Getting started
Volume measures the amount of three-dimensional space an object occupies, expressed in cubic units. Whether you're calculating storage capacity, material requirements, or liquid volume, this calculator handles five common shapes: rectangular boxes, spheres, cylinders, cones, and square pyramids. Input your dimensions, select the shape, and get an instant result.
The formula
Each shape has its own volume formula:
- Box:
V = l × w × h - Sphere:
V = (4/3) × π × r³ - Cylinder:
V = π × r² × h - Cone:
V = (1/3) × π × r² × h - Square Pyramid:
V = (1/3) × b² × h
Worked example
Example 1: Rectangular box
You have a storage container measuring 8 meters long, 5 meters wide, and 3 meters tall.
- Length = 8 m
- Width = 5 m
- Height = 3 m
- Volume = 8 × 5 × 3 = 120 m³
Example 2: Cylinder
A water tank has a radius of 2 meters and is 6 meters tall.
- Radius = 2 m
- Height = 6 m
- Volume = π × 2² × 6 = π × 4 × 6 = 24π ≈ 75.4 m³
Example 3: Sphere
A spherical storage ball has a radius of 1.5 meters.
- Radius = 1.5 m
- Volume = (4/3) × π × 1.5³ = (4/3) × π × 3.375 ≈ 14.1 m³
Example 4: Cone
An ice cream cone has a radius of 3 cm and height of 10 cm.
- Radius = 3 cm
- Height = 10 cm
- Volume = (1/3) × π × 3² × 10 = (1/3) × π × 90 ≈ 94.2 cm³
Example 5: Square pyramid
A pyramid has a square base with 4-meter sides and a height of 9 meters.
- Base side = 4 m
- Height = 9 m
- Volume = (1/3) × 4² × 9 = (1/3) × 16 × 9 = 48 m³
Common mistakes
Confusing radius and diameter: Many people accidentally use diameter instead of radius for spheres and cylinders. Remember: radius is half the diameter. If a sphere has a 10 cm diameter, use 5 cm as the radius.
Forgetting the cubic units: Volume always has three dimensions, so results must be expressed as cubic units (cm³, m³, ft³). Simply writing "120" without units is incomplete.
Mixing measurement systems: Ensure all dimensions use the same unit before calculating. If you measure length in meters and height in centimeters, convert one to match the other first.
Assuming all pyramids are square: This calculator works only for pyramids with square bases. Triangular or rectangular pyramids require different calculations.