Dormer Calculator
A gambrel roof has two different pitches, so the same dormer behaves differently depending which slope it is cut into. This calculator prices that difference in two numbers: the structural rise a dormer of a given width costs, and the standing-height floor width it actually gains.
Cross-section with the dormer
Main roof Dormer box
| For a 4 ft dormer | Lower slope (60°) | Upper slope (25°) |
|---|---|---|
| Rise the dormer must climb | 6.9 ft | 1.9 ft |
| Width gained per foot of rise | 0.58 ft | 2.14 ft |
| Usable floor width actually gained | 1.5 ft | 0.0 ft |
| Widest dormer this run allows | 6.0 ft | 6.0 ft |
A 4.0 ft dormer costs 6.9 ft of rise on the 60° lower slope versus 1.9 ft on the 25° upper slope — the upper slope needs about 3.7× less structure for the same width.
Upper slope vs. lower slope: which one actually gains you more
The intuitive story about gambrel dormers is that the shallow upper slope is the better place to cut one, because its ceiling line "rises slowly" and so a dormer there should recover more usable width per foot of dormer width. That story does not survive contact with the actual geometry, and it is worth showing why rather than repeating it, because the real answer changes where you should put the dormer.
Roof height increases continuously from the eave up to the ridge. That means the stretch of roof immediately below the knuckle — the top of the lower slope — is, by definition, never taller than the stretch immediately above the knuckle — the bottom of the upper slope. If a section of roof is below your standing-height threshold, the lower-slope side of the knuckle is always at least as likely to be below it as the upper-slope side, usually more so. At this page's default 24 ft span, 60°/25° pitches, 50% knuckle and 6 ft threshold, a 4 ft-wide dormer tied to the knuckle recovers about 1.5 ft of new floor width on the lower slope — and 0.0 ft on the upper slope, because the knuckle there is already 10.4 ft up, well past the 6 ft line, so that whole stretch of upper roof was already walkable before any dormer was cut into it.
What is true, and stays true regardless of where your particular roof's standing-height line happens to fall, is the cost side: a dormer of a given width always costs less vertical rise on the shallower upper slope than on the steeper lower slope, in a fixed ratio of tan(θ) / tan(φ) — about 3.7× at the default pitches here. If you have already used the attic space calculator and found your lower slope already clears your headroom threshold on its own, the upper slope's cheaper structure is where a dormer earns its keep instead.
The two numbers, and the formulas behind them
The calculator above tracks two genuinely different questions, and keeps them separate rather than folding them into one "headroom gained" figure.
Structural rise (slope-intrinsic — always true)
rise = dormerWidth · tan(pitch)
efficiency = 1 / tan(pitch) (width gained per foot of rise)
pitch is θ on the lower slope or φ on the upper slope. Because θ > φ always, rise is always smaller and efficiency always larger on the upper slope, for any dormer width.
Usable width actually gained (configuration-specific)
lower slope: gain = wd − clamp(x1 − h/tan(θ), 0, wd)
upper slope: gain = clamp((h − y1)/tan(φ), 0, wd)
h is the standing-height threshold, x1 and y1 the knuckle's run and height. Both formulas clamp to zero once that stretch of roof was already tall enough without a dormer.
The rise/efficiency ratio depends only on the two pitch angles — not on dormer width — which is why doubling the dormer's width does not change which slope is structurally cheaper, only how much of that cheaper structure you are buying.
Rise required by pitch pair, at a fixed 4 ft dormer width
The steeper the lower pitch and the shallower the upper pitch, the bigger the structural gap between the two placements gets. Every row here uses the same 4 ft dormer width so only the pitch pair changes.
| Pitch pair (θ/φ) | Rise, lower slope | Rise, upper slope | Efficiency, upper slope | Upper is …× cheaper |
|---|---|---|---|---|
| 60° / 25° | 6.9 ft | 1.9 ft | 2.14 ft/ft | 3.7× |
| 55° / 20° | 5.7 ft | 1.5 ft | 2.75 ft/ft | 3.9× |
| 50° / 15° | 4.8 ft | 1.1 ft | 3.73 ft/ft | 4.4× |
| 45° / 10° | 4.0 ft | 0.7 ft | 5.67 ft/ft | 5.7× |
A flatter pitch pair (45°/10°) still favours the upper slope structurally, but by a smaller margin than a steep barn-style pair (60°/25°) — the wider the gap between the two pitches, the more the upper slope's cost advantage grows.
Placing a dormer against the knuckle line
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Run your attic space numbers first
Use the attic space calculator to find your existing standing-height floor width before adding a dormer to the picture.
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Find which side of the knuckle is short
If the knuckle height already clears your threshold, the lower slope near the eave is where the shortfall is — that is where a dormer recovers real new width.
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Tie the dormer's inner wall to the knuckle
Placing the dormer so its header lines up with the knuckle keeps the roof-plane transition to one line instead of two, which simplifies flashing.
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Check the rise against the available run
Confirm the required rise fits comfortably within the slope's own rafter run — the calculator's "widest dormer this run allows" row is the hard ceiling.
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Size it, then hand it to a framer
Once width and rise are settled, the header, jack rafters and valley framing are a structural detail — see the framing guide for the sequence a dormer has to tie into.
Practical limits
What this calculator does not tell you
Header and jack rafters
A dormer opening needs a header sized for the rafters it interrupts, and jack rafters carrying load around it. That sizing is a structural calculation, not a headroom one.
Valleys catch drift
Every dormer creates two small valleys where its roof meets the main slope, and valleys accumulate snow faster than an open plane. Check the snow load calculator before finalizing width in a snowy region.
The knuckle tie-in is the hard part
Tying a dormer's cheek flashing into an existing knuckle line is a genuine detail to get right — get it wrong and the knuckle, already a load-path concern, becomes a leak path too.
Related tools
Dormer Questions
Does a dormer on the upper slope always gain more usable width than one on the lower slope?
No — that is the intuitive assumption, and it does not hold up numerically. Because roof height rises continuously from eave to ridge, the stretch of roof just below the knuckle is always at least as far below any given standing-height line as the stretch just above it. Run the calculator above at the default 60°/25° pitches and a 6 ft threshold: a 4 ft dormer recovers about 1.5 ft of new floor width on the lower slope and 0 ft on the upper slope, because the upper slope there is already taller than 6 ft without any dormer at all. What is genuinely true, and slope-independent, is the structural cost side below.
So what is actually cheaper about an upper-slope dormer?
The rise, not the width gained. A dormer of a given width costs vertical rise equal to width × tan(pitch), and the upper pitch is always shallower than the lower one on a gambrel, so the same width always costs less climb, less cheek-wall height and less roof penetration on the upper slope. At 60° and 25°, that ratio is tan(60°) / tan(25°) ≈ 3.7× — independent of how wide the dormer is. Whether that cheaper structure is also gaining you new floor space depends on where your roof's own standing-height line already falls, which is why the calculator shows both numbers rather than one.
Where should a dormer sit relative to the knuckle line?
Tied to it, not floating in the middle of a slope. A dormer built with its inner wall at the knuckle ties its header into the one place the roof already changes plane, which keeps the flashing detail to a single transition instead of two. Cut into the lower slope, it runs from the knuckle out toward the eave; cut into the upper slope, it runs from the knuckle up toward the ridge. Either way, keep it well inside the rafter run available on that slope (the calculator reports the widest dormer each run allows) so full-length jack rafters remain on both sides of the opening.
Is this a substitute for a structural dormer design?
No. This is a planning estimate for headroom and rise only — it says nothing about header beam sizing, jack-rafter spacing, valley framing, or the roof-to-wall flashing detail, all of which need an engineer or a framer's layout once you have settled on a width and location. See the framing guide for the raising sequence a dormer has to tie into.
Do dormers create snow problems on a gambrel roof?
They can, because a dormer interrupts a continuous roof plane and creates two small valleys where its own roof meets the main slope. Valleys collect drifting snow at a higher rate than the open field of a plane, and on a gambrel that valley usually lands close to the knuckle, which is already a load-path detail worth checking. Work through the drift cases on the snow load calculator before finalizing a dormer's width and position in a snowy climate.