A rafter is a hypotenuse pretending to be a piece of timber. Its length is not the span, not the span plus a bit for luck — it is the square root of run² + rise² over half the building’s width, stretched by whatever overhang the eaves need. This rafter calculator does that geometry properly: enter the span and the pitch (as rise-over-run or as an angle), add the horizontal overhang and the spacing, and it returns the true rafter length with and without overhang, the total rise, the pitch angle and the number of rafter pairs along the building. Everything in one unit — feet or metres — as long as every input uses the same one.
The geometry, once and for all
On a symmetrical gable roof each rafter climbs from the wall plate to the ridge over exactly half the span. That half-span is the run. Multiply it by the pitch ratio (rise ÷ run) and you have the rise; Pythagoras turns the pair into the slope length. Check it against the oldest triangle in the world: a span of 8 with a 3-in-4 pitch gives a run of 4 and a rise of 3, and the rafter is exactly 5 — the 3-4-5 triangle every carpenter knows. Overhang is where estimates usually go wrong: an eaves overhang is a horizontal projection, so it extends the run, and the rise grows with it at the same pitch. Adding 0.5 of overhang to that same roof stretches run to 4.5 and rise to 3.375, and the rafter becomes √(4.5² + 3.375²) = 5.625 — not 5 + 0.5.
The imperial example in the tool
The calculator opens with a 24 ft span at the common 6/12 pitch: run 12 ft, rise 6 ft, rafter √(144 + 36) = 13.42 ft before overhang. With 1 ft of horizontal overhang the run becomes 13 ft and the rise 6.5 ft, giving √(169 + 42.25) = 14.53 ft of rafter, at a pitch angle of 26.6°. Spaced at 2 ft along a 40 ft building that is floor(40 ÷ 2) + 1 = 21 pairs — 42 rafters. Order the next standard length above 14.53 ft; a rafter bought at exactly the line length leaves nothing for the cuts at either end.
The birdsmouth note — read before cutting
The lengths here are line lengths: the theoretical slope from ridge centre to the outside of the wall plate. Real layout adjusts them in three places. First, each rafter meets the ridge board, not the ridge line — deduct half the ridge board’s thickness at the top (measured along the slope). Second, the plumb cut at the tail and the seat cut of the birdsmouth consume stock beyond the line. Third, the birdsmouth itself: the horizontal seat cut where the rafter sits on the plate must not notch away more than about a third of the rafter’s depth, or the heel becomes the weak point of the roof — the notch transfers the load; it does not need to be deep to do it. Lay out one rafter as a pattern, test-fit it, then batch-cut from it.
What the count assumes, and what the tool is not
The pair count assumes a plain gable: pairs evenly spaced, one at each gable end. Hips, valleys, dormers and jack rafters are additional pieces this count does not include — count them from the roof plan. And this is a geometry tool, not a structural one: rafter size, grade and maximum span for your loads and snow are a span-table or engineering question. What it settles exactly is how long each common rafter is and how many the building takes — the two numbers the timber order is written from. If your roof’s beam count by spacing is all you need (slope length already known), our Spanish companion counts beams that way instead.
Related tools
Versión en español: Calculadora de Cabios para Techo a Dos Aguas: Longitud según la Pendiente, con Alero y Cantidad de Pares · Concrete Volume Calculator.
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