How to Figure the Volume of a Hip Roof
A hip, or hipped, roof is made up of sides that all slope down toward the ground. That means that no part of the exterior walls will go above the roof length. A hipped roof with a pyramidal structure is also called a pavilion roof. Knowing the volume of a hip roof can be useful when you're planning to remodel or simply doing some home decoration. The volume of your hipped roof should be expressed in cubic feet.
Determine where each measurable section of the hipped roof begins and ends. You want to split the into simple three-dimensional shapes whose volumes are easy to calculate. A typical hip roof, for example, contains a central triangular prism and a half-pyramid shape on each end of the roof.
Measure the width, length and height of each shape in feet. You can also refer to your blueprints for exact lengths.
Determine the volume of the central triangular prism by multiplying 1/2 width times height times length. Note that the formula "1/2 width times height" represents the area of a vertical cross section of the triangular prism. If you're working with a prism that is 8 by 10 by 20, your total would be 800 cubic feet.
Multiply the length of the half-pyramid by the width. Double the figure if the pyramids are the same size so that you can find the total volume for both ends of the roof at once. That's the area of the base of a full pyramid. So if the length of your full pyramid is 5 and the width is 8, the total area is 40.
Find the volume of the two pyramids at once by using the base area you just calculated in the formula "1/3 times base area times height." If the height is 10, then multiply 1/3 times 10 times 40 to get your total volume of 133.3 cubic feet.
Add the totals for both shapes together to find the total volume. In the example, the total volume would be 933.3 cubic feet.
Things You Will Need
- Measuring tape
- If the pyramids are different sizes, just calculate volume at 1/3 times area of the base times the height and then half the calculated total. You would add the volume of the central triangle shape and the volume of both half-pyramids to find the total volume.
- For a more exact measurement, consider using an online calculator.
- Don't forget to calculate extra volume for features like chimneys or architectural designs that add or remove volume under the house.