# Rafter Length Calculator

> A common rafter's line length is run × √(1 + (pitch ÷ 12)²) for a pitch given as rise-per-12, or run ÷ cos(angle) for a pitch in degrees. For a 12 ft run at 6/12 pitch: 12 × 1.118 = 13.42 ft ≈ 13' 5" of rafter, with 6 ft of rise and a 26.6° plumb cut.

Enter the run — half the span for a symmetric gable — and the pitch as either rise-per-12 or degrees. You get the line length, the rise, the plumb-cut angle, and the per-unit factor (rafter length per 1 unit of run). The math is unit-agnostic: feed feet, read feet; feed meters, read meters.

Line length is the theoretical distance from the ridge to the outside of the wall plate, measured along the slope. It deliberately excludes two things you apply afterwards: the ridge deduction (half the ridge board's thickness, taken off the run) and the overhang (added separately). Both are covered in the FAQ.

## Formula

`length = run × √(1 + (rise ÷ 12)²) — equivalently, run ÷ cos(pitch angle)`

1. Find the run: span ÷ 2 for a symmetric gable, measured from the outside of the wall plate to the ridge centerline.
2. Express the pitch as rise per 12 units of run (4/12, 6/12, 8/12 …) or as an angle in degrees.
3. Compute the per-unit factor √(1 + (rise/12)²). At 6/12 the factor is 1.118 — every 1 ft of run needs 1.118 ft of rafter.
4. Line length = run × factor. Rise = run × (pitch ÷ 12). Plumb-cut angle = arctan(pitch ÷ 12).
5. Before cutting: shorten by half the ridge thickness (measured horizontally) and add the overhang, measured along the slope.

## Worked example: a 24 ft wide gable at 6/12

Given:

- Building span 24 ft → run = 24 ÷ 2 = 12 ft
- Pitch 6/12 (6 in of rise per 12 in of run)
- Ridge board 1½ in thick (deduction applied at the end)

Steps:

1. Per-unit factor: √(1 + (6/12)²) = √1.25 = 1.118
2. Line length: 12 × 1.118 = 13.42 ft ≈ 13' 5"
3. Rise: 12 × (6 ÷ 12) = 6 ft
4. Plumb-cut angle: arctan(6 ÷ 12) = 26.6°

**The theoretical rafter is 13' 5". Take ¾ in off for the ridge (half of 1½ in, measured along the run), add your overhang along the slope, and buy the next standard length up — with a typical 1–2 ft overhang that's a 16-footer.**

## FAQ

### Is the run half of the building span?

For a symmetric gable, yes: run = span ÷ 2, measured from the outside of the wall plate to the ridge centerline. Roofs with unequal pitches split the span at the ridge position instead, so each side has its own run.

### Does rafter length include the overhang?

No. Line length stops at the outside of the wall plate. To add an overhang, multiply its horizontal projection by the same per-unit factor — a 1 ft overhang at 6/12 adds 1.118 ft of rafter — and keep the tail long until you snap a line for the fascia cut.

### What is the ridge deduction?

Rafters meet a ridge board, not each other, so each rafter gives up half the ridge thickness: subtract it from the run before calculating, or shorten the plumb cut by that amount measured horizontally. A standard 1½ in ridge board costs each rafter ¾ in of run.

### How do I convert roof pitch to degrees?

angle = arctan(rise ÷ 12). Common pitches: 4/12 = 18.4°, 6/12 = 26.6°, 8/12 = 33.7°, 10/12 = 39.8°, 12/12 = 45°. The calculator accepts either form and shows the other.

### What length of lumber should I buy?

Stock length ≈ line length − ridge deduction + overhang slope length, rounded up to the next standard length (2 ft increments in the US). The 13' 5" example with a 1 ft overhang needs about 14' 6" — buy a 16-footer and trim.

---

_Line length only — deduct half the ridge thickness and add your overhang before cutting. Rafter sizing (depth, spacing, allowable span) is structural and code-governed. Estimate only — verify against local code._

Interactive version (free, no signup): https://tenon.tools/calculators/rafter-length/

This file is the markdown mirror of that page. All mirrors: https://tenon.tools/llms.txt