Gambrel Roof Calculator

24 Foot Gambrel Roof Span

Twenty-four feet is the width this whole site keeps coming back to. The homepage calculator defaults to a 24 ft span, and most of its worked examples — the 12.00 ft lower rafter, the 6.21 ft upper rafter, the 197 ft² cross-section in its own FAQ — are this exact building. This page goes deeper on that one running example than a single table row can: every figure below is solved independently, then checked against what the homepage itself claims.

The 24 ft span, solved

Pre-filled at 24 ft, 60° lower pitch — the same defaults GambrelCalculator.astro ships on the homepage, just using the half-circle method. Every stat below should match the homepage's own reference table once you allow for the overhang difference explained below.

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 24 ft, total height H 12.00 ft. Lower rafter R1 12.00 ft at 60.0 degrees, upper rafter R2 6.21 ft at 15.0 degrees. θ 60.0° φ 15.0° W = 24.0 ft x₁ = 6.00 x₂ = 6.00 y₁ = 10.4 y₂ = 1.61 H = 12.0 ft R₁ = 12.0 ft R₂ = 6.21 ft Ridge Knuckle
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″ to the ridge
Roof area (both slopes)
808.5 ft²
incl. 1.00 ft overhang
Attic / loft volume
3,934 ft³
196.7 ft² cross-section
Clear floor width
17.07 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 24 ft span, 60° lower pitch and 15° upper pitch, a 20 ft building length and a 1 ft overhang:

W
24 ft span, wall plate to wall plate.
R₁
12.00 ft lower rafter, 60.0° (20.8:12).
R₂
6.21 ft upper rafter, 15.0° (3.2:12).
H
12.00 ft total height, half the span.
Area
808.5 ft² of roofing, both slopes, 20 ft long with a 1 ft overhang.
Vol.
3,934 ft³ of enclosed loft space.

Cross-section: 196.7 ft² — the figure the homepage's own FAQ rounds to "about 197 ft²" when it explains why barns use this shape.

This span's real question

Cross-checked against the homepage's own table

The homepage's table states its figures at 0 ft overhang; this page's convention uses 1 ft. Rafter lengths, height and cross-section never touch overhang, so they should — and do — match exactly:

solveHalfCircle(width: 24, lowerPitch: 60, upperPitch: 15) at two overhang settings
FigureHomepage table (0 ft overhang)This page (1 ft overhang)
Lower rafter R₁12.00 ft12.00 ft
Upper rafter R₂6.21 ft6.21 ft
Total height H12.00 ft12.00 ft
Attic cross-section196.7 ft²196.7 ft²
Roof area, 20 ft length728.5 ft²808.5 ft²

Only roof area shifts, by exactly the overhang's contribution — 80.0 ft² for a 1 ft overhang on a 20 ft building. Everything upstream of overhang is identical, the point of solving both from the same function rather than copying figures between pages.

Worked example: the homepage's own 24 ft truss

  1. Halve the span

    W = 24 ft, so the half-span is 12 ft.

  2. Fix the lower rafter

    At 60°, R₁ = 12.00 ft — one 12 ft board, no offcut.

  3. Fix the upper rafter

    The half-circle rule forces 15°, giving R₂ = 6.21 ft up to the ridge.

  4. Check the height

    y₁ + y₂ = 10.39 + 1.61 = 12.00 ft — the identity this whole method is built on.

  5. Confirm the volume claim

    Cross-section 196.7 ft² is 1.366× a same-height gable's 144.0 ft² — exactly what the homepage's "35% to 40% more volume" FAQ answer describes.

Practical guidance for a 24 ft garage or barn-bay gambrel

Reference point

Use this span to sanity-check other tools

Every homepage calculator and worked example defaults here, so this is the width to plug into angle tables or dimension references first, to confirm you're reading them the same way.

Lumber buying

Lower rafters land on 12 ft stock

Order 12 ft boards for the lower rafters with no offcut; the 6.21 ft upper rafters fit a 8 ft board with material left for gusset blanks.

Truss spacing

The edge of the simple rule of thumb

24 in on-centre with 2×6 members is usual up to about this span — treat 24 ft as the point to double-check rather than assume it still applies.

Connections

Basic gussets, but check your snow load

Site-built plywood gussets are still standard at 24 ft; the knuckle is more often sized by snow load than by span here.

24 ft next to its neighbours

20, 24 and 30 ft compared at the same 60°/15° pitch, 20 ft length, 1 ft overhang
SpanR₁R₂HeightVolumeHeadroom width
20 ft span10.00 ft5.18 ft10.00 ft2,732 ft³13.07 ft
24 ft span (this page)12.00 ft6.21 ft12.00 ft3,934 ft³17.07 ft
30 ft span15.00 ft7.76 ft15.00 ft6,147 ft³23.07 ft

24 ft span FAQ

Why does the homepage use 24 ft as its example?

Because it is a common building width — a two-and-a-half car garage or mid-size barn bay — and the numbers at a 60° lower pitch are clean enough to sanity-check by hand: R₁ = 12.00 ft, R₂ = 6.21 ft, height 12.00 ft. This page runs those inputs through solveHalfCircle() independently and gets the identical result.

Do the figures on this page match the homepage calculator?

Rafter lengths, height and cross-section match exactly — those never depended on overhang. Roof area differs only because this page uses a 1 ft overhang (808.5 ft²) against the homepage table's 0 ft (728.5 ft²). Set overhang to 0 above and they line up.

Why isn't the upper rafter a round number like the lower rafter?

R₁ is always exactly W ÷ 2 under this method. R₂ has no equivalent shortcut — it comes out to 2 × (W⁄2) × sin(15°) = 6.21 ft, which is why it carries decimals.

How much less roof area would a 24 ft gambrel need with no overhang?

80.0 ft² less — 728.5 ft² instead of 808.5 ft². Overhang adds a fixed strip regardless of span, so its share shrinks as the span grows.