Four ways to figure a rafter by hand — Pythagoras, the pitch multiplier, a framing square and a speed square — with one roof worked end to end so you can check your own numbers against it.
Every method in this guide — pencil-and-paper or stamped in steel — is doing the same job: finding the long side of a right triangle. Get the two short sides right and the rafter length follows, whichever method you use to get there. Measure the building first, and write the six numbers down before any maths starts.
The one that trips people up is the run. A common rafter only crosses half the building, from the wall plate up to the ridge, so the run is half the span. Work with the full span by mistake and the 'rafter' you calculate will overshoot the ridge and come out nearly twice as long on the slope. Halve first, always.
This is the method underneath all the others, and the one to fall back on when a roof does not fit a table. A rafter, its run and its rise form a right triangle, so the rafter length is the hypotenuse: length = √(run² + rise²). Any calculator — including a phone — does it in seconds, and it works for any pitch, including the fractional ones no chart prints.
Take a 24 ft span at 6/12. The run is 12 ft, the rise over that run is 6 ft, and the square root of 180 is 13.416 ft — a line length of 13 ft 5 in. Hold on to the phrase line length: it is the distance from the wall plate to the ridge centreline along the top of the board, and it is not yet the length you cut. The worked example at the end of this guide turns it into one.
Because the pitch fixes the triangle's shape, the rafter is always the same multiple of the run. That multiple is √(1 + (pitch ÷ 12)²), and framers call it the pitch multiplier. Once you have it, rafter length is a single multiplication, which is why it is the fastest pencil method on site and the one every printed chart is built from.
The multiplier has a second virtue: it works in any unit and at any scale. A run of 3.6 m at 6/12 needs 3.6 × 1.118 = 4.02 m of rafter, and the overhang tail of any roof is just the flat overhang multiplied by the same number. Learn the multipliers for the pitches you build most — 4/12 is 1.054, 6/12 is 1.118, 8/12 is 1.202, 12/12 is 1.414 — and most line lengths become mental arithmetic. If you would rather not multiply at all, the free rafter calculator on the homepage runs this exact method with the ridge and overhang adjustments included.
Every multiplier used above is printed in the rafter length chart, with the line length for standard runs already multiplied out.
A framing square is a calculator you can drop off a roof. Stamped into the face of the blade is a rafter table: under each inch mark — which stands for the unit rise — sits the length of a common rafter per foot of run for that pitch. It is the pitch multiplier again, expressed in inches (13.42 in per foot at 6/12 is 1.118 × 12), printed a century before electronic calculators existed.
The square also lays the rafter out full-size. With the tongue set to the unit rise and the blade to 12, the tongue's edge draws the plumb cut and the blade's edge draws the seat cut. Stepping the square along the board once for each foot of run transfers the geometry to the timber without a single number being written down — slow by calculator standards, but self-checking, because a stepping error shows up as a step that does not land cleanly.
A speed square will not give you a length, and it is a mistake to ask it to. What it gives you, faster than anything else on the belt, is the two cut angles at the ends of the rafter. Lengths come from the triangle; angles come from the square.
The geometry is worth understanding once. At a pitch angle of 26.6° (6/12), the seat cut — the flat cut that sits on the wall plate — runs at 26.6° to the top edge of the board, and the plumb cut at the ridge runs at 63.4° to the same edge. If you know either angle you know both, because they are complements. The same relationship is why a circular saw set to the pitch angle cuts a correct plumb line when the board lies flat.
Here is the whole job in one place: a 24 ft span, a 6/12 pitch, a 12 in overhang and a standard 1½ in ridge board. Follow the five steps and check each one against the cards below — this is the same roof used as the example across the site, so the chart and the calculators will confirm every figure.
Notice what the two adjustments do. The overhang adds more than 12 in, because the tail runs downhill at the pitch angle. The ridge takes off less than the full board thickness, because only half of it belongs to this rafter — the other half belongs to the rafter rising from the other side. Both adjustments are converted with the same 1.118 multiplier, because both are measured flat and cut on the slope.
√(12² + 6²) = 13.416 ft along the top edge, plate to ridge centreline.
12 in of flat overhang, converted to the slope: 12 × 1.118 = 13.42 in.
Half the 1½ in ridge (¾ in), converted to the slope: 0.75 × 1.118 = 0.84 in.
Line 160.997 in + tail 13.42 in − ridge 0.84 in, carried unrounded. This is the board length you mark and cut.
Most wrong rafters are not wrong by much — they are wrong by one small, repeatable misunderstanding, applied identically to thirty boards. These are the six that account for nearly all of them:
Every result on this page comes from the method described above, using standard framing geometry and the published data credited below. Found a number that looks wrong? Use Report an Error — every report is read.
No — pitch alone only fixes the shape of the triangle. You also need the run, which comes from the building: halve the span. Two roofs can both be 6/12 and need rafters of completely different lengths.
Convert it: pitch = 12 × tan(angle). A 30° roof works out to 12 × 0.577 = 6.9/12, which most framers treat as 7/12. A 45° roof is exactly 12/12.
From inside the attic or off a ladder, hold a 12 in level run against the underside of a rafter and measure the vertical rise from the level's end to the rafter — that rise over 12 in is the pitch. A speed square laid on the rafter reads the same thing on its common scale.
It does not change the total length of the board. The birdsmouth is a notch cut into the rafter at the point where the line length crosses the wall plate, so it is located from the ridge end of the line length. What it does fix is the HAP — the height of rafter left standing above the plate — and the notch must never remove more than a quarter of the board's depth.
About 20 ft of finished cut length — line length plus tail, minus ridge deduction. Solid-sawn stock is commonly sold up to 20 ft, and long straight boards over 16 ft are often special-order. Past that, the usual answers are a splice detail, engineered lumber, or a design with a structural ridge or purlins that shortens each rafter's run.
Almost — the same three methods work, but the unit run changes. A hip rafter crosses a 45° plan angle, so its unit run is 16.97 in (12√2) instead of 12 in, and the framing square's hip scale is built on that number. The dedicated hip calculator handles the cheek cuts and deductions as well.
The full common rafter: length, angles, birdsmouth and materials.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
Where two roof planes meet — valley length and its cut angles.
First jack length and the common difference for your spacing.
Single-slope rafters between two different wall heights.
Seat cut, heel height and HAP, checked against the IRC one-quarter limit.
Plumb, seat and cheek angles — plus the saw settings to cut them.
Convert pitch, rise/run, degrees and percent, both ways.
How far a board can span — IRC tables by species, grade and load.
The lumber size a span actually needs. The inverse of the span tool.
Two pitches, one roof — upper and lower rafter lengths.
The full pitch × run table, printable for the workshop wall.