The volume is:
Table of Contents
Volume of cubes, cylinders, rectangles & spheres
Pick a shape, enter its dimensions, and this calculator returns the volume — the amount of three-dimensional space the object occupies. Use it for tanks, containers, packages, sports balls, fish tanks and any other geometry where you need to know “how much fits inside.”
The formulas
Each shape has its own formula, all in the same family — base area times height, generalised:
| Shape | Formula | Inputs |
|---|---|---|
| Cube | V = s³ | side length s |
| Rectangular prism | V = L × W × H | length, width, height |
| Cylinder | V = πr²h | radius, height |
| Sphere | V = (4/3)πr³ | radius |
For the cube the calculator uses the length input as the side. For the cylinder it uses width as the radius and height as the cylinder’s height. For the sphere it uses width as the radius.
Worked example
Using the defaults (length 20 cm, width 50 cm, height 100 cm) on a rectangular prism:
- Multiply length and width: 20 × 50 = 1,000.
- Multiply by height: 1,000 × 100 = 100,000.
So V = 100,000 cm³ = 100 litres — about the volume of a small chest freezer.
For comparison, the cube formula with side 20 gives V = 20³ = 8,000 cm³ (8 litres). The cylinder formula with radius 50 cm and height 100 cm gives V = π × 50² × 100 ≈ 785,398 cm³ (785 litres). The sphere formula with radius 50 cm gives V = (4/3) × π × 50³ ≈ 523,599 cm³ (524 litres).
Reference table
Volume in cm³ for unit measurements, to compare how shapes scale:
| Linear size | Cube (s³) | Sphere ((4/3)πr³) | Cylinder (πr²h, h=r) |
|---|---|---|---|
| 1 | 1.00 | 4.19 | 3.14 |
| 2 | 8.00 | 33.51 | 25.13 |
| 5 | 125.00 | 523.60 | 392.70 |
| 10 | 1,000.00 | 4,188.79 | 3,141.59 |
| 20 | 8,000.00 | 33,510.32 | 25,132.74 |
Doubling the linear dimension gives 8× the volume for every shape — that’s the cube law at work.
Unit conversions
Volume units depend on the length unit cubed:
- 1 m³ = 1,000,000 cm³ = 1,000 litres
- 1 litre = 1,000 cm³ = 1,000 mL
- 1 US gallon ≈ 3,785 cm³ ≈ 3.785 L
- 1 UK (imperial) gallon ≈ 4,546 cm³ ≈ 4.546 L
- 1 ft³ ≈ 28.32 L ≈ 7.481 US gal
- 1 in³ ≈ 16.39 cm³
Common applications
- Aquariums. A 60 × 30 × 30 cm tank holds 54,000 cm³ = 54 L. Stocking rules of thumb (e.g. one inch of fish per US gallon) all start from volume.
- Shipping & freight. Carriers charge by “dimensional weight,” calculated from L × W × H. Volume can cost you more than mass.
- Concrete & bulk materials. Concrete is ordered in m³; gravel and topsoil in m³ or yards³. Always work in the supplier’s unit.
- Sports. A FIFA-spec football has a circumference of 68–70 cm, giving a radius near 11 cm and a volume around 5,575 cm³.
Limitations & gotchas
- All dimensions must use the same length unit. Mixing inches and centimetres breaks the result.
- Don’t confuse radius with diameter for cylinders and spheres. Halve the diameter before entering it.
- These formulas describe the internal volume of an idealised shape. Real containers have wall thickness; subtract it if you need the holding capacity.
- Irregular or composite shapes (a cone-bottomed tank, a hexagonal prism) need additional formulas or decomposition into the four supported shapes.
Sources & references
- Weisstein, Eric W. “Cube,” “Cylinder,” “Sphere.” Wolfram MathWorld.
- NIST Physical Measurement Laboratory, “SI Units — Volume.”
- Britannica, “Volume (mathematics).” Encyclopaedia Britannica.
FAQs
Cube volume is V = s³, where s is the length of one edge. All edges of a cube are equal, so cubing one side gives the total internal space. For a 5 cm cube, V = 5³ = 125 cm³.
Cylinder volume is V = πr²h, where r is the radius of the circular base and h is the height. It’s the base area (πr²) multiplied by how tall the cylinder is. A can with r = 4 cm and h = 12 cm holds π × 16 × 12 ≈ 603 cm³.
Sphere volume is V = (4/3)πr³, where r is the radius. The cube on the radius is why a sphere’s volume grows fast as it gets bigger: doubling r increases volume by a factor of 8. A football with r = 11 cm has V ≈ 5,575 cm³.
Volume is the amount of three-dimensional space an object occupies; capacity is how much fluid that space can hold. They measure the same thing but with different units — 1,000 cm³ equals 1 litre. A water bottle has both a volume (the space inside) and a capacity (the litres of water it holds).
Yes — halve it first. For a cylinder: V = π(d/2)²h. For a sphere: V = (4/3)π(d/2)³ = πd³/6. Using the diameter directly without halving is the single most common volume-calculation mistake.
Whatever length unit you used for the inputs, cubed. Centimetres in → cm³ out. Inches in → in³ out. Useful conversions: 1 m³ = 1,000 litres = 1,000,000 cm³; 1 US gallon ≈ 3,785 cm³; 1 cubic foot ≈ 28.32 litres.