Four numbers decide the whole shaft
A skylight over a cathedral ceiling is a hole with a trim ring. A skylight over an attic is a shaft, and the shaft is most of the work. What sets its shape is the roof opening, the pitch, how deep the attic is below that point, and the splay angles you choose for the four walls. Everything else follows from those.
The pitch does something people miss. The roof opening is measured up the slope, but the shaft rises vertically, so the plan length of the opening is shorter than the opening itself. A 46.5 inch opening on a 6/12 roof projects to about 41.6 inches in plan, and the high edge of the opening sits about 20.8 inches above the low edge. That means the two ends of the shaft are different heights before you have splayed anything: 36 inches at the low wall becomes about 56.8 inches at the high one.
What the splay buys
A plumb shaft delivers a ceiling opening exactly the plan size of the roof opening. Flaring the walls makes the opening larger at the bottom, and it does two useful things: it spreads the light further into the room rather than dropping it in a rectangle, and it takes the hard edge off the boundary between the lit patch and the rest of the ceiling.
The gain is straightforward trigonometry — the wall moves out by the shaft height times the tangent of the splay angle — and the leverage is uneven. The low wall is short, so 30 degrees there gains about 20.8 inches. The high wall is tall, so even a small angle there moves a lot, which is exactly why it is often left plumb: flaring the high wall throws light back up the slope toward the wall it is already nearest. Splaying the sides is the cheapest gain of the three, because there are two of them and they run the full length.
Running the defaults through: 41.6 inches of plan length plus 20.8 from the low wall gives a 62.4 inch opening, and 22.5 inches of width plus 15 degrees on each side wall over an average height of 46.4 inches gives about 47.4 inches. That is 20.5 square feet at the ceiling from 7.3 square feet of roof opening — nearly three times the area.
The finish is all bevels
Every splayed wall meets its neighbours at a compound angle, and the four walls are all different: two different heights at the ends, two identical sides, no two corners the same. Board cut for the low wall does not fit the high wall, and an offcut from one side is the wrong hand for the other. Fifteen percent waste on the shaft finish is a floor, not a cushion, and the corners are the part that takes the time.
The shaft area figure here averages the top and bottom width of each face, which is honest for the flat-ish walls and slightly approximate for the warped ones, and it is close enough to order board and insulation from. What it does not include is the framing of the shaft itself, the insulation in the shaft walls, or the air sealing where the shaft meets the ceiling plane, and that last one matters more than its size suggests: a shaft is a chimney reaching from a heated room to a cold attic, and any gap around it leaks warm humid air directly to the sheathing. The condensation side of that thinking is on the wall condensation risk organizer.
Before the saw comes out
Two questions come first and neither is on this page. Does the opening cross framing, and what is that framing. The calculator flags whether the width fits between two members at your spacing, and if it does not, the work becomes framing rather than finishing — headers, trimmers and cripples, counted on the roof opening framing take-off. Whether those members may be cut and what has to carry the load afterwards is a span and structure question for the building department and an engineer. If the roof is trussed, the answer is simpler and firmer: a truss is an engineered assembly and cutting one is not a field decision.
The second is the flashing. A skylight is the single most demanding penetration on a roof, sitting in the path of everything running down the slope above it, and the flashing kit for the unit is the only detail that matters. That is manufacturer instruction territory. The other penetrations on the same roof are counted on the roof penetration flashing take-off, and the glazing-to-floor question for the room as a whole, counting the windows in the walls as well, is on the window glass area and daylight ratio calculator.
Questions people ask
Why is the ceiling opening so much bigger than the roof opening?
Two effects, and they pull against each other. The splay is the one doing the work: each wall moves outward by the shaft height times the tangent of its angle, and with a deep attic that height is large, so even modest angles move a wall a long way. Working the other direction is the projection, because the roof opening sits on a slope while the ceiling opening is a plan rectangle — 7.27 square feet of opening on a 6/12 roof projects to only 6.5 square feet before anything is splayed at all. On the defaults here the ceiling opening comes out at 20.5 square feet, 2.8 times the roof opening, and all of that gain comes from the four splayed walls rather than from the geometry.
Should I splay all four walls?
It depends on what you want the light to do, and there is no single answer. Splaying the low wall throws light further into the room and is the most common single choice. Splaying the sides widens the lit patch and is cheap because both sides gain at once. Splaying the high wall pushes light back toward the wall the skylight is already nearest, which is usually the least useful direction, and it makes the tallest wall taller in slant length, so it costs the most to build. Many shafts are built with the high wall plumb for exactly that reason.
How do I measure the attic depth at the opening?
From inside the attic, drop a plumb line or a tape from the underside of the deck at the downslope edge of where the opening will be, down to the top of the ceiling framing, and add the thickness of the ceiling finish. Do it at the actual location, not near the hatch, because the depth changes across the attic at the rate of the pitch. If there is a duct, a chimney chase or a brace in the way, that is worth discovering now rather than after the roof is open.
Does a tubular daylight device need this calculation?
Not this one. A tube is a fixed diameter from the roof to the ceiling with no splay and no framed well, and its whole point is that it passes between framing members without touching them, so there is no shaft geometry to compute and usually no rafter to cut. What it shares with a skylight is the roof penetration and the flashing, and the diameter and maximum tube length are product specifications. Use this page for a framed shaft with a finished well.
What is the rafter interruption line telling me?
Whether your roof opening width fits in the clear space between two framing members at the spacing you entered. It adds one member thickness to the opening width, divides by the spacing and rounds up, which gives the number of bays the opening spans, then subtracts one to get the members inside it. Zero means the unit drops into an existing bay and no structure is touched. One or more means members are being cut, and at that point the page stops being useful on its own and the question moves to the framing take-off, a span table, and whoever has authority over the work.