Volume is the amount of three-dimensional space an object occupies, and finding it comes down to measuring the right dimensions and plugging them into the right formula. For simple shapes like boxes and cylinders, you only need a tape measure and basic math. For irregular objects, a container of water does the trick.
Volume of a Rectangular Box or Cube
The simplest volume calculation is for any rectangular box, sometimes called a rectangular prism. Multiply length × width × height, and you have your answer. If you measure in inches, the result is in cubic inches. If you measure in centimeters, you get cubic centimeters.
A cube is a special case where all three sides are the same length. The formula simplifies to V = a³, where “a” is the length of one side. So a cube with 4-inch sides has a volume of 4 × 4 × 4 = 64 cubic inches.
Volume of a Cylinder
A cylinder is any shape with a circular base and straight sides, like a can or a pipe. The formula is V = πr²h, where “r” is the radius of the circular base (half the diameter) and “h” is the height. Pi (π) is approximately 3.14159.
For example, a cylinder with a radius of 3 inches and a height of 10 inches has a volume of 3.14159 × 3² × 10 = 282.7 cubic inches. If you only know the diameter, divide it by two to get the radius before plugging it in.
Volume of a Sphere
A sphere is a perfectly round ball shape. The formula is V = (4/3)πr³. You only need one measurement: the radius.
A basketball with a radius of about 4.7 inches, for instance, has a volume of (4/3) × 3.14159 × 4.7³ = roughly 435 cubic inches. Since measuring the radius of a sphere directly can be awkward, measure the diameter (the widest distance across) and divide by two.
Volume of a Cone
A cone has a circular base that narrows to a point. Its formula is V = (1/3)πr²h, where “r” is the radius of the base and “h” is the height from base to tip. Notice this is exactly one-third the volume of a cylinder with the same base and height.
Finding Volume of Irregular Objects
Not everything is a neat geometric shape. For oddly shaped objects like a rock, a piece of fruit, or a small figurine, the water displacement method is the most practical approach. It works because a submerged object displaces a volume of liquid exactly equal to its own volume.
Start by filling a graduated cylinder or measuring cup with enough water to fully cover the object. Record this initial water level. When reading the water line, look at the bottom of the meniscus, the slight U-shaped curve the water surface forms against the container wall. Then tilt the container slightly and slide the object in gently to avoid splashing. Set the container upright and read the new water level. Subtract the initial level from the new level, and the difference is the object’s volume.
For example, if the water starts at 50 mL and rises to 73 mL after you drop in a stone, the stone’s volume is 23 mL, which equals 23 cubic centimeters. One milliliter always equals one cubic centimeter.
Calculating Volume for Shipping
If you need volume for packing or shipping, the standard approach is the same rectangular formula: length × width × height. In international freight, this is typically expressed in cubic meters (CBM). Measure each dimension in centimeters, multiply them together, and divide by 1,000,000 to convert to cubic meters.
When you have multiple boxes of different sizes, calculate the volume of each size separately and add them together. For cylindrical packages, some carriers treat them as if they were rectangular by using the diameter as both the width and the height. Others use the actual cylinder formula. Check with your carrier to know which method they apply.
Air cargo carriers also use a concept called volumetric weight, which converts a package’s size into an equivalent weight. The standard formula is length (cm) × width (cm) × height (cm) ÷ 6,000. The carrier then charges based on whichever is greater: the actual weight or the volumetric weight.
Converting Between Volume Units
Once you have a volume measurement, you may need to convert it to different units. Here are the most common conversions:
- Liters to gallons: multiply by 0.264
- Gallons to liters: multiply by 3.785
- Liters to milliliters: multiply by 1,000
- Milliliters to liters: multiply by 0.001
- Cubic centimeters to liters: multiply by 0.001
- Cubic centimeters to cubic meters: multiply by 0.000001
One liter equals 1,000 cubic centimeters, and one milliliter equals one cubic centimeter. These two facts handle most metric conversions you will run into. For a quick U.S. reference, one gallon is about 3.785 liters, so a 5-gallon bucket holds roughly 18.9 liters.