Volume of Shapes Calculator

Volume Formulas for Common 3D Shapes

Volume is the amount of three-dimensional space enclosed within a solid shape. All volume formulas produce results in cubic units (e.g., cm³, m³, in³, ft³).

Rectangular Prism (Box)

V = length × width × height

The most fundamental volume formula. Used for rooms, boxes, tanks, and any rectangular container.

Cube

V = side³

A special case of a rectangular prism where all sides are equal.

Cylinder

V = π × r² × h

Where r = radius of the circular base, h = height. Used for cans, pipes, tanks, and pillars.

Sphere

V = (4/3) × π × r³

The volume of a perfect ball. A sphere has 2/3 the volume of its circumscribed cylinder, meaning the shortest cylinder it fits inside, one as tall as it is wide. Archimedes considered that his greatest result and asked for the diagram on his tombstone.

Cone

V = (1/3) × π × r² × h

A cone has exactly 1/3 the volume of a cylinder with the same base and height. Pour water from a cone into a cylinder of the same size: it fills exactly 1/3.

Triangular Prism

V = (1/2) × base × height × length

Where base and height define the triangular cross-section, and length is how far the prism extends.

Square Pyramid

V = (1/3) × base² × height

The Great Pyramid of Giza, with a base of approximately 230 meters and an original height of 146 meters, has a volume of about 2.6 million cubic meters.

Hemisphere

V = (2/3) × π × r³

Exactly half the volume of a full sphere.

Useful Relationships to Remember

Unit Conversion Table

Real-World Applications

• Concrete: How many cubic meters of concrete for a foundation slab?
• Aquariums: Volume determines water capacity in liters or gallons
• Shipping: Box volume determines dimensional weight for freight pricing
• Medicine: Drug dosage is calculated per volume of body surface or organ size
• Cooking: Recipe scaling sometimes requires knowing the volume of a bowl or pan