Volume Calculator
Volume of boxes, cylinders, spheres and cones.
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Work out how much a shape holds or contains. Choose a box, cylinder, sphere, or cone, enter the dimensions, and this calculator gives the volume in cubic units plus litres and gallons for practical use.
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Volume — The Quick Answer
A box's volume is length × width × height; a cylinder is πr²h; a sphere is (4/3)πr³; a cone is one-third of the matching cylinder, ⅓πr²h.
Shortcut
Box: LWH | Cylinder: πr²h | Sphere: (4/3)πr³ | Cone: ⅓πr²h
Volume formulas by shape
| Shape | Formula | Inputs |
|---|---|---|
| Box / prism | V = L × W × H | length, width, height |
| Cylinder | V = πr²h | radius, height |
| Sphere | V = (4/3)πr³ | radius |
| Cone | V = ⅓πr²h | radius, height |
A cone holds exactly one-third of the cylinder with the same base and height — a relationship worth remembering, and it's why cones are so much lighter than their footprint suggests.
How It Works
The Formulas
Volume by shape
Formula
Box: V = L × W × H Cylinder: V = π r² h Sphere: V = (4/3) π r³ Cone: V = ⅓ π r² h
Variables
Radius
Half the diameter. Appears squared in cylinder and cone formulas, so small changes in radius matter a lot.
Height
The perpendicular height — for a cylinder, the distance between the flat circular ends.
Box dimensions
The three side lengths of a rectangular box, all in the same unit.
Note: For a pyramid or cone, the volume is always one-third of the prism or cylinder that boxes the same base and height — a simple pattern worth remembering.
Worked Example: A 3 × 2 × 2 ft Box
Volume, then capacity
Pick the shape
Box / rectangular prism
Apply V = L × W × H
3 × 2 × 2
Compute
= 12 cubic feet
Convert to capacity
12 cu ft ≈ 340 litres ≈ 90 US gallons
Reference Guide
| Shape | Formula | Inputs |
|---|---|---|
| Box / prism | V = L × W × H | length, width, height |
| Cylinder | V = π r² h | radius, height |
| Sphere | V = (4/3) π r³ | radius |
| Cone | V = ⅓ π r² h | radius, height |
Reading the Result & Units
Base area × height, and converting capacity
A box is length × width × height; a cylinder is its circular base (πr²) times height. Once you see that, prisms and cylinders are the same idea — the area of the base, multiplied by how tall the shape is.
Best for: Understanding the common pattern
A sphere is (4/3)πr³ — radius cubed, so size has an outsized effect (double the radius, eight times the volume). A cone or pyramid is exactly one-third of the cylinder or prism that shares its base and height.
Best for: Remembering the special cases
Cubic units and litres/gallons measure the same quantity: 1 m³ = 1,000 L, and 1 cu ft ≈ 28.3 L ≈ 7.48 US gallons. Keep every measurement in one unit before multiplying, and the result is in cubic units.
Best for: Working out how much a tank or space holds
How to Calculate Volume
Volume is the three-dimensional cousin of area — how many unit cubes fit inside a shape, measured in cubic units. For most shapes the rule is 'base area × height': a box is length × width × height, a cylinder is πr² × h. A sphere is (4/3)πr³, where the cubed radius means size matters enormously, and a cone or pyramid is always exactly one-third of the cylinder or prism that boxes it. Volume and capacity describe the same thing in different units — 1 m³ is 1,000 litres; 1 cu ft is about 28.3 litres. This calculator handles boxes, cylinders, spheres, and cones and converts the result to litres and gallons.
Key Features
💡 Pro Tips
- →For a tank's capacity, calculate the volume then read the litres or gallons figure directly.
- →Remember a cone or pyramid holds a third of the cylinder or box with the same base and height.
- →A sphere's volume grows with the cube of its radius, so small size changes have large effects.
- →Keep every dimension in the same unit before multiplying; the answer comes out in cubic units.
Common Mistakes
Mixing units
Multiplying metres by centimetres gives a wrong answer. Convert all three dimensions to one unit before calculating.
Forgetting the one-third for cones and pyramids
A cone is not the same as its enclosing cylinder — it holds exactly a third. Using the cylinder formula overstates a cone's volume threefold.
Using diameter instead of radius
Cylinder, sphere, and cone formulas use the radius (half the diameter). Plugging in the diameter inflates the volume by a factor of four or eight.
Research & Citations
Sources and standards referenced for the factual claims on this page
- [1]
Archimedes (-225). On the Sphere and Cylinder. Classical mathematics.
Classical derivation of sphere and cylinder volumes.
View source - [2]
Euclid (-300). Elements, Book XII — the one-third relationship for cones and pyramids. Classical mathematics.
Classical basis for the cone/pyramid one-third rule.
View source
This calculator is a reference tool, not a substitute for professional advice. Verify important health, financial, legal, or safety decisions with a suitably qualified professional.
Last updated: October 7, 2026
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Frequently Asked Questions
How do I calculate the volume of a box?
Multiply length × width × height: V = L × W × H. A box 3 ft × 2 ft × 2 ft has a volume of 12 cubic feet. Keep all three measurements in the same unit.
What's the volume of a cylinder?
V = π × r² × h, where r is the radius of the circular base and h is the height. A cylinder with a 2 ft radius and 5 ft height holds π × 4 × 5 ≈ 62.8 cubic feet.
How do I find the volume of a sphere?
Use V = (4/3) × π × r³. A sphere with a 3 ft radius has a volume of (4/3) × π × 27 ≈ 113.1 cubic feet. Note the radius is cubed, so volume grows very fast with size.
How do I convert volume to litres or gallons?
One cubic metre is 1,000 litres; one cubic foot is about 28.32 litres or 7.48 US gallons. This calculator does the conversions automatically, so you don't need to look them up.