FinanceCalcs
Volume Calculator
Volume is the amount of 3D space a shape takes up — like how much water a container can hold. Choose any 3D shape, enter the measurements, and get the volume with the formula and step-by-step working.
Step-by-Step Working
Volume in Other Units
"Archimedes discovered how to find the volume of a sphere by noticing that a ball submerged in water displaces water equal to its own volume. He reportedly jumped out of the bath shouting ‘Eureka!’ (I found it!)"
Volume formulas at a glance
| Shape | Formula |
|---|---|
| Cube | V = s³ |
| Rectangular prism | V = l × w × h |
| Cylinder | V = πr²h |
| Sphere | V = &frac43;πr³ |
| Cone | V = ⅓πr²h |
| Square pyramid | V = ⅓ × s² × h |
Quick Questions
What units is volume measured in?
Volume is measured in cubic units. If your lengths are in cm, the volume is in cm³ (cubic centimeters). The key ones to know: 1 liter = 1000 cm³, 1 milliliter = 1 cm³, 1 cubic meter = 1000 liters. So a 10cm × 10cm × 10cm box holds exactly 1 liter!
Why do cones and pyramids have a ⅓ in the formula?
A cone takes up exactly one third of the cylinder that surrounds it (same base, same height). A pyramid takes up exactly one third of the prism that surrounds it. This was proved by Cavalieri’s principle — if you slice them at every height, the cone slices are always one third the area of the cylinder slices.
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