How To Calculate Cubic Meters

What is a cubic meter? Even as you read, it's likely that your mind is having difficulty figuring out what physical value or quantity this represents. Even if you know that cubic meters (m³) represent a unit of volume in physical science, you might have a hard time picturing a cubic meter.

The metric system, also called the SI or international system of units, was devised in the 18th century and implemented in Europe in the 1790s. Its core purpose was to replace the imprecise and inconvenient units of feet, inches and so on with units that were both easier to work with and based on absolute standards.

The meter was thus chosen to represent one-ten millionth of the presumed distance from the equator to the North Pole, and the kilogram was selected to be the mass of one liter of water. A liter in turn was defined as the volume occupied by a cube-shaped space 0.1 m (10 centimeters, or cm) on a side or the equivalent volume in any other solid shape.

These definitions have been modified from their original values only to reflect the advent of increasingly precise measuring tools over time.

A cubic meter is a space in the shape of a cube 1 m on a side or the equivalent. For example, a rectangular box with a length of 2 m, a width of 1 m, and a height of 0.5 m would have a volume of 1 m³ (1 × 2 × 0.5 = 1).

The cubic meter is also called the stere, though this has become largely a term of antiquity and is not an acceptable term on its own in the SI system. It remains in use for measuring piles of cut wood in the timber industry.

The stere or cubic meter is equivalent to 35.315 cubic feet (ft³) or 0.276 cord, another lumber-industry term. It is fairly easy to imagine a row of logs a little over 1 foot wide, 10 feet long and 3 feet tall; this would work out to about a stere.

1\. What is the volume of an aquarium tank 20 m long, 20 m wide and 10 m deep?

The calculation is straightforward: 20 × 20 × 10 = 4,000 m^3. What is remarkable is the sheer mass of the water inside. If you recall that 1 L of water has a mass of 1 kilogram, then a cubic meter, which is 10 times larger on a side than a liter, holds 1,000 kg of water. This is over 2,200 pounds, and is called a metric ton or tonne. A traditional ton, by comparison, is exactly 2,000 pounds.

A volume of water of 4,000 m³ thus has a mass of 4,000 tonnes or about 4,400 tons. Imagine the strength of the glass required to hold all of this in, to say nothing of the inhabitants!

2\. You are given a giant ball 2 m (about six and a half feet) wide. How much air can this ball hold when fully inflated? That is, what is its volume?

To solve, you need only know or refer to the volume of a sphere and recognize that you can treat the ball as such for purposes of a physics problem. This volume is given by the formula V = 4πr³. Since the ball is 2 m across, its diameter is 2 m, and its radius therefore is 1 m. The volume of this ball is therefore (4π)(1)2 = 4π m³, or 12.57 m³.

You can refer to any number of online calculator tools to work with ease between cubic meters and other units of volume. An example of such a tool is found in the Resources. This lets you input a value in a common unit of volume such as a gallon, or a less-common unit such as a cubic yard, and return a number giving the equivalent in cubic meters.