Gambrel Roof Calculator: Barn Roof Rafter Lengths, Pitches, Height and Roof Area

How it works

lower rise y₁ = x₁ × tan θ · upper run x₂ = W ÷ 2 − x₁ · upper rise y₂ = x₂ × tan φ · H = y₁ + y₂ · R₁ = √(x₁² + y₁²) · R₂ = √(x₂² + y₂²) · roof area = 2 × (L + 2g) × (R₁ + e ÷ cos θ + R₂) · gable area = x₁y₁ + 2x₂y₁ + x₂y₂ · semicircle: φ = θ − 45°, H = W ÷ 2

A gambrel roof has two slopes on each side: a steep lower slope θ from the wall to the break (the knee) and a shallow upper slope φ from the break to the ridge. Each slope is a right triangle, so once you know the span W, the two pitches and where the break sits, the rises, rafter lengths and height follow from tan and Pythagoras. You can fix the break by its level distance from the wall (lower run) or by the overall roof height; with the height known, the lower run is (H − W/2 × tan φ) ÷ (tan θ − tan φ). The semicircle option is the classic barn layout: draw a half circle as wide as the building and put the breaks on it. The roof height is then half the span, the upper pitch is always 45° less than the lower, and 67.5°/22.5° gives four equal rafters, which is handy when cutting them from the same stock. Pitches can be typed as degrees, rise/run (21/12) or percent. Besides rafters, the calculator gives the roof area to order sheathing and roofing (including the eave tail and gable overhangs), the area of each gable end for siding, the attic volume and how wide the loft floor is at a chosen headroom, with a profile chart. It is geometry for a symmetric gambrel; the roof pitch and rafter calculators handle a single-slope gable roof. It does not size rafters or check snow and wind loads, so have the framing checked against your local code.

Worked example

A 24 ft wide, 36 ft long barn with a 60° lower pitch, 25° upper pitch and the break 4 ft in from each wall: the lower rise is 4 × tan 60° = 6.93 ft and the lower rafter √(4² + 6.93²) = 8.00 ft. The upper run is 12 − 4 = 8 ft, its rise 8 × tan 25° = 3.73 ft and the upper rafter 8.83 ft, so the roof is 10.66 ft (10 ft 7 7/8 in) high. A 1 ft level eave overhang adds a 1 ÷ cos 60° = 2.00 ft tail. With 6 in gable overhangs the roof area is 2 × 37 × (10.00 + 8.83) = 1,393 sq ft (13.9 squares); each gable end is 168 sq ft, the attic holds 6,063 cu ft and 15.69 ft of the loft floor has at least 7 ft of headroom.

Sources: Omni Calculator: Gambrel roof (two-pitch and half-circle methods, worked example)

Frequently asked questions