The rafter length calculator above works out the geometry of a pitched roof: how long each common rafter has to be, what the plumb and seat cuts are, how long a hip or valley rafter runs across the corner, and how much shorter each successive jack rafter gets. It handles the two details that trip up hand calculations — the deduction for half the ridge board thickness and the fact that the overhang is specified horizontally but cut along the slope.
This is a preliminary layout and teaching tool from Arb Digital. It gives lengths and angles, not member sizes. Whether a rafter of a given size, species and grade can carry the roof over that span is a structural question answered by span tables and by the code adopted where you are building, and confirmed by a licensed professional. Nothing here should be treated as a design or built from without that check.
What This Rafter Length Calculator Does
It solves the right triangle that every pitched roof is built on, then applies the practical corrections. The horizontal run is half the span minus half the ridge thickness. The pitch, entered as rise per 12, as degrees or as a percent slope, sets the angle. From those two the rafter measuring line follows directly, the overhang is added along the slope, and the plumb and seat cut angles come from the same angle.
It then extends to hip and valley rafters, which travel diagonally across the corner and are therefore longer and shallower than a common rafter of the same roof, and to jack rafters, which run from the plate to the hip and shorten by a fixed step each time. That step, the common difference, is the number a framer actually uses on site: cut one jack, then take the same amount off each subsequent one.
Two live tools sit next to this one and the boundaries are worth stating. Our roof pitch calculator converts between pitch expressions — rise over run, degrees, percent and ratio — and does not produce member lengths. Our roofing calculator works out covering materials, squares, bundles and underlayment for a roof area, and does not deal with framing at all. This page is the framing geometry in between them.
How to Use It
- Enter the span, not the run. Span is the full outside-to-outside width of the building. The tool halves it and applies the ridge deduction itself, which is where hand calculations most often go wrong.
- Set the pitch in whatever form you have it. Rise per 12, degrees or percent all describe the same slope, and the tool converts internally.
- Give the ridge board thickness. A nominal two-by ridge is 1.5 inches thick, so each rafter loses 0.75 inches of run. On a structural ridge beam the deduction is much larger.
- Enter the overhang horizontally. Soffit and fascia dimensions are set out on plan, so the horizontal projection is what drawings give. The tool converts it to the sloping tail length.
- Read the cut angles alongside the length. A correct length with a wrong plumb cut still leaves a gap at the ridge.
The Formula / How It's Calculated
Start with the run: run = span ÷ 2 − ridge thickness ÷ 2. The pitch angle is θ = arctan(rise ÷ 12) when pitch is given as rise per 12. The rafter measuring line is run ÷ cos θ, which is the same thing as run × √(12² + rise²) ÷ 12 — the familiar unit-length-per-foot-of-run that a framing square encodes. The overhang adds horizontal overhang ÷ cos θ along the slope.
Worked example with the loaded defaults. A 24 foot span with a 1.5 inch ridge gives a run of 12 − 0.0625 = 11.9375 feet. At 6/12 the angle is 26.57 degrees and the cosine is 0.8944. The measuring line is 11.9375 ÷ 0.8944 = 13.347 feet. A 12 inch horizontal overhang becomes 1.118 feet along the slope, so the total rafter length is 14.464 feet, which is 14 feet 5 9/16 inches. The rise above the plate is 11.9375 × 0.5 = 5.969 feet.
The hip travels diagonally, so its horizontal run is run × √2 on an equal-pitch roof, and its length is √((run × √2)² + total rise²). Here that is √(16.882² + 5.969²) = 17.906 feet. This is the origin of the framing square rule that hips are laid out on 17 rather than 12: √2 × 12 is 16.97, which carpenters round to 17. The jack rafter common difference is spacing ÷ cos θ, so at 16 inches on centre each jack is 17.89 inches shorter than the last. The plumb cut sits θ degrees off square at 26.57, and the seat cut is its complement at 63.43.
The Ridge Deduction and Why It Is Half
Two rafters meet a ridge board from opposite sides. The board occupies its full thickness between them, so each rafter gives up half of it. Skip the deduction and both rafters are too long by 0.75 inches on a nominal two-by ridge, which pushes the ridge up and spreads the walls. Over a whole roof that error is consistent, so it does not look like a mistake — the roof simply ends up a little wider and a little taller than drawn, with the plumb cuts not quite bearing.
Structural ridge beams change the arithmetic materially. A 5.25 inch engineered ridge beam removes 2.625 inches of run from every rafter, more than three times the two-by case. And where rafters are hung from the side of a ridge beam on hangers rather than bearing against it, the geometry changes again, because the seat of the hanger sets the height rather than the plumb cut. Check what the drawing actually shows before assuming a 1.5 inch ridge.
Hip and Valley Rafters Are a Different Roof
A hip rafter runs at 45 degrees in plan on a square-cornered equal-pitch roof, which means its horizontal run for a given rise is longer by a factor of √2. The consequence is that its slope angle is shallower than the common rafter's even though it reaches the same ridge height. For a 6/12 common roof, the hip sits at about 19.5 degrees, not 26.57. Cutting a hip with common-rafter angles is a classic and expensive error.
Two further hip details matter. The plumb cut at the top of a hip is a double cheek cut, mitred on both faces so the hip nests between the two common rafters at the corner — the tool gives the plumb angle but the cheek angles depend on how the corner is framed. And the hip needs a backing bevel, a shallow chamfer along its top edge, if the sheathing is to lie flat across it; without backing, the hip's top corners sit proud and the sheathing rocks. Some framers drop the hip instead, setting it slightly lower so its corners fall below the plane.
Valley rafters follow the same geometry as hips but in reverse, running down into the internal corner where two roof planes meet. The lengths this tool gives apply to both.
Jack Rafters and the Common Difference
Jack rafters fill between the plate and the hip. Each one has a shorter run than its neighbour by exactly the rafter spacing, so its length is shorter by the spacing divided by the cosine of the pitch angle. That constant step is why jacks are cut in a run rather than measured individually: cut the longest, then take the common difference off each successive one.
The step for 16 inch spacing at 6/12 is 17.89 inches, at 24 inch spacing it is 26.83 inches, and at 12 inch spacing it is 13.42 inches. Each jack also needs a single cheek cut where it meets the hip, normally at 45 degrees for an equal-pitch square corner. Unequal-pitch roofs break that 45 degree convenience entirely and need a different treatment, which is beyond a general calculator.
What Sets the Rafter Size, and What Does Not
Nothing on this page selects a member. Rafter depth depends on the span, the spacing, the species and grade of the timber, the dead load of the roof covering, the live or snow load, the deflection limit applied and whether there are ceiling loads or collar ties. Prescriptive span tables handle the common cases, and they are published through the American Wood Council resource hub alongside the National Design Specification for Wood Construction, the ANSI-approved standard those tables derive from. The requirements themselves sit in the building code adopted by your jurisdiction, and local amendments differ by state, province and country.
The load side has its own tools. Our snow load calculator covers the design snow load a roof has to carry, and the wood beam span calculator deals with beams rather than rafters. For a plain geometric check on any right triangle in the roof, the Pythagorean theorem calculator does the arithmetic without the framing conventions. A roof also has to resist wind uplift and, in some regions, seismic demand, and the connections at the plate are frequently what governs — that is a design matter, not a length.
Arb Digital builds free calculators and interactive tools that earn search traffic for roofing, carpentry and construction businesses. Browse the full library, or tell us what your customers keep asking you to work out.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Forgetting the ridge deduction — each rafter loses half the ridge thickness, and skipping it spreads the walls and lifts the ridge.
- Treating the overhang as a sloping length — drawings give the horizontal projection, and the tail along the rafter is always longer.
- Cutting a hip at the common rafter angle — the hip runs diagonally, so it is longer and shallower, and it needs cheek cuts and backing that a common rafter does not.
- Buying stock at the calculated length — the plumb cut, the tail and the birdsmouth all need material beyond the measuring line, so order the next length up.
- Reading a length as a design — geometry says how long, span tables and code say how deep, and the two are different questions.
Related Free Tools From Arb Digital
Pair this with the roof pitch calculator for converting slope expressions, the roofing calculator for covering materials, the snow load calculator for design snow load, the wood beam span calculator for supporting beams and the Pythagorean theorem calculator for plain right-triangle work. The full free online tools hub lists every calculator we publish.
Frequently Asked Questions
With a 1.5 inch ridge the run is 11.9375 feet, so the measuring line is 13.347 feet. Adding a 12 inch horizontal overhang gives a total rafter length of 14.464 feet, about 14 feet 5 and 9/16 inches.
Because two rafters meet the ridge board from opposite sides and the board sits between them. Each rafter therefore gives up half its thickness. Skipping the deduction makes both rafters too long and pushes the ridge up.
A hip runs at 45 degrees in plan, so its horizontal run is the square root of two times the common run. Twelve times the square root of two is 16.97, which framers round to 17 on a framing square.
It is the rafter spacing divided by the cosine of the pitch angle. At 16 inches on centre and 6/12 pitch it is 17.89 inches, so each jack is that much shorter than the previous one.
The pitch angle itself, measured from a square cut. At 6/12 that is 26.57 degrees. The seat cut of the birdsmouth is the complement, 63.43 degrees, which is beyond most mitre saws and is normally cut with a circular saw and a handsaw.
No. Depth, species and grade come from span tables and the building code adopted where you build, and depend on loads, spacing and deflection limits. A licensed professional must confirm the structure.
A shallow chamfer along the top edge of the hip so the sheathing from both roof planes lies flat across it. Without it the hip's top corners sit proud of the roof plane. Some framers drop the hip slightly instead.
No. Order the next standard length up. The plumb cut, the birdsmouth and the tail all consume material beyond the measuring line, and cutting to exact length leaves nothing for error.
This tool gives roof geometry for layout and planning only. It is not a structural design, it is not stamped, and rafter sizing must be confirmed against span tables and local code by a licensed professional.
