Rafter Length Calculator: Common, Plumb, Seat, and Tail Cuts

How to figure rafter length — step by step

How to figure rafter length from a building's dimensions reduces to a six-step procedure that you can do longhand or with the calculator above. The same procedure tells you how to figure length of rafters, how to get rafter length, how to measure the rafter, and how to calculate the length of rafters from any pitch-and-span combination.

1. Measure the building's span — the full horizontal distance across the building, from outside wall plate to outside wall plate. For a 24-foot-wide single-story house, span is 24 feet.
2. Calculate run = span ÷ 2. The run is half the span, because a common rafter goes from the wall plate to the ridge centerline (which sits over the building's centerline). A 24-foot span gives a 12-foot run.
3. Determine the pitch — rise inches per 12 inches of run. A 6/12 pitch means 6 inches of rise per 12 inches of run. If you do not know the pitch, measure it from an existing roof using the level-and-tape method, or pick one based on your design constraints (4/12 minimum for asphalt shingles, 6/12 typical residential, 8/12 for steep aesthetic).
4. Calculate total rise = run × (pitch ÷ 12). For a 12-foot run on 6/12 pitch: 12 × (6/12) = 6 feet total rise. This is the vertical distance from the wall plate to the ridge.
5. Apply the Pythagorean theorem: rafter length = √(run² + rise²). For our example: √(144 + 36) = √180 ≈ 13.42 feet. This is the distance from the ridge centerline to the wall plate edge.
6. Adjust for ridge thickness and overhang. Subtract half the ridge board thickness from the run before computing the hypotenuse (a 1.5" ridge takes 0.75" off each side). Add overhang as additional length at the same pitch — a 16" overhang at 6/12 adds about 17.9" to the rafter, since the overhang is also a hypotenuse at the same angle.

The basic rafter length formula

A common rafter is the hypotenuse of a right triangle with the run as the base and the rise as the height. The Pythagorean theorem gives you the length directly: c² = a² + b², so the rafter's length = √(run² + rise²).

For a 6/12 pitch on a 24-foot-wide building, the run is 12 feet and the rise per foot of run is 6 inches, so the total rise is 6 feet. The hypotenuse is √(144 + 36) = √180 ≈ 13.42 feet. That is the rafter from the centerline of the ridge to the outside edge of the wall plate, before adjusting for ridge thickness and overhang.

In framing-square shorthand, you express rise as inches per 12 of run, so the calculation often looks like this: for every foot of run, the rafter travels √(144 + rise²)/12 inches. For a 6/12 that's √180/12 ≈ 1.118 — meaning the rafter's linear distance per foot of run is 1.118 feet. Multiply by your total run to get the total length. This per-foot multiplier (sometimes called the "rafter length factor" or "line length per foot of run") is the standard shortcut framers use to find rafter length quickly: a 12-foot run on 6/12 = 12 × 1.118 = 13.42 feet, the same answer the Pythagorean formula gives directly.

Ridge thickness and overhang

The basic formula gives you the rafter from ridge centerline to wall plate edge. In real framing you have to account for two things: the ridge board has thickness, and the rafter usually extends past the wall plate to form an overhang.

Ridge thickness is half the ridge board's width subtracted from the run, because the rafter only goes from the ridge's outer face inward, not all the way to the centerline. A 1.5-inch nominal 2x ridge board takes 0.75 inches off each side — your effective run is 0.75 inches less than half the span.

Overhang is the horizontal distance the rafter projects past the outside edge of the wall plate. A typical residential overhang is 12 to 24 inches. The overhang projects at the same pitch as the main rafter, so you treat it as additional run when calculating the total dimension.

The three standard cuts

Every common rafter has three cuts: the plumb cut at the ridge, the bird's mouth (a notch with a seat cut and a heel cut) at the wall plate, and the tail cut at the eave end. Each cut's angle is determined by the pitch.

The plumb cut at the ridge is the angle that, when the rafter is in place, results in a perfectly vertical face matching the ridge board. This angle is 90° minus the pitch angle. For a 6/12 pitch (26.57°), the plumb cut is 63.43° from the rafter's long axis.

The seat cut (the horizontal portion of the bird's mouth) sits flat on top of the wall plate. Its angle equals the pitch angle — 26.57° for 6/12. The heel cut is the vertical portion behind the seat cut, parallel to the wall framing.

The tail cut at the eave end can be either plumb (matching the ridge plumb cut) for a traditional fascia, or square to the rafter's length for an exposed tail. Plumb tail cuts are more common in modern construction because they make fascia installation cleaner.

Hip roof rafter calculator — different math

A hip roof calculator handles a slightly more complicated geometry than a common-rafter calculation: hip rafters run diagonally from a corner of the building up to the ridge end, traversing a 45° plan angle in addition to the vertical pitch. Their length is longer than a common rafter at the same pitch.

The hip rafter's "run" in plan view is the diagonal of a square with side length equal to the common rafter's run. For a building with a 12-foot run on each side: hip rafter's plan run = √(12² + 12²) = √288 ≈ 16.97 feet. The pitch is the same as the common rafter (6/12 here), but the rise is calculated against the hip's longer plan run: 16.97 × (6/12) = 8.49 feet rise. Hip rafter dimension = √(16.97² + 8.49²) = √(288 + 72.06) ≈ 18.97 feet.

The shortcut: hip rafter length per foot of common-rafter run uses a "hip rafter length factor". For a 6/12 pitch, the common rafter runs 1.118 feet per foot of common run; the hip runs 1.581 feet per foot of common run. Multiply your common run (the run for the common rafter, NOT the hip's plan run) by 1.581 to get the hip rafter dimension: 12 × 1.581 = 18.97 feet, matching the Pythagorean calculation. Different pitches have different multipliers — most framing squares have the multipliers stamped on the blade for easy reference.

Hip rafters also have a more complex bird's mouth and tail cut than common rafters because they meet the wall plate at a 45° plan angle rather than 90°. The plumb cut at the top is "compound" — both a plumb angle (matching the pitch) and a side cut (45° to fit against the ridge). For complex hip-roof framing, an experienced framer or detailed framing square reference is helpful.

Laying out a pattern rafter

Pick the straightest, cleanest stick of lumber for your pattern rafter — every other rafter on the building gets cut from this template, so accuracy matters. Lay it crown-up on a pair of sawhorses with the soon-to-be-top edge facing you.

Set your framing square with the rise on the tongue (short leg) and 12 on the blade (long leg). For a 6/12, that means 6 inches on the tongue and 12 inches on the blade. Place the square so the 12-inch mark on the blade lines up with the upper edge of the lumber, and the 6-inch mark on the tongue is also on the upper edge. Trace along both legs to mark the plumb-cut angle on one end.

Step the square along the rafter, advancing 12 inches per step, for as many steps as your run requires. Each step represents 1 foot of run — for a 12-foot run, step the square 12 times. Mark the heel of each step on the upper edge.

At the wall-plate end, mark the bird's mouth: the seat cut sits flat on the plate and is typically 3.5 inches deep (matching a 2x4 plate). The heel cut is plumb, parallel to the ridge plumb cut. Below the bird's mouth, continue the line for your overhang — additional steps of the framing square at the same pitch.

Cut the pattern rafter, then test-fit it on the building before cutting the rest. If the seat does not sit flush on the plate or the plumb cut does not meet the ridge cleanly, your pitch is slightly off — adjust before cutting more lumber.

Lumber sizing for rafters

Rafter size depends on span, spacing, dead load, snow load, and species/grade of the lumber. Most residential framing uses 2x6, 2x8, 2x10, or 2x12 dimension lumber on 16-inch or 24-inch centers.

A rough guideline: 2x6 rafters span up to about 10 feet on 16-inch centers in moderate snow loads. 2x8 spans to about 13 feet, 2x10 to 16 feet, 2x12 to 19 feet. These numbers shrink in heavy snow regions and stretch in mild climates. Always cross-check with the IRC R802 rafter span tables for your specific load conditions, or have an engineer size the rafters for any non-standard situation.

Engineered I-joists and LVL beams are increasingly common for longer spans where dimension lumber would be marginal or excessive. They cost more per linear foot but allow for thinner, stronger members and reduce material waste.

Rafter dimensions calculator — picking depth and spacing

A rafter dimensions calculator returns both the length (covered above) and the depth (cross-section) of the rafter lumber needed for a given span, spacing, and load combination. The depth question is what determines whether you can use 2x6, 2x8, 2x10, or 2x12 lumber for the rafter.

IRC R802.5.1 prescriptive tables give maximum allowable rafter span for each combination of: lumber size (2x6 through 2x12), on-center spacing (12, 16, or 24 inches), dead load (10 or 20 psf depending on roof finish weight), and ground snow load (20, 30, 50, or 70 psf depending on region). For a typical residential application — moderate dead load, 30 psf ground snow — the spans break down as: 2x6 at 16" OC reaches about 10 feet of horizontal span; 2x8 reaches 13 feet; 2x10 reaches 16 feet; 2x12 reaches 19 feet. Stretching beyond these spans is allowed at tighter spacing (12 inches OC instead of 16) or with engineered lumber.

Spacing affects both lumber count and individual rafter capacity. 16-inch on-center is the residential default, balancing lumber cost against load capacity. 24-inch on-center reduces lumber count by one-third but requires either thicker lumber, shorter spans, or engineered design for higher loads. 12-inch on-center is used for tall walls and heavily-loaded shear walls in seismic regions.

The calculator above outputs the rafter length; for sizing, cross-check the result against IRC R802 tables for your load conditions. For any non-standard situation — large open spans, heavy snow loads, structural ridge beams instead of ridge boards — get the design from an engineer rather than relying on prescriptive tables.

Common rafter vs other rafter types

A common rafter runs perpendicular from the wall plate to the ridge in a typical gable roof. Most rafter calculators (including this one) compute common rafter length, which is the most-used calculation in residential roof framing.

A hip rafter runs diagonally from a building corner to the ridge end on a hip roof — covered in the hip-rafter section above. Longer than common rafters at the same pitch, with compound cuts.

A jack rafter runs from a wall plate up to a hip rafter (instead of the ridge), and is shorter than a full common rafter. Each jack rafter is a different length depending on its position along the wall. Most modern framing software calculates jack rafter lengths automatically; manual calculation uses the same Pythagorean approach with the run shortened to where the rafter meets the hip.

A valley rafter runs along the inside corner where two roof planes meet. It is similar to a hip rafter in length and cut complexity but reversed — the valley collects water from both adjacent slopes.

For deeper coverage of rafter anatomy and naming, the house rafter guide on this site covers each type with diagrams and explains how they fit together in a complete roof framing system.

How we sourced these numbers

The Pythagorean formula above is accepted geometric identity, not sourced to a single citation. Lumber span tables come directly from the 2024 International Residential Code (IRC) Section R802 — specifically R802.5.1 (rafter span tables), R802.4 (rafter framing details), and R802.10 (engineered design alternatives). The American Wood Council's Wood Frame Construction Manual provides additional reference for engineered conditions and high-load situations not covered by IRC prescriptive tables.

The "rafter length factor" (1.118 for 6/12 pitch, etc.) values are accepted framing-square reference data, stamped on most quality framing squares and documented in standard carpentry references including the Carpenter's Manual. Where IRC tables are updated (every three-year code cycle), the corresponding sections of this page are reviewed and updated to match.