" — for a 6/12 pitch it is about 1.118, meaning every foot of run needs about 13\u2044 in of rafter.

Getting the rafter length right matters for more than just cutting a board to size: rafters that are too short leave gaps at the ridge or the birdsmouth seat, while rafters that are too long waste lumber and can throw the eaves out of line. On a roof with many rafters, even a small error multiplied across dozens of pieces adds up to significant material waste and rework. That is why framers typically add a small allowance for the ridge cut and birdsmouth and verify layout with a test rafter before cutting the full set.

Assumptions, Limitations, and Practical Tips

Symmetric gable roof: the calculator assumes a simple pitched roof where each rafter spans half the total span. For an asymmetric roof, use half the actual run of the side you are calculating instead of the full span.
Overhang measured along the slope: the value you enter for the overhang is added directly to the rafter length, so measure it along the slope, not horizontally.
No deduction for the birdsmouth: the result is the theoretical rafter line length. In practice, the birdsmouth cut removes material but the ridge plumb cut shortens the effective length, and these roughly offset — check against your framing square layout.
Buy longer stock: round up to the next available lumber length. In the example above, 12.18 ft means buying 14 ft boards and trimming, since 12 ft stock is slightly too short.
Check local codes: rafter size, spacing, and span limits depend on snow load, wind, and lumber grade. Once you know the length, verify the member size can span it, or use the Maximum Floor Live Load Capacity Calculator as a starting point for load checks.

While planning the rest of the project, you may also find our Concrete Footing/Slab Pours Calculator useful for the foundations that carry the roof loads, and the Floor Tile Estimator for interior finishing.

Frequently Asked Questions

How do I calculate rafter length by hand without a calculator?

Use the Pythagorean theorem: rafter length = √(run² + rise²). For a gable roof, the run is half the span, and the rise is run × (pitch/12). Example: 12 ft run at 6/12 pitch gives a 6 ft rise, so the rafter is √(144 + 36) = √180 ≈ 13.42 ft. Add the overhang (measured along the slope) to get the total board length.

What is the rafter multiplier (slope factor) and how do I use it?

The rafter multiplier is the ratio of rafter length to run: √(1 + (P/12)²). Multiply the run by it to get the rafter length. Common values: 3/12 → 1.031, 4/12 → 1.054, 5/12 → 1.083, 6/12 → 1.118, 8/12 → 1.202, 10/12 → 1.302, 12/12 → 1.414. Carpenters memorize these to estimate material quickly on site without doing any square roots.

How do I convert the result from feet to feet and inches, or to meters?

Multiply the decimal part by 12 for inches: 12.18 ft = 12 ft + 0.18 × 12 ≈ 12 ft 2⁄16 in, roughly 12 ft 2⅛ in. For metric, multiply feet by 0.3048, so 12.18 ft ≈ 3.71 m. Lumber is sold in standard lengths (8, 10, 12, 14, 16 ft), so always round the result up to the next available board length.

What pitch or angle should I enter for my roof?

Pitch is the rise per 12 inches of run — a roof that rises 6 inches per foot is 6/12, so enter 6. If you only know the angle, common pairs are: 4/12 ≈ 18.43°, 6/12 ≈ 26.57°, 8/12 ≈ 33.69°, 12/12 = 45°. You can convert either way with A = arctan(P/12) or P = 12 · tan(A). Most residential roofs fall between 4/12 and 9/12.

Does the calculator account for the birdsmouth cut and ridge board thickness?

No — it returns the theoretical line length from ridge to tail. The birdsmouth notch removes material at the wall plate, while the ridge board (typically 1½ in thick) shortens the rafter run by about ¾ in per side. These roughly offset on standard framing, but for critical work lay out one rafter with a framing square, test-fit it, and adjust the full set from that pattern.

Can I use this calculator for a hip or valley rafter?

Not directly. Hip and valley rafters run diagonally at 45° to the common rafters, so they are longer — multiply the common rafter run by 16.97 (inches per foot of run) instead of 12, and use a shallower effective pitch (about 8/12 for a 12/12 roof). For an asymmetric roof, enter twice the actual run of the side you need rather than the full span.

What are the most common mistakes when measuring rafter length?

The biggest is confusing span with run — the calculator divides span by 2, so entering the run as the span doubles the result. Others include measuring the overhang horizontally instead of along the slope, forgetting to add the ridge cut allowance, and ignoring that the result is a line length, not the cut board length. Always cut a test rafter first and check the birdsmouth seat and ridge fit before cutting the whole set.