Volume is the measure of the amount of three-dimensional space occupied by an object. It is typically measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).

How do you calculate the volume of a sphere?

The volume of a sphere is calculated using the formula V = (4/3)πr³, where 'r' is the radius of the sphere and π (pi) is approximately 3.14159.

What is the difference between volume and surface area?

Volume measures the space inside a 3D object, while surface area measures the total area of all its outer surfaces. For example, the volume of a cube is side³, while its surface area is 6 × side².

Volume Calculator (Cube, Sphere, Cylinder, etc.)

How Does This Calculator Work?

This calculator uses standard geometric formulas to find the volume of the 3D shape you select. Volume is the measure of the three-dimensional space an object occupies.

Cube: Volume = Side³
Sphere: Volume = (4/3) × π × radius³
Cylinder: Volume = π × radius² × Height
Cone: Volume = (1/3) × π × radius² × Height
Rectangular Prism (Box): Volume = Length × Width × Height

You simply select your shape, enter the required dimensions, and the calculator applies the correct formula to give you the result.

The Surprising History of Archimedes' "Eureka!" Moment

One of the most famous stories in the history of science is about measuring volume. The ancient Greek mathematician and inventor, Archimedes, was tasked by King Hiero II to determine if his new crown was made of pure gold or if the goldsmith had mixed in cheaper silver.

Archimedes knew he could determine this by measuring the crown's density (mass/volume), but he struggled to find the volume of such an irregularly shaped object. The solution came to him in the bath. As he stepped in, he noticed the water level rise and realized that the volume of water displaced was equal to the volume of his body submerged. Overjoyed by this breakthrough, he supposedly ran through the streets naked, shouting "Eureka!" ("I have found it!"). He used this principle of water displacement to find the crown's volume, prove the goldsmith had cheated, and establish a fundamental principle of physics.

Explore More Related Tools

While you're here, check out some of our other popular math and science calculators:

Area Calculator: Calculate the 2D surface of shapes.
Scientific Calculator: For advanced mathematical calculations.
Unit Converter: Easily convert between different units of volume (e.g., cubic meters to liters).
Percentage Calculator: Useful for many real-world problems.
Fraction Calculator: For calculations involving fractional dimensions.
Ratio Calculator: Understand the proportions of shapes.
Exponent & Root Calculator: For calculations involving powers and roots.
Logarithm Calculator: The inverse of exponentiation.
Standard Deviation Calculator: A key tool for statistics.
Quadratic Equation Solver: Solve for unknowns in equations.

Frequently Asked Questions (FAQ)

What units should I use for volume?

You can use any unit of measurement (e.g., cm, meters, feet, inches), as long as you are consistent for all dimensions of a shape. The resulting volume will be in the cubic of that unit (e.g., cm³, m³, ft³, in³).

What's the volume of a flat, 2D shape like a square?

A two-dimensional shape has no thickness, so it has no volume. Volume is a property that only applies to three-dimensional objects. A 2D shape has an area, but its volume is zero.

How do I find the volume of an irregular object?

This calculator is for standard geometric shapes. For an irregular solid object, you can use the water displacement method, made famous by Archimedes. Submerge the object in a container of water and measure the volume of the water that is displaced—this will be equal to the volume of the object.

Volume Calculator

Volume: