Calculate Volume of a Box

Whether you need to to mail a package or pass you next test, finding the volume of a box is easy. Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

Steps

Calculating the Volume of Rectangular Boxes

  1. Understand the volume of a rectangle equals it's length x width x height. If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as V = l x w x h.
    • Sample Question: "If I have a box with a length of 10cm, width of 4cm, and height of 5cm, what is the volume of the box?"
    • V = l x w x h
    • V = 10cm x 4cm x 5cm
    • V = 200cm3
    • "Height" may be replaced with "depth." For example, "The box has a length of 10cm, width of 4cm, and is 5cm deep."
  2. Measure the length of a box. If your are looking down at your box, the top appears to be a flat rectangle/The length the longest side of this rectangle. Write this number down as "length."
    • Make sure you use the same measurement for each side -- if you measure one side in inches, you need to measure them all in inches.
  3. Measure the width of the box next to the length. The width of the box is the other edge next to the length. If you are looking one side of the box, the width is the side the forms an "L" with the length. Write down this measurement as "width."
    • The width is always the shorter side.
  4. Measure the height of the box. This is the last side you have not measured, and is the the distance from the top of the box to the ground. Write this measurement down as "height."
    • Depending on how the box is laying, which side you call "height" or "length" might be different. However, it doesn't matter what side you call the length, just that you measure 3 different sides.
  5. Multiply the three sides together. Remember, the equation for volume is V = length x width x height, so simply multiply all three sides together to get your volume. Be sure to include the units you used to measure with as well, so you don't forget what your numbers mean.
  6. Add the "units3" to your volume. Volume is a measurement, but if you don't know what the measuring system your number will be meaningless. The correct way write out volume is with your type of measurement cubed. For example, if I measured all the sides in inches, my final answer would be in "inches3." For example.
    • Sample Question: "If I have a box with a length of 2 feet, width of 1 foot, and height of 3 feet what is the volume of the box?"
    • V = l x w x h
    • V = 2ft x 1ft x 4ft
    • Volume = 8ft3
    • Advanced Note:' This is because volume tell you how many small cubes you could fit in the box. In the previous example, this means we could fit eight separate 1 foot cubes in our box.

Calculating Different Shaped Boxes

  1. Find the volume of cylinders. Cylinders are tubes, where the top and bottom are circles. To find volume of a cylinder, use the equation V = pi x r2 x h. Where pi = 3.14, r is the radius of the top circle, and h is the height.
    • To find the volume of a cone, or pyramid with a circle for the bottom, use the same equation time 1/3. So, Volume of a Cone = 1/3(pi x r2 x h)
  2. Find the volume of a pyramid. Pyramids have one side, or base, and all of the other sides comes to a point. To find volume, multiply the area the base by the height, and then multiply that by the fraction 1/3. Thus, Volume of a Pyramid = 1/3(base x height).
    • Most pyramids have square or rectangular bases. The area of a base is found by multiplying the length of the base by the width.
  3. Add the volume of the parts together to find the volume of complicated shapes. For example, if I need to find the volume of an "L" shaped box, there are more than three sides to measure. If you view the box as two smaller boxes, however, you can find the volume of each smaller box and add them together to get the final volume. With our "L" shaped box, for example, we can view the vertical line as a rectangular box and the bottom horizontal line as a square box.

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