Barn Roof Calculator
- Lower rafter R₁
- 12.00 ft 12′ 0″ · 60.0° · 20.8:12
- Upper rafter R₂
- 6.21 ft 6′ 2 9/16″ · 15.0° · 3.2:12
- Total height H
- 12.00 ft 12′ 0″ above the wall plate · = W ÷ 2
- Total roof area
- 1,455.2 ft² both slopes, 1.00 ft eave overhang
- Loft volume
- 7,081 ft³ 196.7 ft² cross-section
- Loft clearance at 6 ft working height
- 17.07 ft usable hay-loft floor width, 6 ft clear
Rafter lengths are measured along the top edge of the rafter, wall plate to knuckle (R₁) and knuckle to ridge (R₂), before birdsmouth or ridge-plumb-cut deductions. Loft clearance is the floor width where the underside of the roof is at least 6 ft above the loft floor — the practical figure for hay storage and moving around upright, not a code headroom minimum.
Why Barns Use a 60°–67.5° Lower Pitch
A barn roof is a gambrel built for one job above all others: hold as much usable loft volume as possible over a given footprint. Everything about the traditional 60°–67.5° lower-pitch range follows from that one requirement.
On the main gambrel calculator a 24 ft span held to 12 ft of height already shows the gap: a gambrel encloses about 197 ft² of cross-section against 144 ft² for a gable of the same span and height, and it offers 6 ft of standing clearance across 17.1 ft of floor against the gable's 12.0 ft. A barn pushes that gap further on purpose, because a hay loft with a wedge-shaped ceiling is a loft you can only half-fill.
The lower rafter does the actual work here. Every degree added to the lower pitch θ keeps the roof surface closer to vertical for longer before it breaks at the knuckle, which is exactly what widens the loft floor at working height. On a 30 ft barn held to the half-circle method, loft clearance runs from 21.6 ft at a 55° lower pitch up to 26.78 ft at 75°, while the total height never moves off 15.0 ft — see the pitch comparison further down this page for the full spread.
The other half of the reasoning is entirely practical: a hay door needs a real wall behind it. A door and its track have to mount on something close to vertical, at height, without eating into the loft floor directly beneath — which is precisely the wall a steep lower slope provides and a shallow gable does not. Traditional barn framing put the door at the knuckle line for exactly that reason, and the two-pitch shape that makes room for a hay door is the same shape that made two short rafters easier to raise by hand than one long one: a 30 ft barn needs members of about 15.0 ft and 7.76 ft rather than a single rafter run the full half-span.
Reference
Common Barn Footprints, Solved at 60°/15°
Every row below uses the modern 60° lower pitch / 15° upper pitch pairing, 1 ft of eave overhang, and the half-circle method, so height always lands at exactly half the width. Loft clearance is the floor width with 6 ft of headroom — the number that decides how much of the loft is actually storable rather than just enclosed.
| Footprint (W × L) | Lower rafter R₁ | Upper rafter R₂ | Height H | Roof area | Loft clearance |
|---|---|---|---|---|---|
| 20 ft × 30 ft | 10.00 ft | 5.18 ft | 10.00 ft | 1,030.6 ft² | 13.07 ft |
| 24 ft × 36 ft | 12.00 ft | 6.21 ft | 12.00 ft | 1,455.2 ft² | 17.07 ft |
| 30 ft × 40 ft | 15.00 ft | 7.76 ft | 15.00 ft | 1,981.2 ft² | 23.07 ft |
| 36 ft × 48 ft | 18.00 ft | 9.32 ft | 18.00 ft | 2,814.5 ft² | 29.07 ft |
| 40 ft × 60 ft | 20.00 ft | 10.35 ft | 20.00 ft | 3,882.3 ft² | 33.07 ft |
Two patterns are worth reading straight off the table. Height tracks width exactly — it is always half the span under the half-circle method, so a 40 ft barn stands 20.0 ft to the ridge no matter which of the traditional pitch pairings frames it. And loft clearance grows faster than width alone would suggest, because a wider barn also has a longer lower rafter reaching further out before the knuckle. Plug your own footprint into the calculator above for figures that fall between these rows, or for the traditional 67.5°/22.5° pairing.
Hay Door Placement and Loft Floor Framing
A barn loft is only as useful as what can get in and out of it. These five decisions cover the framing specific to a working hay loft — beyond the truss and knuckle details common to every gambrel, which are covered on the framing guide.
Set the door under the knuckle line
Centre the opening on the gable end wall at the height where the knuckle sits — the point where the loft floor is widest close to the wall, so whatever comes through lands where there is room to stack it.
Size it for the track hardware
A hay door usually carries a track or hoist beam above the opening, not just a door slab. Size the header for that load and run jack studs down to the sill, the same logic as any wall opening with heavier hardware hanging off it.
Block across the opening
The purlin running the knuckle line ties every truss to its neighbours. Where a hay door interrupts it, add solid blocking across the gap so the trusses either side stay tied together instead of each fending for itself.
Run them off the collar ties
The collar tie that stops the knuckles spreading apart doubles as the loft floor joist in a working barn. Check it against the storage load you actually plan to put in the loft, not just the roof load it was sized for structurally.
Deck the floor before you sheath
It is far easier to lay loft decking with the trusses open overhead than to thread sheets up through a finished roof later. Floor first, then sheathe and flash the door opening in the same pass as the rest of the roof.
How to Calculate a Barn Roof
A barn built to the half-circle method uses the same construction as the main calculator's half-circle tab: the eave, the knuckle and the ridge all sit on one semicircle of radius r = W ÷ 2, which is what locks the upper pitch at θ − 45° and the height at exactly r. Work through it in this order:
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Pick a footprint
Choose one of the common barn footprints (20 × 30, 24 × 36, 30 × 40, 36 × 48, 40 × 60) or type your own width and length. The width is the roof span — the number every other figure is built from.
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Choose the pitch pairing
Use the half-circle method: pick a lower pitch θ between 46° and 84°, and the upper pitch φ locks automatically at θ − 45°. The two traditional barn pairings are 60°/15° and 67.5°/22.5°.
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Read the rafter lengths
R₁ (lower rafter, wall plate to knuckle) and R₂ (upper rafter, knuckle to ridge) are solved as R₁ = 2r·sin(u/2) and R₂ = 2r·sin((90° − u)/2), where r = W ÷ 2 and u = 2 × (90° − θ).
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Check the total height
Under the half-circle method, height is always H = W ÷ 2, no matter which pitch you pick within the method. A 30 ft barn stands 15.0 ft to the ridge whether it is framed at 55° or 75°.
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Read the loft clearance
The calculator reports the usable hay-loft floor width where the underside of the roof clears 6 ft — the practical figure for storage and moving around upright, separate from raw attic volume.
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Add the overhang and total the roof area
Divide the horizontal eave overhang by cos θ for its sloped length, add it to R₁, then roof area = 2 × (R₁ + R₂ + sloped overhang) × building length, counting both slopes.
Written out as formulas, that procedure is:
Working formulas
r = W ÷ 2
u = 2 × (90° − θ)
R₁ = 2r × sin(u ÷ 2)
R₂ = 2r × sin((90° − u) ÷ 2)
H = r
u is the central angle from the eave to the knuckle. Solve it from your chosen lower pitch θ, then both rafter lengths and the total height fall straight out — nothing else needs choosing.
At the traditional 67.5°/22.5° pairing, u lands at exactly 45° — half of the 90° quarter-circle — which makes R₁ and R₂ come out equal. It is the one pitch pairing where both rafters are the same length, which is part of why it reads as "the" barn roof angle.
- Half-span. r = 30 ÷ 2 =
15 ft. - Central angle. u = 2 × (90 − 60) =
60°. - Lower rafter. R₁ = 2 × 15 × sin(30°) = 30 × 0.5 =
15.00 ft. - Upper rafter. R₂ = 2 × 15 × sin(15°) = 30 × 0.2588 =
7.76 ft. - Height. H = r =
15.00 ft, regardless of θ. - Roof area, 40 ft length. Sloped overhang = 1 ÷ cos(60°) = 2.00 ft.
Area = 2 × (15.00 + 7.76 + 2.00) × 40 =
1,981.2 ft².
Pitch vs. Loft Clearance on a 30 ft Barn
Height cannot change under the half-circle method — it is locked at half the span. What moves when you change the lower pitch is where the knuckle sits, and that is what changes how much of the loft floor is actually usable at 6 ft. All four cards below hold the width at 30 ft and the height at exactly 15.0 ft.
55° lower pitch
Upper pitch locks at 10°. The knuckle sits further out, so less of the wall stays vertical.
21.60 ft loft clearance60° lower pitch
The most common modern pairing — a good balance of rafter length and loft width.
23.07 ft loft clearance67.5° lower pitch
Splits the quarter-circle exactly in half, so R₁ and R₂ come out equal.
25.03 ft loft clearance75° lower pitch
Close to vertical for most of its run; several codes want it detailed as a wall.
26.78 ft loft clearanceGoing from 55° to 75° on the same 30 ft barn adds 5.18 ft of usable loft width without moving the ridge an inch — the entire gain comes from where the knuckle lands, not from building any taller.
Snow, Ventilation and Loft Loads on a Barn
A barn carries the same two-surface wind and snow behaviour as any gambrel — the steep lower slope sheds almost everything, so nearly the full snow load and any drift surcharge lands on the shallow upper slope and the knuckle connection, while the lower rafters are sized by span. The gambrel snow load cases and wind load connection path work through both in detail.
Barns add one wrinkle most house roofs do not have: they are usually unheated and often unlined, so ridge and soffit ventilation has to move real volumes of air to stop condensation dripping onto stored hay — a moisture problem, not just a rot problem. And because the loft floor is a working surface rather than decorative attic storage, the collar ties that double as joists need checking against an actual stacked-hay load, not the light live load a residential attic floor assumes.
None of that changes the geometry on this page — rafter lengths, height and area are pure trigonometry regardless of what the building is used for. It does change what you check before you cut: confirm truss spacing and joist sizing against your local snow load and your real storage plan, and treat every number above as the starting geometry, not the finished structural design. The truss design guide covers member sizing by span and load.
Barn Roof FAQ
What roof pitch should a barn have?
Most barn roofs use a lower pitch between 55° and 70°, with 60° and 67.5° the two most common. Both are half-circle pairings: 60° locks the upper pitch at 15°, and the traditional 67.5° locks it at 22.5°. Either gives a barn the tall, square-shouldered loft the shape is built for — a 30 ft barn stands 15.0 ft to the ridge under either pairing, because height only depends on the span under this method.
Go lower than about 50° and the roof stops reading as a barn shape and starts giving back the loft space it exists to create. Go past about 75° and the lower slope is close enough to vertical that most codes want it detailed like a wall. Pitch conversions covers degrees, rise-in-12 and grade side by side.
How much loft space does a 30 × 40 barn gambrel roof give you?
At the 60°/15° pairing, a 30 × 40 barn stands 15.0 ft to the ridge and gives 23.07 ft of loft floor width with 6 ft of clearance — roughly three-quarters of the full 30 ft span usable at working height. The lower rafter comes out to 15.00 ft and the upper rafter to 7.76 ft, and the loft cross-section holds 12,294 ft³ over the 40 ft length.
Move to the traditional 67.5°/22.5° pairing on the same footprint and clearance widens to 25.03 ft, because the steeper lower slope keeps the walls closer to vertical for longer before it breaks at the knuckle. Height does not change — it is still exactly half the span, 15.0 ft — only the knuckle position and the two rafter lengths move. Attic space by span and pitch has the full breakdown.
Why do barn roofs have two different pitches?
A steep lower pitch keeps the loft walls close to vertical, and a shallow upper pitch closes the roof over the top without wasting height on a triangle nobody can stand in. One unbroken slope has to pick between headroom and rafter length; splitting it at a knuckle lets a barn have a tall loft and a modest ridge height at the same time.
It also comes from how barns were actually raised. Two shorter rafters were far easier to cut, carry and lift into place by hand than one long one — a 30 ft barn needs members of about 15.00 ft and 7.76 ft rather than a single 17.32 ft rafter run at a single 60° slope the whole way (and that single-slope version would only reach 15.0 ft with no shallow cap, which is a different, steeper-looking roof entirely). The framing walkthrough covers the knuckle joint that ties the two rafters together.
Where does the hay door go on a gambrel barn?
Almost always in the gable end wall, centred on the knuckle line, where the loft floor is wide enough to actually store what comes through the door. Framing it any higher runs into the shallow upper slope and loses floor width right at the opening; framing it lower wastes wall height that the steep lower slope worked to keep.
The opening needs its own header sized for whatever track or hoist beam mounts above it, jack studs carrying that header down to the sill, and — if the door interrupts the knuckle purlin — solid blocking across the gap so the purlin still ties the trusses either side of the opening together. Rafter length tables give the cut lengths either side of a door-interrupted truss bay.
How far apart should barn roof trusses be spaced?
24 in on centre is standard for site-built 2×6 barn trusses at spans up to about 30 ft; drop to 16 in for heavy snow, wider spans, or a loft floor rated for storage load. A 40 ft barn at 24 in centres needs 21 trusses; the same barn at 16 in centres needs 31.
Spacing is a load question, not a barn-specific one — the roof pitch does not change it. Confirm it against your local ground snow load and whatever the loft floor needs to carry before ordering timber.