Gambrel Rafter Lengths

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The Gambrel Rafter Lengths calculator computes the upper and lower rafter lengths, attic width and total height based on the upper and lower pitch, span and loft height.

INSTRUCTIONS: Choose units and enter the following:

(S) Span of Roof
(LH) Loft Height
(P1) Lower Pitch
(P2) Upper Pitch

Gambrel Rafter Length (RL): The calculator returns the following:

(LR) Lower Rafter Length
(UR) Upper Rafter Length
(TH) Total Height
(LW) Loft Width

The Math / Science

The Loft Width must be less than the span. With that constraint, the rest is simple trigonometry of triangle.

LR = LH / sin(P1)
x = sqrt(LR²-LH²)
LW = S - 2x
y = LW/2
UR = (LW/2) / cos(P2)
z = sqrt(UR² - y²)
TH = LH + z

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