Volume Calculator
Calculate the volume of cuboids, cylinders, spheres, cones, and pyramids — formula, substitution, and step-by-step working shown.
Volume calculator
Step by step calculations
Choose a shape, enter measurements and press Calculate to see the step by step formula and working.
Volume Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
When would you actually use this?
Every time you fill something — a fish tank, a concrete post hole, a storage crate — you're calculating volume. A standard fish tank 60 cm long, 30 cm wide and 35 cm deep holds exactly 63 litres of water (60 × 30 × 35 = 63,000 cm³ = 63 litres). That's volume in action.
Worked example
"You're filling a raised garden bed with concrete. It's 1.2 m long, 0.6 m wide and 0.15 m deep. How much concrete do you need?"
Formula: V = l × w × h
V = 1.2 × 0.6 × 0.15
Result: 0.108 m³
Ready-mix concrete bags cover roughly 0.018 m³ each — so you'd need 6 bags.
The ⅓ rule — cones and pyramids
A cone holds exactly ⅓ the volume of a cylinder with the same base and height. Fill a cone-shaped party cup with water and pour it into a matching cylinder — it takes precisely 3 fills. This is why an ice cream cone can't hold much, but a tin can holds far more than it looks.
Mistake to avoid
Using the slant height instead of the perpendicular height for a cone or pyramid. The formula always needs the height measured straight down — not along the sloped edge.
Volume — key concepts
Volume vs Capacity
Volume is the amount of 3D space a shape occupies (measured in cm³, m³). Capacity is how much liquid a container holds (measured in litres, ml). 1 cm³ = 1 ml, so 1000 cm³ = 1 litre.
The ⅓ rule for pyramids and cones
Any pyramid has exactly ⅓ the volume of the prism with the same base and height. A cone has ⅓ the volume of a cylinder. You can prove this by filling a cone-shaped cup exactly 3 times to fill a cylinder of the same size.
Sphere formula — where does it come from?
V = &frac43;πr³ was first proved by Archimedes. He showed a sphere fits perfectly inside a cylinder with height 2r and radius r — and the sphere’s volume is exactly ⅔ of that cylinder. (Vcyl = πr²×2r = 2πr³, ⅔ of that = &frac43;πr³)
Scaling volumes
If you double all dimensions of a shape, the volume increases by 2³ = 8 times. Triple the dimensions → 27 times the volume. This is why a giant version of something is so much heavier than you’d expect — volume (and mass) scales with the cube of the linear dimension.