Volume Calculator – 3D Shapes
Calculate the volume of common 3D shapes: cube, sphere, cylinder, and cone.
Common Volume Formulas
Volume measures the three-dimensional space occupied by an object. Common formulas:
- Cube: V = side³
- Rectangular prism (box): V = length × width × height
- Cylinder: V = pi × r² × h
- Sphere: V = (4/3) × pi × r³
- Cone: V = (1/3) × pi × r² × h
- Pyramid: V = (1/3) × base area × height
All volumes are expressed in cubic units (cm³, m³, ft³, etc.).
Converting Volume Units
Key conversions: 1 m³ = 1,000 liters = 264.2 US gallons. 1 ft³ = 7.48 US gallons = 28.32 liters. 1 US gallon = 3.785 liters. 1 cubic yard = 27 cubic feet = 764.6 liters.
For practical applications: a standard bathtub holds about 300 liters (80 gallons). A swimming pool (10m × 5m × 1.5m) holds 75,000 liters (75 m³). A shipping container (20ft) holds about 33 m³.
Practical Volume Applications
Aquariums: Calculate water volume to determine filter size and fish capacity. Concrete: Calculate cubic yards needed for a project. Moving: Estimate box and truck sizes needed. Cooking: Convert between cups, liters, and milliliters. Gardening: Calculate soil or mulch needed to fill a raised bed.
Frequently Asked Questions
How do I calculate the volume of an irregular shape?
For irregular shapes, use water displacement: submerge the object in a known container of water and measure how much the water level rises. The volume of water displaced equals the volume of the object.
What is the difference between volume and capacity?
Volume is the amount of space an object occupies. Capacity is the amount a container can hold. For practical purposes they are often the same, but technically a thick-walled container has a larger volume than capacity.
How many liters in a cubic meter?
Exactly 1,000 liters = 1 cubic meter. This makes conversion easy: divide liters by 1,000 to get cubic meters, multiply cubic meters by 1,000 to get liters.