How to Calculate Height From Volume

By Chance E. Gartneer; Updated April 24, 2017
The volume formula for a cylinder is radius squared times height times pi.

Height is an integral dimension in determining an object's volume. Finding the height measurement of an object depends on the shape of the object. One of the easiest ways to think of height as it corresponds to volume is to think of the other dimensions as a base area. The height is just that many base areas stacked upon each other. Individual object volume formulas can be rearranged to calculate height.

Divide the volume by the product of the length and width to calculate the height of a rectangular object. For this example, the rectangular object has a length of 20, a width of 10 and a volume of 6,000. The product of 20 and 10 is 200, and 6,000 divided by 200 results in 30. The height of the object is 30.

Calculate the cube root of a cube's volume to find its height. A cube's height, length and width are all equal. For this example, the cube has a volume of 27. The cube root of 27 is 3. The height of the cube is 3.

Divide the volume of a cylinder by the amount of the radius squared multiplied by pi, which is an unending constant that begins with the number 3.14, to calculate its height. For this example, the volume of the cylinder is 300 and the radius is 3. Squaring 3 results in 9, and multiplying 9 by pi results in 28.274. Dividing 300 by 28.274 results in 10.61. The height of the cylinder is 10.61.

Triple the volume of a pyramid and then divide that amount by the area of the base to calculate its height. For this example, the volume of the pyramid is 200 and the area of its base is 30. Multiplying 200 by 3 results in 600, and dividing 600 by 30 results in 20. The height of the pyramid is 20.

Divide the volume of a prism by its base to calculate its height. For this example, the volume of the prism is 500 and its base area is 50. Dividing 500 by 50 results in 10. The height of the prism is 10.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.