Volume of Shapes Calculator
Calculate the volume of any 3D shape — sphere, cylinder, cone, rectangular prism, pyramid, and more.
Includes unit conversion for all common units.
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
| Shape | Volume |
|---|---|
| Cone | = 1/3 of cylinder |
| Hemisphere | = 1/2 of sphere |
| Sphere | = 2/3 of circumscribed cylinder |
Unit Conversion Table
| From | To | Multiply by |
|---|---|---|
| 1 ft³ | liters | 28.317 |
| 1 in³ | cm³ | 16.387 |
| 1 m³ | liters | 1,000 |
| 1 gallon | liters | 3.785 |
| 1 cm³ | mL | 1 (exact) |
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