How to Find Cubic Feet
Four Methods:Square or Rectangular ShapeCylindrical ShapeThree-Sided PyramidFour-Sided Pyramid
Have you ever needed to fill a sandbox, a post hole, or any other three-dimensional space? Doing this requires “cubic measurement,” which is just another way of measuring volume. To calculate the volume of a square, rectangular, cylindrical, or pyramidal shape in cubic feet, follow these easy steps.
Steps
Method 1 Square or Rectangular Shape
- 1Measure the length of the object. If it doesn’t measure well into whole feet, feel free to measure it in inches for now.
- Ex. 8 inches (20.3 cm).
- 2Measure the width of the object. If you measured the length in inches instead of feet, be sure to do the same with the width to stay consistent.
- Ex. 16 inches (40.6 cm).
- 3Multiply the length by the width. This gives the two-dimensional area of the base of the object.
- Ex. 8 inches (20.3 cm) x 16 inches (40.6 cm) = 128 square inches.
- 4Measure the height of the object. Write down this number.
- Ex. 27 inches (68.6 cm).
- 5Multiply the two-dimensional area of the base by the height. This gives you a three-dimensional, or cubic, measurement.
- Ex: 128 square inches x 27 inches (68.6 cm) = 3456 cubic inches.
- 6Convert to cubic feet if necessary. To convert from cubic inches to cubic feet, divide the result by 1728.
- Ex. 3456 cubic inches / 1728 = 2 cubic feet.
Method 2 Cylindrical Shape
- 1Measure the width of one circular end and divide by half. Half the width of a circle is also known as the radius. If it doesn’t measure well into whole feet, feel free to measure it in inches for now.
- Ex. 20 inches (50.8 cm) / 2 = 10 inches (25.4 cm).
- 2Multiply the radius by itself. This is the same thing as the radius squared.
- Ex. 10 inches (25.4 cm) x 10 inches (25.4 cm) = 100 square inches.
- 3Multiply the squared radius by pi. If you don’t have the pi button on your calculator (or would prefer an approximation), multiply by 3.14. This gives you the two-dimensional area of the circular end of the object.
- Ex. 100 inches (254.0 cm) x 3.14 = 314 square inches.
- 4Measure the distance between the two circular ends. Depending on how the cylinder is oriented, this may be its length or height. Write down this number.
- Ex. 11 inches (27.9 cm).
- 5Multiply the two-dimensional area of the circular end by this distance. This gives you a three-dimensional, or cubic, measurement.
- Ex: 314 square inches x 11 inches (27.9 cm) = 3454 cubic inches.
- 6Convert to cubic feet if necessary. To convert from cubic inches to cubic feet, divide the result by 1728.
- Ex. 3454 cubic inches / 1728 = 2 cubic feet.
Method 3 Three-Sided Pyramid
- 1Measure the “base” of the bottom of the pyramid. This is the length of one side of the triangular base. If it doesn’t measure well into whole feet, feel free to measure it in inches for now.
- Ex. 9 inches (22.9 cm).
- 2Measure the “height” of the bottom of the pyramid. This is the distance between the side you previously measured and the point directly opposite it on the triangular base. If you measured the base in inches instead of feet, be sure to do the same with the height to stay consistent.
- Ex. 12 inches (30.5 cm).
- 3Multiply the “base” of the bottom by its “height” and divide by two. This gives you the two-dimensional area of the triangular base of the pyramid.
- Ex. 9 inches (22.9 cm) x 12 inches (30.5 cm) = 108 square inches
- 108 square inches / 2 = 54 square inches
- Ex. 9 inches (22.9 cm) x 12 inches (30.5 cm) = 108 square inches
- 4Measure the height of the pyramid. Be sure to measure in a straight vertical line from the bottom to the top, not a diagonal line that follows one of the sloping sides. Write down this number.
- Ex. 32 inches (81.3 cm).
- 5Multiply the two-dimensional area of the base by the height. This gives you a three-dimensional, or cubic, measurement.
- Ex: 54 square inches x 32 inches (81.3 cm) = 1728 cubic inches.
- 6Divide this number by three. Since the length times width times the height gives you the volume of a cube, not a pyramid, you must modify this result to find the volume of a pyramid instead. To do this, divide by three. This works with all pyramids.
- Ex. 1728 cubic inches / 3 = 576 cubic inches.
- 7Convert to cubic feet if necessary. To convert from cubic inches to cubic feet, divide the result by 1728.
- Ex. 576 cubic inches / 1728 = 1/3 cubic foot.
Method 4 Four-Sided Pyramid
- 1Measure the length of the base of the pyramid. If it doesn’t measure well into whole feet, feel free to measure it in inches for now.
- Ex. 8 inches (20.3 cm).
- 2Measure the width of the base of the pyramid. If you measured the length in inches instead of feet, be sure to do the same with the width to stay consistent.
- Ex. 18 inches (45.7 cm).
- 3Multiply the length by the width. This gives you the two-dimensional area of the base of the pyramid.
- Ex. 8 inches (20.3 cm) x 18 inches (45.7 cm) = 144 square inches.
- 4Measure the height of the pyramid. Be sure to measure in a straight vertical line from the bottom to the top, not a diagonal line that follows one of the sloping sides. Write down this number.
- Ex. 18 inches (45.7 cm).
- 5Multiply the two-dimensional area of the base by the height. This gives you a three-dimensional, or cubic, measurement.
- Ex: 144 square inches x 18 inches (45.7 cm) = 2592 cubic inches.
- 6Divide this number by three. Since the length times width times the height gives you the volume of a cube, not a pyramid, you must modify this result to find the volume of a pyramid instead. To do this, divide by three. This works with all pyramids.
- Ex. 2592 cubic inches / 3 = 864 cubic inches.
- 7Convert to cubic feet if necessary. To convert from cubic inches to cubic feet, divide the result by 1728.
- Ex. 864 cubic inches / 1728 = 1/2 cubic foot.
Tips
- The term “cubic feet” can also be written as feet^3; don’t let this confuse you, as it is simply a shorthand way of writing the word “cubic,” not an additional aspect of the math
- The basic idea when calculating three-dimensional space is to find the two-dimensional area of the base and multiply it by the height to incorporate that third dimension. Of course, this gets more complicated with irregularly-shaped bases (ex. circles, triangles) or sloping sides (ex. pyramids, cones).
- When converting cubic inches to cubic feet, it may help to think of 1728 as 12 multiplied by itself three times; there are 12 inches (30.5 cm) to a one-dimensional foot, another 12 to a two-dimensional foot, and another 12 to a three-dimensional foot.
Things You'll Need
- A measuring device
- Pen (Optional)
- Paper (Optional)
- Calculator (Optional)
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