Volume Calculator

Volume versus area

Volume is a three-dimensional measure: how much space a shape takes up, or how much material (water, air, sand) it can hold. While area is measured in square units (m², cm²), volume is measured in cubic units (m³, cm³) — because you multiply three dimensions: length × width × height.

Every 3D shape has its own formula. The constant π (pi, about 3.14159) appears in every round shape: cylinder, sphere and cone. Notice that a cylinder and a cone with the same base and height — the cone has only a third of the volume of the cylinder that encloses it!

Three worked examples

• Fish tank 30×40×20 cm: V = 30·40·20 = 24,000 cm³ = 24 litres.
• Cylinder r=5, h=10: V = π·5²·10 = 250π ≈ 785.4.
• Sphere r=6: V = (4/3)·π·6³ = 288π ≈ 904.8.

Common mistakes

• Remember to check units (cm vs m): 1 m³ = 1,000,000 cm³.
• A hemisphere = ½ V of a full sphere — don't forget the half.
• A cone and a pyramid both have a third (1/3) — a common mistake is to calculate them like a cylinder/cuboid.
• For a sphere you cube, not square — V = (4/3)·π·r³.
• Surface area ≠ volume: both are useful, but they measure different things.

Why does this matter?

💼 Building, packaging, working out how much water a pool holds, fridge capacity, fuel volume in a tank, how much raw material a production run needs — any time you need to know "how much fits inside" or "how much space this takes up".