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Volume is the three-dimensional space an object occupies — a measure of how much fits inside. How many litres an aquarium holds, a tank's capacity, how many cubic metres of concrete you need, a parcel's shipping volume: all start with a volume calculation. Every solid has its own formula, and placing the height and radius correctly determines the result.
Pick a solid, enter the dimensions, and the volume is calculated instantly in the cube of your unit (cm³, m³…).
How is it calculated?
Formulas
| Solid | Volume formula |
|---|---|
| Cube | side³ |
| Rectangular prism | length × width × height |
| Cylinder | π × radius² × height |
| Sphere | (4 ÷ 3) × π × radius³ |
| Cone | (1 ÷ 3) × π × radius² × height |
Units and litre conversion
- The volume comes out in the cube of whatever unit you enter: metres → m³, centimetres → cm³.
- 1 m³ = 1,000 litres, 1 litre = 1,000 cm³ (1 dm³). For an aquarium or tank, convert to litres: 0.3 m³ = 300 litres.
Common mistakes
- Radius vs diameter: the cylinder, sphere and cone formulas use the radius; if you have the diameter, halve it.
- Cone and sphere coefficients: a cone is one-third of a cylinder with the same base and height; forget the 4/3 in the sphere formula and the result is wrong.
- Correct height axis: in a cylinder and cone the height is the length perpendicular to the base.
For a surface calculation use an area calculator.
Worked example
A cylindrical water tank with a radius of 3 m and a height of 10 m: π × 3² × 10 = 3.14159 × 9 × 10 = 282.74 m³ — that is, it holds 282,743 litres. For comparison, a sphere of radius 6 m is 904.78 m³, and a cone with a 4 m radius and 9 m height is 150.80 m³. Note that the cone is exactly one-third of a cylinder with the same base and height: forgetting that 1/3 coefficient is the most common calculation error.
FAQ
How is volume calculated?+
By solid type: cube is side³, prism is length × width × height, cylinder is π × radius² × height, sphere is (4/3)πr³, cone is (1/3)πr² × height. Pick the solid and enter the dimensions.
How do I convert cubic metres to litres?+
1 cubic metre = 1,000 litres. So 282.74 m³ = 282,743 litres. For small volumes use 1 litre = 1,000 cm³ (1 dm³).
What is the formula for the volume of a cylinder?+
The base circle area (πr²) times the height: π × radius² × height. A cylinder with radius 3 and height 10 is 282.74 cubic units.
How are cone and cylinder volumes related?+
A cone with the same base and height is exactly one-third of the cylinder. That is why the cone formula has the 1/3 coefficient; omit it and the volume comes out three times too large.
How do I find how many litres an aquarium holds?+
For a rectangular aquarium, length × width × height, then convert to litres: 50 cm × 30 cm × 40 cm = 60,000 cm³ = 60 litres. If it is not full to the top, use the actual water height.
What unit does volume come out in?+
The cube of the length unit you enter: metres → m³, centimetres → cm³. For litres, multiply an m³ result by 1,000 or divide a cm³ result by 1,000.