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. Note: a sphere has 2/3 the volume of its circumscribed cylinder (the smallest cylinder that fits around it) — a fact discovered by Archimedes that he considered his greatest achievement.

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