Volume measures the three-dimensional space inside a solid object. Unlike surface area (which covers the outside), volume tells you how much a shape can hold — useful for tanks, containers, packaging, and construction estimates.
What Is Volume?
Volume is the amount of space enclosed within a 3D shape. It is measured in cubic units such as m³, cm³, ft³, or in litres (L) and millilitres (mL). One litre equals 1,000 cm³.
Cylinder Volume
Where r = radius of circular base, h = height (or length) of the cylinder.
The cylinder is one of the most common volume calculations. Think of cans, pipes, drums, and silos. The base area (πr²) is multiplied by the height.
Example: A cylinder with r = 3 cm and h = 10 cm → V = π × 9 × 10 = 282.74 cm³.
Sphere Volume
Where r = radius of the sphere.
The sphere formula is derived from integral calculus. The key insight: volume grows with the cube of the radius, so doubling r gives 8× the volume.
Example: A sphere with r = 5 cm → V = (4/3) × π × 125 = 523.60 cm³.
Cone Volume
Where r = base radius, h = perpendicular height.
A cone is exactly one-third the volume of a cylinder with the same base and height. This relationship is fundamental in geometry.
Example: A cone with r = 4 cm and h = 9 cm → V = (1/3) × π × 16 × 9 = 150.80 cm³.
Cube Volume
Where a = side length of the cube.
The simplest volume formula. All edges are equal, so you multiply the side length by itself three times.
Example: A cube with a = 6 cm → V = 216 cm³.
Rectangular Prism (Cuboid) Volume
Where l = length, w = width, h = height.
Boxes, rooms, shipping containers, and bricks are all rectangular prisms. Multiply the three perpendicular dimensions.
Example: A box 5 m × 3 m × 2 m → V = 30 m³.
Pyramid Volume
Where B = area of the base, h = perpendicular height from base to apex.
For a square-based pyramid with side a: B = a². For a triangular base with side a: B = (√3/4)a². Any pyramid is one-third the volume of a prism with the same base and height.
Example: Square base a = 4 cm, h = 9 cm → V = (1/3) × 16 × 9 = 48 cm³.
Triangular Prism Volume
Where b = triangle base, hₜ = triangle height, L = prism length.
Calculate the triangle cross-section area first ((1/2)b × hₜ), then multiply by the length of the prism.
Example: b = 6 cm, hₜ = 4 cm, L = 10 cm → V = (1/2) × 6 × 4 × 10 = 120 cm³.
Common Volume Mistakes
- Using diameter instead of radius — always halve the diameter first.
- Forgetting the 1/3 factor for cones and pyramids.
- Mixing units — convert all dimensions to the same unit before calculating.
- Confusing height with slant height — volume uses perpendicular height only.
- Forgetting cubic units — volume is cm³, not cm².
Volume Unit Conversions
| Unit | Equivalent |
|---|---|
| 1 m³ | 1,000 L = 1,000,000 cm³ |
| 1 L | 1,000 mL = 1,000 cm³ |
| 1 ft³ | 28.317 L = 7.481 US gal |
| 1 US gal | 3.785 L = 231 in³ |
Use the Cylinder Volume Calculator, Sphere Volume Calculator, or any of the volume calculators for instant results with unit conversion.