Roof Rafter Length Calculator

Rafter cutting is the most geometry-intensive task in residential framing. Each rafter has three critical cuts — the plumb cut at the ridge, the birdsmouth at the wall plate, and the tail cut at the eave — and getting any one wrong means the rafter does not fit.

1. Calculate the rafter length from the numbers above. The calculator gives you the total length along the slope, including the overhang. This is the measurement you need for ordering lumber — always order the next standard length up from the calculated value because you cannot splice a rafter mid-span.

2. Mark the plumb cut at the ridge end. Set your framing square with the pitch rise on the tongue and 12 inches on the blade. The line along the tongue is the plumb cut. For a 6/12 pitch, the tongue reads 6 and the blade reads 12. This cut sits against the ridge board: a gable in this calculator always has a ridge board thickness above 0, and the 0 option runs the full span as a shed roof. If you have not pinned down the roof's pitch yet, work it out from a measured rise and run before laying out the square.

3. Measure and mark the birdsmouth. From the long point of the plumb cut, measure the main rafter length along the top edge to the wall plate location: 13.35 ft in the first worked example, not the 14.46 ft total, which adds the overhang beyond the plate. The birdsmouth is a notch cut where the rafter sits on the wall plate: it consists of a seat cut (horizontal, equal to the plate width, typically 3.5 inches for a 2x4 wall) and a plumb cut (vertical). The notch sits at the wall plate, and its depth limit depends on whether the rafter ends there. If the rafter ends at the plate, the seat may cut no deeper than one-fourth of the rafter depth (IRC 2021 Section R802.7.1, which sends sawn rafters to R502.8.1). If the rafter runs on into an overhang, the code text does not say whether the birdsmouth counts as a notch on that overhang. Ask your building official first. If it counts, IRC 2021 Section R802.7.1.1 asks for at least 3-1/2 inches of the rafter to remain, on an overhang of 24 inches or less. If it does not, the birdsmouth is not at the end of the member, so IRC 2021 Section R502.8.1 holds it to one-sixth of the rafter depth. IRC 2021 Section R502.8.1 also caps the length of a notch at one-third of the rafter depth, measured along the rafter, which can make the seat shorter still. Until you have that reading, hold the birdsmouth on an overhanging rafter to one-sixth of the depth. Settle the birdsmouth size with your building official or an engineer before you cut the full set. The birdsmouth section below works out each limit and the seat sizes they allow.

4. Mark the tail cut past the birdsmouth. From the birdsmouth, measure the overhang length along the top edge and mark another plumb cut. This is the tail cut — the end of the rafter at the fascia board. Some builders cut the tail plumb (vertical) and others cut a combination plumb and level cut for a decorative tail profile.

5. Cut a pattern rafter first. Cut one rafter carefully, test-fit it on the actual building, verify the ridge fit, birdsmouth seat, and overhang dimension, then use it as a template for all remaining rafters. Never cut the full batch from calculations alone — minor framing variations always exist.

6. Verify with a chalk line. After installing several rafters, snap a chalk line along the top edges. Any rafter that sits high or low relative to the line usually has a birdsmouth error. Fix it before sheathing: plywood over a misaligned rafter creates a visible hump or dip in the finished roof.

The pitch multiplier converts horizontal run to actual rafter length along the slope. It is the most important number in rafter layout because it determines how much longer the rafter is than the run.

The jump from 6/12 to 12/12 more than triples the extra length, from 12% to 41%. The length added runs from 1.4% at 2/12 to 41.4% at 12/12. This is why steep roofs use more lumber than low-slope roofs of the same span width. A 12/12 pitch roof with a 12-foot run needs a 17-foot rafter versus 13.4 feet at 6/12.

For projects where pre-fabricated trusses make more sense than stick-framing, the truss cost estimator estimates what factory-built trusses cost, a figure you can set against the labour and material of site-cut rafters.

The birdsmouth is the notch cut into the rafter where it sits on the top plate of the wall. It looks simple — a right-angle notch — but its depth determines the rafter's remaining bending strength at the bearing point. Cut too deep and the rafter loses bending strength at the bearing point. Cut too shallow and the rafter does not seat firmly on the plate.

The birdsmouth sits at the wall plate, where the rafter bears on the wall. The seat cut (the horizontal cut that sits on the plate) sets how deep it notches the rafter. The depth limit depends on whether the rafter stops at the plate or runs past it. IRC 2021 Section R802.7.1 sends notches in sawn rafters to R502.8.1, with its own rule for the overhang (R802.7.1.1). Each limit below carries the fraction or dimension the code prints:

• A rafter that ends at the wall plate (no overhang): the birdsmouth is a notch at the end of the member, no deeper than one-fourth of the rafter's depth (IRC 2021 Section R502.8.1).
• A rafter that runs past the wall into an overhang, a cantilevered portion (the part of the rafter that sticks out past the wall): IRC 2021 Section R802.7.1.1 permits notches on that portion if at least 3-1/2 inches of the rafter remains and the cantilever is no longer than 24 inches. It points to its Figure R802.7.1.1 for the notch it means, and its text does not say whether that includes the birdsmouth. If it does not, the birdsmouth is not at the end of the member, so the one-sixth depth and one-third length limits below apply. Hold to those until your building official gives a reading. The overhang input above goes up to 36 inches, so an overhang past 24 inches falls outside this permission: ask your building official about the birdsmouth on such a rafter.
• Notch length: no longer than one-third of the rafter's depth, measured along the rafter (IRC 2021 Section R502.8.1). The code prints this limit with no location, and its sentence on notches at the ends sets a depth only.
• Elsewhere along the rafter, outside the middle third: a notch no deeper than one-sixth of the rafter's depth (IRC 2021 Section R502.8.1).
• The middle third of the span: no notch at all (IRC 2021 Section R502.8.1).
• The tension side (the edge pulled apart under load) of members 4 inches or more in nominal thickness (the thickness in the lumber's name, as in a 4x10; a 2x rafter is 2 inches by name): no notch except at the ends (IRC 2021 Section R502.8.1).

For a 2x8 rafter (7.25 inches actual) that ends at the plate, the one-fourth limit of IRC 2021 Section R502.8.1 is about 1.81 inches (7.25 / 4 = 1.8125). A notch elsewhere on the same rafter stops at about 1.21 inches (7.25 / 6 = 1.2083). For a 2x10 (9.25 inches actual) that ends at the plate, the one-fourth limit is about 2.31 inches (9.25 / 4 = 2.3125), and elsewhere about 1.54 inches (9.25 / 6 = 1.5417). The one-third length limit of IRC 2021 Section R502.8.1 is about 2.42 inches on a 2x8 (7.25 / 3 = 2.4167) and about 3.08 inches on a 2x10 (9.25 / 3 = 3.0833). On an overhanging rafter, the 3-1/2 inches IRC 2021 Section R802.7.1.1 asks to remain counts only if your building official reads that rule as covering the birdsmouth, and the 24-inch limit on the overhang still applies. Without that reading, a birdsmouth on an overhanging rafter is not at the end of the member, so hold it to one-sixth of the depth, not one-fourth. A standard 2x4 wall plate is 3.5 inches wide. On a 2x8 rafter at a 6/12 pitch, a full 3.5-inch seat cuts about 1.57 inches deep (3.5 x sin 26.6°). For a rafter that ends at the plate, that passes the 1.81-inch one-fourth depth test (1.57 < 1.81). No full seat passes the length limit, though. A 3.5-inch seat makes a notch at least 3.5 inches long along the rafter, because 3.5 divided by the cosine of any pitch is 3.5 or more. That is over the one-third length limit on every size this page works: about 1.83 inches on a 2x6 (5.5 inches actual, 5.5 / 3 = 1.8333), 2.42 inches on a 2x8 and 3.08 inches on a 2x10. So a full seat is never the cautious choice. If you shorten a seat, keep at least 1-1/2 inches of bearing on the wood plate (IRC 2021 Section R802.6).

The plumb cut of the birdsmouth (the vertical face that sits against the outer edge of the plate) is cut at the same angle as the ridge plumb cut. Together, the seat cut and plumb cut create a clean right-angle notch that locks the rafter onto the plate. The bearing point transfers the rafter load vertically into the wall stud below.

A full 3.5-inch seat cuts deeper into the rafter as the pitch rises: about 0.85 in at 3/12 and 1.94 in at 8/12 (3.5 x sin 14.0° and 3.5 x sin 33.7°). Check notch depth on steep pitches; low pitches barely notch the rafter. On a 2x8 that ends at the plate at 8/12, the full seat cuts past the 1.81-inch one-fourth limit of IRC 2021 Section R502.8.1 (1.94 > 1.81). Shorten that seat to 3.26 inches or less to hold the depth limit alone (1.8125 / sin 33.7° = 1.8125 / 0.5547 = 3.267, rounded down so the notch stays inside the 1.81-inch limit). Length is a separate test. A horizontal seat of s inches makes a notch s / 0.8321 inches long along the bottom edge of the rafter, where 0.8321 is the cosine of the 8/12 angle (cos 33.69° = 0.8321). Held to the 2.42-inch length limit of IRC 2021 Section R502.8.1, a 2x8 seat is about 2.0 inches or less (2.4167 x 0.8321 = 2.011). The 3.26-inch seat above makes a notch about 3.92 inches long (3.26 / 0.8321 = 3.918), so it holds the depth limit but not the length limit. If the rafter runs into an overhang, the full seat leaves 7.25 - 1.94 = 5.31 inches, more than the 3-1/2 inches IRC 2021 Section R802.7.1.1 asks to remain. Only your building official can say whether that rule covers the birdsmouth, and only that reading lets you cut more than the cautious hold. The cautious hold is one-sixth of the depth and one-third of the depth in length. Those are the limits of IRC 2021 Section R502.8.1 for a notch away from the end of the member. Use them whenever you are unsure which case governs. On a 2x8 at 8/12, one-sixth is 1.2083 inches, so a seat of 2.178 inches or less holds the depth (1.2083 / 0.5547 = 2.178, where sin 33.69° = 0.5547). The length limit still holds that seat to about 2.0 inches (2.011 < 2.178). At 6/12, the pitch angle has a sine of 0.4472 and a cosine of 0.8944 (6 / 13.4164 and 12 / 13.4164, where 13.4164 is the square root of 6 x 6 + 12 x 12 = 180). There the depth allows a 2x8 seat of 2.702 inches (1.2083 / 0.4472 = 2.702). The length allows 2.161 inches (2.4167 x 0.8944 = 2.161), so the seat is about 2.16 inches or less. On a 2x10 at 8/12, one-sixth is 1.5417 inches and one-third is 3.0833 inches. The depth allows a seat of 2.779 inches (1.5417 / 0.5547 = 2.779). The length allows 2.566 inches (3.0833 x 0.8321 = 2.566), so the seat is 2.56 inches or less, rounded down. On a 2x10 that ends at the plate, the full seat passes the one-fourth depth test at 8/12 (1.94 < 2.31) but fails the length test, so the same 2.56-inch seat applies. Each of these seats keeps more than the 1-1/2 inches of bearing IRC 2021 Section R802.6 asks for. The one-fourth depth, the one-third length and the 3-1/2-inch remaining rule of IRC 2021 Section R802.7.1.1 do not all read the same way for a birdsmouth. Settle its size with your building official or an engineer before you cut a full set of rafters.

If the roof span is long enough to require structural support at mid-span, consider the shed roof truss calculator for truss configurations that eliminate mid-span bearing walls.

Site-cut rafters and factory-built trusses both frame roofs, but they serve different project types.

Rafters (stick framing) give you full use of the attic space. With no web members filling the triangle, the attic is open for storage, HVAC equipment, or future conversion to living space. Rafters are cut and installed one at a time on site by a framing crew. The trade-off is labour intensity — a skilled crew needs 2-3 days to cut and install rafters for a typical 1,500-square-foot roof, versus a single day for trusses. Rafters also need one of two arrangements: a ridge board with a tie against outward thrust (rafter ties, ceiling joists connected so that they act as ties, or another approved rafter tie method under IRC 2021 Section R802.5.2.2), or a ridge designed as a beam that needs no tie. Collar ties, where used, sit in the upper third of the attic space (IRC R802.5.2 and R802.4.6, in the next section).

Trusses are engineered and manufactured in a factory, then delivered and crane-set in a single day. They span longer distances than rafters of the same lumber size because the web members distribute forces efficiently. A truss can span 30-40 feet without interior bearing walls, where rafters of the same size might need a mid-span support beam. The trade-off is that the web members fill the attic triangle, making it unusable as living or storage space.

For homes where attic access matters (bonus room over garage, future attic conversion, or simply accessible storage), rafters are the right choice despite higher labour cost. For production homes, large commercial roofs, and any project prioritising speed, trusses win on economics. The cost difference varies: trusses typically run $3-$7 per square foot of roof area including installation, while stick-framed rafters run $4-$10 per square foot depending on crew rates and complexity.

When ordering either option, the bundle count tool estimates the shingle quantities once the roof area is known.

Rafters push outward against the walls (a force called thrust). Two of the three framing members below deal with that thrust: rafter ties (or ceiling joists connected to act as ties) hold the walls together, and a ridge beam carries the rafter peaks so that no tie is needed. The third, collar ties, resist wind uplift, not thrust.

Rafter ties connect opposing rafters near the top plate. They act as tension members, preventing the walls from spreading apart under roof load. IRC R802.5.2 (2021 edition) ties the requirement to how the ceiling joists run and prints no slope threshold. Where ceiling joists run parallel to the rafters and sit in the bottom third of the rafter height, the joists are fastened to the rafters as Table R802.5.2(1) sets out (IRC 2021 Section R802.5.2). Where ceiling joists sit above the bottom third, the ridge must be designed as a beam. Where ceiling joists do not run parallel to the rafters, each rafter is tied across the structure with a rafter tie, or the ridge is designed as a beam. That bottom-third rule is printed for the ceiling joists, not for the rafter tie. IRC 2021 Section R802.5.2.2 sets the rafter tie itself: wood rafter ties at least 2x4, spaced no more than 24 inches on centre, with other approved tie methods permitted. The nail count per connection comes from Table R802.5.2(1) in the code your jurisdiction adopts, so confirm it with your building department. With rafters at 16 inches OC, that spacing means a tie at every pair: every second pair would put the ties 32 inches apart (2 x 16 = 32, over 24). At 24 inches OC every pair needs a tie too, while at 12 inches OC every second pair lands at exactly 24 inches (2 x 12 = 24).

Collar ties connect opposing rafters in the upper third of the attic space (IRC R802.4.6). They resist wind uplift forces, not lateral thrust. Collar ties can be lighter (1x4 nominal minimum under IRC R802.4.6; 2x4 is common) and are spaced up to 4 feet on centre rather than at every rafter. They are not substitutes for rafter ties — a roof with collar ties but no rafter ties will still push the walls outward.

Ridge beams eliminate the need for rafter ties entirely by supporting the rafter peaks on a structural beam instead of a non-structural ridge board. A ridge beam is a heavy timber or engineered beam (LVL, PSL) sized to carry the full roof load and transfer it through posts to the foundation. Ridge beams are common in cathedral ceiling designs where rafter ties and collar ties would be visible and unwelcome. The beam size is significant — a 20-foot span at 6/12 pitch with typical residential loading might require a 5.25" x 11.875" LVL.

The choice between rafter ties and a ridge beam is primarily an aesthetic and functional decision. Rafter ties are cheap and effective but fill the attic space. Ridge beams are expensive (the beam alone can cost $500-$2,000) but create clean, open ceiling lines.