Rafter Length Calculator
Get rafter lengths without climbing on anything. Enter the horizontal run in feet, pick the roof pitch in x/12, and add an eave overhang in inches to see the rafter length to the ridge, the total with overhang, the rise, and the plumb cut angle.
Example: with Run (ft) — wall to ridge, horizontal 12 · Roof pitch 6/12 · Eave overhang (inches, horizontal) 12 → Rafter length to ridge line: 13.42 ft (13 ft 5 in).
- Total length incl. overhang14.53 ft (14 ft 6.4 in)
- Total rise6.00 ft
- Plumb cut angle26.6° from horizontal
Computed by the calculator below using its default values. Change any input to see your own numbers.
Rafter length = √(run² + rise²) — plain Pythagoras. At 6/12 that works out to 1.118 ft of rafter per foot of run.
Pythagoras with a tape measure
A common rafter is the hypotenuse of a right triangle: the run (horizontal distance from the outside of the wall plate to the ridge line) and the rise (run × pitch ÷ 12) are the legs, so length = √(run² + rise²). Equivalently, multiply the run by the slope factor √(144 + pitch²) ÷ 12 — at 6/12 that factor is 1.118, so a 12-foot run needs a 13.42-foot rafter to the ridge line. Overhang is usually specified as a horizontal projection; it rides the same slope, so a 12-inch overhang adds 1 × 1.118 ≈ 1.12 feet of tail.
The run is half the building span only when the ridge is centered — measure your actual run on offset ridges, additions, and shed roofs.
From calculated length to a cut rafter
The length here runs to the center of the ridge. If you frame against a ridge board, subtract half its actual thickness measured along the horizontal — three-quarters of an inch for a 1.5-inch-thick board — before laying out. The plumb cut at the ridge and the level seat cut of the birdsmouth both come from the same angle shown here (26.6° for 6/12), and the birdsmouth notch does not change the rafter length, only the bearing. Buy lumber one stock size up: a 14.53-foot rafter means 16-foot stock.
How it’s calculated
Slope factor = √(12² + pitch²) ÷ 12. Rafter to ridge = run × factor; total = (run + overhang ÷ 12) × factor; rise = run × pitch ÷ 12; plumb cut angle = arctan(pitch ÷ 12). Run in feet, overhang in horizontal inches. Lengths are to the ridge centerline — deduct half the ridge board thickness before cutting.
Assumes a straight common rafter on a symmetric plane — hips, valleys, and jack rafters use different factors (hip/valley factor is √(288 + pitch²) ÷ 12).
Rafter length for a 12 ft run
| Pitch | Slope factor | Rafter (12 ft run) |
|---|---|---|
| 4/12 | 1.054 | 12.65 ft |
| 5/12 | 1.083 | 13.00 ft |
| 6/12 | 1.118 | 13.42 ft |
| 8/12 | 1.202 | 14.42 ft |
| 10/12 | 1.302 | 15.62 ft |
| 12/12 | 1.414 | 16.97 ft |
Computed as 12 × √(144 + pitch²) ÷ 12; rounded to 0.01 ft.
Common mistakes
- Using the full building span instead of the run — on a centered ridge the run is half the span.
- Forgetting to deduct half the ridge board thickness, leaving every rafter 3/4 inch long.
- Treating the overhang as measured along the rafter when the plans give horizontal projection (or vice versa).
- Buying stock to the exact calculated length with no room for the tail plumb cut.
Frequently asked questions
What is the rafter length formula?
Rafter = √(run² + rise²), with rise = run × pitch ÷ 12. Or in one step: run × √(144 + pitch²) ÷ 12. A 12-foot run at 6/12 gives 12 × 1.118 = 13.42 feet to the ridge line.
Does the birdsmouth change the rafter length?
No. The birdsmouth is a notch that lets the rafter bear on the wall plate; the layout length from ridge to the plate line stays the same. What you must subtract is half the ridge board thickness at the top.
How do I handle the overhang?
Plans usually give overhang as a horizontal projection. Convert it to slope length by multiplying by the same factor as the run — a 16-inch projection at 8/12 adds 16 × 1.202 ≈ 19.2 inches of actual rafter tail.
Is the run half the width of the house?
Only for a gable with a centered ridge. Measure from the outside face of the bearing wall to the ridge line for your actual roof — shed roofs use the full horizontal distance between supports.