Pythagoras builds rafters
A common rafter is the hypotenuse of a right triangle: half the building span is the run, and the pitch's rise per foot of run is the height. Rafter length = √(run² + rise²) — the calculator also reports the resulting pitch so you can confirm it matches the plans.
Add the overhang after
The calculated length runs from the wall plate to the ridge centerline. Rafter tails overhanging the eaves (usually 12–24 inches) add length beyond that, measured along the same slope. Birdsmouth cuts — the notch that seats the rafter on the plate — don't change the length but do limit how deep you can cut.
The rafter length formula
Common rafters are right triangles: the run is horizontal (half the building span, plus any overhang), the rise is vertical, and the rafter is the hypotenuse.
Rafter length = √(rise² + run²) · or · Rafter = run ÷ cos(pitch angle)
Both give the same answer. The second form is easier on site because roof pitch is normally quoted as a ratio (a "6/12 roof") and the pitch ratio converts to a single multiplier you can carry in your head.
| Pitch | Angle | Multiplier (rafter per foot of run) |
|---|---|---|
| 1/12 | 4.8° | 1.0035 |
| 2/12 | 9.5° | 1.0138 |
| 3/12 | 14.0° | 1.0308 |
| 4/12 | 18.4° | 1.0541 |
| 5/12 | 22.6° | 1.0833 |
| 6/12 | 26.6° | 1.1180 |
| 7/12 | 30.3° | 1.1577 |
| 8/12 | 33.7° | 1.2019 |
| 9/12 | 36.9° | 1.2500 |
| 10/12 | 39.8° | 1.3017 |
| 12/12 | 45.0° | 1.4142 |
Read the table as a shortcut: measure the run in feet, multiply, and you have the rafter length. A 13 ft run under an 8/12 roof is 13 × 1.2019 = 15.6 ft.
Three worked examples
Example 1 — a 24 ft span, 6/12 pitch, 12-inch overhang
Run = half the span plus the overhang = 12 + 1 = 13 ft. Multiplier for 6/12 is 1.1180. Rafter = 13 × 1.1180 = 14.53 ft. That fits 16 ft stock with the birdsmouth cut and ridge allowance to spare — but only just, so measure the actual span rather than trusting the drawing.
Example 2 — a 30 ft span, 8/12 pitch, 18-inch overhang
Run = 15 + 1.5 = 16.5 ft. Multiplier 1.2019. Rafter = 16.5 × 1.2019 = 19.83 ft. In practice this means either 20 ft lumber on a long span, or a splice — and a spliced rafter is a structural decision, so check with the design before assuming you can butt two pieces together.
Example 3 — a 20 ft span, 4/12 pitch, no overhang
Run = 10 ft, multiplier 1.0541. Rafter = 10.54 ft. A low pitch like this is common on porches and sheds, and the near-1 multiplier is why low-pitch roofs use relatively little extra material — the same 10 ft run under a 12/12 roof would need 14.14 ft.
From rafter length to a cut list
- Deduct half the ridge thickness. The measured run normally goes to the outside face of the wall; the rafter sits against the ridge board, so a 1.5-inch ridge means deducting about 0.75 inch from the rafter length at the top end.
- The birdsmouth seat cut shortens the effective span. The seat cut removes material at the wall plate. The overhang is measured from the outside of the wall to the tail, so get the overhang right first and the rafter follows.
- Order stock longer than the calculated length. Rafter length is the finished length; you need extra for the ridge cut and the plumb cut at the tail. Round up to the nearest available stock size — 14.53 ft becomes 16 ft stock, not 15 ft.
- Cut one, test it, then batch. Every roof has small variations in span. Cut a single rafter, set it in place, confirm the fit, and only then use it as the pattern for the rest.
- Check the pitch in the field. A pitch quoted as 6/12 on a plan assumes the span and the wall heights are exactly as drawn. Measure the rise before ordering; a 4-inch error over a 13 ft run moves the pitch enough to change every cut.
Roof geometry also drives the decking order — count sheathing panels with the plywood calculator once you know the total roof area, and check roof drainage with the roof pitch calculator.
Tools for cutting rafters
Rafter layout is where cheap tools cost you a roof. The two squares below are the same references the calculator assumes you are marking with.
- Framing square — The rafter tables printed on the blade are the fastest independent check on the length this calculator gives you.
- Speed square — For marking plumb and seat cuts at the ridge and the birdsmouth without needing a second pair of hands.
- 7-1/4 inch circular saw — Cuts every rafter on a typical house. Check the bevel detent is actually square before you trust a single cut.
- Chalk line and 25 ft tape — For snapping the ridge and fascia lines and checking every rafter length before you nail anything down.
As an Amazon Associate I earn from qualifying purchases. The links above are affiliate links — if you buy through one, the price you pay is unchanged and a small commission helps keep these calculators free. Tools are listed because the job calls for them, not because of commission rates.
Sources and standards
Where these figures come from
Every formula on this page is implemented from the published reference material below. Where a value depends on a regional code, the calculator lets you override it rather than assuming one jurisdiction.
- American Wood Council — span tables, lumber design values and the Wood Frame Construction Manual.
- APA — The Engineered Wood Association — panel span ratings and sheathing installation guidance.
Figures, formulas and reference tables last verified: 19 September 2026.