If you've seen an old barn, you likely recognise a gambrel roof's characteristic two-pitch-per-side design, which incorporates a flatter upper portion. This shape allows more room beneath the roof when designing living or storage space. If you want to put a gambrel roof on your new home or determine how much space the roof will enclose, measure its dimensions and angles during the design phase by using basic geometry formulas.
Things you need
Ruler or straight edge
Draw a cross-section design of the roof, using each square to represent 1 foot.
Draw a horizontal line at the bottom of the first slope of the roof, dividing the gambrel roof cross-section into a triangle and a trapezoid.
Draw a vertical line down the middle of the diagram and mark it as the height.
Measure and record the lengths of the base and each side of the roof, including the horizontal dividing line between the two halves. As an example, let the bottom base have a measurement of 15 feet and the top base have a measurement of 10 feet.
Record the height of the roof from base to tip and halve it to get the heights for each section of the roof. For example, if the total height of your gambrel roof design is 10 feet, each section will measure 5 feet.
Use the formula for trapezoid area to determine the area for the bottom half. The University of Illinois gives this formula as 1/2h(b1+b2), where h is the height and b1 and b2 are the two parallel bases. Express the area in square feet:
1/2(5)(15+10)=62.5 square feet.
Determine the area of the top portion of the roof by using the formula 1/2bh, and express the measurement in square units. Using the example measurements, 1/2(10)(5)=25 square feet. Add the two areas to determine the total area of the cross-section: 62.5+25=84.5 square feet total.
To determine volume, multiply the area by the depth of the roof. If your roof has a depth of 20 feet with a cross-section area of 84.5 square feet, its volume would be 1690 cubic feet.
Take half the difference between the two bases to determine the horizontal distance of your pitch for the trapezoidal portion. Bases of 15 and 10 feet, as used in the example, have a horizontal distance of 2.5 feet. The height, or rise, is 5 feet. Divide the rise by the run to get the slope. Convert this to pitch by expressing it as a ratio of 12, according to Southwest Wisconsin Technical College. For example, 5 divided by 2.5 equals 2 and 12 times 2 equals 24, so the first pitch measurement is 24:12.
Calculate the slope of the top portion of the roof by dividing the rise by the run. In this case, the rise and run are both 5 feet, so 5 divided by 5 equals 1 and the pitch of the roof is 12:12.
Things you need
- Graph paper
- Ruler or straight edge
- Scientific calculator