Cutting and Setting Rafters

What this calculation does not cover

• This is plane geometry: every side is a straight line on a flat surface. A tape laid down a slope measures the slope and not the plan distance, so a triangle meant for a plan, a plot or a slab needs horizontal measurements — stepped down the slope or taken along a level line — or the figures describe a different triangle from the one being set out.
• A right triangle takes exactly two values. Knowing a third does not make the answer better, it makes a check: solve from the two you trust most and compare the third with what the page returns, because a disagreement is a measuring error somewhere.
• Angles are typed in decimal degrees. A reading in degrees and minutes has to be converted first — thirty degrees and fifteen minutes is 30.25 — and a roof pitch given as a rise per unit of run belongs on the rise and run fields, not in an angle box.
• The lengths are line lengths between points, not cut lengths. A rafter's line runs from the ridge's centre line to the outside of the wall plate; the ridge deduction — half the ridge's thickness, measured square to the ridge — the overhang and the seat cut all come afterwards and are worked on the rafter pages, and a stringer's cutting length depends on how its ends are detailed.
• Small angular errors grow with distance. One degree off over 10 m (33 ft) moves the far end about 175 mm (7 in), so an angle that sets out a long line wants measuring as carefully as the lengths, and a long triangle is better fixed by its three sides than by an angle.
• Values that cannot make a triangle are not repaired. The page returns zero with the reason and the amount by which the figures miss, rather than guessing which of them was meant.

What this calculation does not cover

• The angle is the slope of the plane and carries no height with it. How far the ridge actually stands above the plate comes from the run — half the span on a symmetrical gable — times the rise per foot, so a given pitch puts four times the ridge height over a span four times as wide. Choose a pitch on the angle alone and the ridge can land above a planning height limit, below an existing eaves line, or with an attic room that has no headroom in it.
• Pitch is a load case before it is a geometry. Snow standards hold the full design snow on the roof until the slope passes a threshold — around 30 degrees on a shingled surface that snow will not slide off — and reduce it only above that, while wind on the windward plane swings from suction toward positive pressure as the roof steepens. Changing a pitch is a rafter, tie and hold-down question, not just a change in covering quantity.

What this calculation does not cover

• The run is taken as exactly half the building width, so the length measures to the ridge centreline of a symmetric gable with equal pitch each side and level wall plates. A real common rafter stops at the face of the ridge board, so half the ridge thickness must be deducted along the slope: for a 38 mm ridge at 6/12 that is about 21 mm off every rafter, and the deduction grows with pitch.
• Pitch here is rise per 12 units of run, not an angle in degrees. Entering a measured roof angle produces a far steeper roof than intended — 22.5 read as a ratio is a 61.9 degree roof, whereas a 22.5 degree roof is a pitch of about 5 in 12.
• The overhang input is the horizontal projection past the wall plate, and the calculator multiplies it by the slope factor itself. Entering the sloped length of the tail measured along the rafter overstates the total by that factor again, about 12 per cent at 6/12. The figure also assumes the tail runs to the plumb cut, with no setback for fascia thickness or a soffit return.
• The result is a line length, not a cut list. The plumb cuts, the birdsmouth and the tail are drawn at full size in the rafter cut templates on this page, with every length marked from the heel point. Neither adds anything for saw kerf, waste or rounding up to a stock timber length, and neither tests whether the birdsmouth leaves enough rafter over the wall plate — that limit is the building code's, not this page's.
• Nothing here checks structural adequacy. The calculator never asks for rafter section, timber grade, spacing or load, so it cannot say whether that span works under snow, wind and imposed loads, or whether purlins, struts, collars or a structural ridge beam are needed. Span tables set that limit, and a long run can exceed any common section. The result is one rafter's length, not a rafter count or a timber order.

What this calculation does not cover

• The seat cut length shown is the plate width measured horizontally, which is not the distance to mark along the sloping edge of the rafter. On a 3.5 in plate at 6/12 the notch spans 3.91 in along the rafter's underside, that being the plate width divided by the cosine of the pitch angle, and the page gives neither that layout dimension nor the position of the notch along the rafter.
• Nothing here tests the section of rafter left above the notch, and no rafter depth is asked for. The 1.75 in heel cut on a 3.5 in plate at 6/12 removes 1.57 in measured square to the rafter's edges rather than 1.75 in, so reading the heel cut height straight against a fraction of the rafter depth overstates the notch.
• Roof pitch is taken strictly as rise per 12 units of run and is never converted, even when the plate width is entered in millimetres. Entering 20 for a 20 degree roof returns 5.83 in instead of 1.27 in, over four times the correct heel cut, because 20 in 12 is a 59 degree slope and that value sits inside the accepted 1 to 24 range.
• The geometry is that of a common rafter meeting the plate square. A hip or valley rafter travels 16.97 in in plan for every 12 in of common run, so at 6/12 its heel cut is about 1.24 in rather than 1.75 in, its seat crosses the plate at the corner instead of sitting square across it, and dropping or backing the hip to line up with the jacks alters the seat cut again.
• A circular saw taken to the intersection of the two cuts overruns the inner corner on the far face of the rafter, so the notch as cut is deeper than these two dimensions describe unless the corner is finished with a handsaw. Saw kerf, a crowned or twisted top plate, and sheathing carried up past the plate are all outside the figures, as are the ridge plumb cut, the half ridge thickness deduction and the tail cut.
• Engineered rafters are a separate matter entirely. I-joists and structural composite lumber permit no bird's mouth beyond a manufacturer-detailed seat at the low bearing, with an I-joist flange never notched, so applying this plate width times tangent result to them is not a small error but a prohibited cut.

What this calculation does not cover

• The figure is the theoretical measuring-line length, from the outside corner of the wall plates to the point where the ridge centrelines cross. It deducts nothing for the ridge or the king common rafter the hip butts into, which is half that member's thickness taken on the 45° diagonal, roughly 32 mm off a 45 mm ridge. It also adds no eaves tail, and a hip tail is longer than a common one: a 400 mm horizontal overhang runs about 600 mm along the hip at 6/12, against 450 mm along a common rafter.
• The plumb cut is one angle of a compound one. It is the hip's inclination, arctan((rise/12)/√2) — 19.5° at 6/12 — and it is the setting off a square crosscut; measured against the rafter's top edge the same cut reads as its complement, 70.5°. The cheek bevels are given above and are 45° in PLAN, which is not the angle you set on a saw: the blade figure is arctan(cos θ) taken on the hip's own inclination, 43.3° at 6/12 against the framing square's 43.4°, because the square sets its hip figures out against 17 where the true diagonal is 16.97.
• The backing bevel and the drop above are alternatives, not a sequence: back the top edge to the two roof planes, or leave it square and set the member lower by the drop. Both come from the member thickness entered and nothing else, so a hip of a different thickness needs the figure again. The SEAT is still not produced — it is a compound cut over the corner of two plates rather than the single plumb-and-level birdsmouth of a common rafter, and its geometry depends on how the plates are lapped at that corner, which this page does not ask about.
• The jack figures above are the common difference and the cheek bevel, which is what a set of jacks needs and is not a cut list of them: no jack is counted, none is named, and the first jack's own length depends on where the first spacing falls from the corner, which is a setting-out decision this page does not make. The difference assumes every jack meets the hip at the same 45° in plan and that the spacing is constant — step the spacing anywhere along the run and the arithmetic restarts from that jack.
• No part of this is a structural check. A hip carries the jacks framing into it and a valley collects load from both roof planes, often with a concentrated load where it picks up the minor ridge, so these members are routinely deeper or doubled compared with the commons beside them. The plan run is √2 longer as well, a 4 m (13 ft) common run becoming a 5.66 m (19 ft) diagonal, so common rafter span tables do not apply.