This volume calculator finds the volume of the common 3-D solids — cube, rectangular box, cylinder, sphere and cone. Pick a shape, enter its dimensions, and get the volume with the formula shown.
The Volume Formulas in One Place
| Shape | Formula | Example (verified) |
|---|---|---|
| Rectangular box | l × w × h | 10 × 6 × 4 = 240 |
| Cube | edge³ | 5³ = 125 |
| Cylinder | πr²h | π × 3² × 10 = 282.74 |
| Sphere | (4/3)πr³ | (4/3)π × 5³ = 523.60 |
| Cone | (1/3)πr²h | ⅓ × π × 3² × 10 = 94.25 |
This calculator is part of our Math Calculators collection.
Volume in Real Life
- Tanks and pools: cylinder volumes become gallons (1 ft³ = 7.48 US gallons; 1 m³ = 1,000 liters).
- Concrete and gravel: ordered by the cubic yard (27 ft³) — specialized in our Concrete Calculator.
- From volume to weight: multiply by density — the job of our Density Calculator (water: 1 g per cm³, 62.4 lb per ft³).
- The scaling trap, cubed: doubling every dimension multiplies volume by 8 — why big aquariums are so heavy and why elephants need proportionally thicker legs.
Units Reminders
- Volume is in cubic units: ft³, m³, cm³. 1 m³ = 1,000 L = 35.31 ft³.
- All dimensions must share a unit before you multiply — mixing inches and feet is the classic error.
- A cone is exactly ⅓ of its cylinder, and a sphere is exactly ⅔ of its circumscribing cylinder — relationships Archimedes was so proud of that he put them on his tombstone.
Related Tools
- Density Calculator — volume ⇄ mass
- Concrete Calculator — cubic yards and bags
- Area Calculator — the 2-D counterpart
Frequently Asked Questions
How do I calculate the volume of a box?
Multiply length × width × height: 10 × 6 × 4 = 240 cubic units.
What is the volume of a cylinder?
πr²h — the circular base area times the height. Radius 3, height 10: 282.74.
How many liters are in a cubic meter?
Exactly 1,000. And one liter is 1,000 cm³ — the metric system’s volume ladder is built on the cube.
Why is a cone one third of a cylinder?
It can be proven by calculus — and demonstrated by filling: three cones of sand exactly fill the matching cylinder. The ratio is exact, not approximate.
How do I find the volume of an irregular object?
Water displacement: submerge it and measure the water level rise — that rise is the volume (Archimedes’ bathtub insight). Then mass ÷ volume gives density.
Is this volume calculator free?
Yes — free, instant, no sign-up.