Gambrel Roof Calculator

40 Foot Gambrel Roof Span

Forty feet is a real working farm barn — hay storage filling the loft over an equipment bay wide enough for a tractor below. It is also the span where these numbers stop being about pitch angles and start being about what you can actually buy: the lower rafter works out to exactly 20.00 ft, the longest length most lumberyards carry off the shelf without a special order.

The 40 ft span, solved

Pre-filled at a 40 ft span, half-circle method, 60° lower pitch. Push the width past 40 and watch the lower rafter cross past the point a single stock board can cover.

ft
Wall plate to wall plate.
°
Upper pitch locks to 15.0° automatically — the half-circle method always holds θ − φ = 45°.
ft
Measured along the ridge.
ft
Horizontal, per side.

Cross-section

Lower rafter Upper rafter

Gambrel roof cross-section, half-circle method. Span W 40 ft, total height H 20.00 ft. Lower rafter R1 20.00 ft at 60.0 degrees, upper rafter R2 10.35 ft at 15.0 degrees. θ 60.0° φ 15.0° W = 40.0 ft x₁ = 10.00 x₂ = 10.0 y₁ = 17.3 y₂ = 2.68 H = 20.0 ft R₁ = 20.0 ft R₂ = 10.4 ft Ridge Knuckle
Lower rafter R₁
20.00 ft
20′ 0″ · 60.0° · 20.8:12
Upper rafter R₂
10.35 ft
10′ 4 1/4″ · 15.0° · 3.2:12
Total height H
20.00 ft
20′ 0″ to the ridge
Roof area (both slopes)
1,294.1 ft²
incl. 1.00 ft overhang
Attic / loft volume
10,928 ft³
546.4 ft² cross-section
Clear floor width
33.07 ft
at 6 ft standing height

Solved with the half-circle (barn) method: the knuckle and ridge sit on a semicircle of radius W ÷ 2 struck from the centre of the wall-plate line, which forces θ − φ = 45° and H = W ÷ 2 for every span.

Numbers at a glance

At a 40 ft span, 60° lower pitch and 15° upper pitch, a 20 ft building length and a 1 ft overhang:

W
40 ft span, wall plate to wall plate.
R₁
20.00 ft lower rafter, 60.0° (20.8:12).
R₂
10.35 ft upper rafter, 15.0° (3.2:12).
H
20.00 ft total height, half the span — a genuine two-storey rise.
Area
1,294.1 ft² of roofing, both slopes, 20 ft long with a 1 ft overhang.
Vol.
10,928 ft³ of enclosed loft space.

Clear floor width at 6 ft of standing height: 33.07 ft — more than 83% of the full width is walkable, over a loft big enough to genuinely store a season's worth of hay.

This span's real question

Lumber sourcing at 40 ft

At 20.00 ft, the lower rafter sits exactly at the edge of a single piece of off-the-shelf lumber. Three ways builders get that length on site:

Options for a 20.00 ft rafter member
 Full-length 2× stockEngineered (LVL / glulam)Site-scarfed splice
AvailabilityAt the outer limit of common stockSpecial order, most yardsAny shorter stock on hand
Straightness / consistencyVariableVery consistentDepends on joint quality
Best suited toA build lucky enough to source it locallyA load-checked, code-reviewed trussA crew experienced with structural splices

None of these is a purely carpentry decision at this span — the connection detail has to carry real load, which is why a structural engineer's review belongs in the plan before lumber gets ordered.

Worked example: framing this 40 ft truss

  1. Halve the span

    W = 40 ft, so the half-span is 20 ft.

  2. Fix the lower rafter

    At 60°, R₁ = 20.00 ft — exactly the 20 ft longest common stock length.

  3. Fix the upper rafter

    The half-circle rule forces 15°, giving R₂ = 10.35 ft up to the ridge.

  4. Check the height

    y₁ + y₂ = 17.32 + 2.68 = 20.00 ft — a full 20 ft rise from wall plate to ridge.

  5. Flag it for review

    Confirm rafter stock at 20.00 ft is actually available locally, and get the knuckle and spacing checked against real site loads.

Practical guidance for a 40 ft farm barn gambrel

Loft volume

Plan it like a second building

10,928 ft³ over just a 20 ft section is genuine storage capacity — plan hay-loading access as part of the framing, not an afterthought.

Lumber sourcing

Confirm stock length before design freeze

Call the yard before finalizing the design — a 20.00 ft board is at the edge of what is commonly stocked, and availability varies by region.

Engineering

Not a DIY spec at this scale

A stamped truss design is standard practice — and usually required by code — for a barn this size, with hay load and a tall, wind-exposed profile.

Truss spacing

Expect tighter centres or larger members

16 in on-centre, larger lumber, or both are typical at 40 ft — confirm against the snow and wind load cases for the site.

40 ft next to the size below it

40 ft is the largest span on this site's reference list; the step down is 30 ft, where rafters still come off a single stock board.

30 ft vs. 40 ft, same 60°/15° pitch, 20 ft length, 1 ft overhang
SpanR₁R₂HeightVolumeHeadroom width
30 ft span15.00 ft7.76 ft15.00 ft6,147 ft³23.07 ft
40 ft span (this page)20.00 ft10.35 ft20.00 ft10,928 ft³33.07 ft

40 ft span FAQ

Can I still use standard dimensional lumber at a 40 ft span?

For the lower rafter, just barely — R₁ comes out to exactly 20.00 ft, the longest length most yards stock off the shelf. Any wider and that rafter needs LVL, glulam, or a scarfed splice instead of a single board. The 10.35 ft upper rafter has plenty of room on a 12 ft board.

Do I need an engineer for a 40 ft gambrel barn?

Strongly recommended, and required by code in most jurisdictions at this scale. Hay storage loading, wind uplift on a tall profile, and snow drift at the knuckle all deserve a real engineer's numbers, not a rule of thumb.

How big is the loft at a 40 ft span, really?

10,928 ft³ over a 20 ft building length, with 33.07 ft of clear floor at 6 ft headroom. Scale that to a typical 40–60 ft barn and volume runs into the tens of thousands of cubic feet.

How much roofing material does a 40 ft barn need?

1,294.1 ft² across both slopes for a 40 ft wide, 20 ft long section with a 1 ft overhang. See the metal panel calculator and the build cost breakdown.