Volume Calculator
Formula: Volume = side³
Volume: 125.00 cm³
How to use this calculator
First, pick a shape from the shape selector. You can choose a cube, a cuboid (also called a rectangular box), a cylinder, a sphere or a cone. Only the inputs for the shape you have picked are shown, so you never have to guess which dimensions belong to which shape.
Next, enter the dimensions of that shape, using positive numbers only. A cube needs just its side. A cuboid needs its length, width and height. A cylinder needs its radius and height. A sphere needs only its radius. A cone needs its radius and height. Then pick a unit from the unit selector: centimetres, metres, inches or feet. One unit applies to every dimension you enter, so all of your measurements must be in that same unit.
Finally, read the answer and the formula. The calculator updates live as you type, with no button to press. The answer is given in cubic units, which match the unit you picked: cubic centimetres (cm³) for centimetres, cubic metres (m³) for metres, cubic inches (in³) for inches and cubic feet (ft³) for feet. The formula shown next to the answer is the formula being used for the selected shape, so you can see exactly how the result was worked out.
Worked examples
Cube, side 5 cm: a cube with a side of 5 cm has a volume of 5³, which is 5 times 5 times 5, giving 125 cm³. Every side of a cube is the same length, so only one measurement is needed.
Cuboid, 4 by 3 by 2 m: a rectangular box with a length of 4 m, a width of 3 m and a height of 2 m has a volume of 4 times 3 times 2, giving 24 m³. This is the same idea as counting how many unit cubes would fit inside the box.
Cylinder, radius 3 cm, height 10 cm: a cylinder with a radius of 3 cm and a height of 10 cm has a volume of π times 3² times 10, which is π times 9 times 10, giving 282.74 cm³. The circular base gives the area, and the height stretches that area into a volume.
Sphere, radius 5 cm: a sphere with a radius of 5 cm has a volume of (4/3) times π times 5³, which is (4/3) times π times 125, giving 523.60 cm³. A sphere is the set of points at a fixed distance from its centre, so the radius alone determines its volume.
Cone, radius 4 cm, height 9 cm: a cone with a radius of 4 cm and a height of 9 cm has a volume of (1/3) times π times 4² times 9, which is (1/3) times π times 16 times 9, giving 150.80 cm³. A cone holds exactly one third of the volume of a cylinder with the same radius and height, which is where the factor of one third comes from.
Volume formulas at a glance
| Shape | Formula |
|---|---|
| Cube | side³ |
| Cuboid | length × width × height |
| Cylinder | π × radius² × height |
| Sphere | (4/3) × π × radius³ |
| Cone | (1/3) × π × radius² × height |
The table above is a quick reference for all five shapes. The cube and cuboid formulas use multiplication only, while the round shapes — the cylinder, sphere and cone — all involve π, because they are built from circles. Keep the unit the same for every dimension, and the answer will be in the matching cubic unit.
Frequently asked questions
Which shape do I pick? Pick the shape that matches the object you are measuring. A box-shaped object is a cuboid, a ball is a sphere, a tin or pipe is a cylinder, an ice-cream cone shape is a cone, and a dice shape, with all sides equal, is a cube. If the object is not exactly one of these shapes, pick the closest one and treat the result as an approximation.
Can I mix units? No. Keep one unit for all dimensions. If your length is in centimetres and your width is in metres, convert one of them first so that every dimension uses the same unit. Mixing units would give a meaningless answer, so the calculator applies the unit you pick to every dimension.
What does cubic mean here? Cubic means the answer is a volume, not a length or an area. A length is measured in cm, an area in cm² and a volume in cm³. You can think of cm³ as the number of 1 cm by 1 cm by 1 cm cubes that would fill the shape.
Does it work for hollow objects? No. This calculator gives the volume of the solid shape, as if the shape were filled all the way through. For a hollow object, such as an empty box or a hollow ball, you would need to subtract the volume of the empty space inside, which this calculator does not do.
Why is π in the round shapes? Because circles are involved. The area of a circle is π times the radius squared, and the cylinder, sphere and cone are all built from circles in one way or another. That is why π appears in their volume formulas, while the cube and cuboid, which have only straight edges and flat rectangular faces, do not need it.