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Volume of Common Shapes calculator

Volume and surface area of a cube, box, sphere, cylinder or cone from its dimensions.

What this calculator does

This volume calculator answers the everyday question of how to calculate volume for a shape you can measure: pick the shape, enter its dimensions, and the volume and surface area come out together, in one tool instead of five separate ones.

Every shape here uses its own volume formula, from a cube's simple a³ up to a cone's (1/3)πr²h, but they share the same idea underneath: volume is the amount of three-dimensional space a shape occupies, always expressed in cubic units, whether that is cubic centimetres, cubic metres, or litres once divided by 1,000.

The formula

FormulaCube: a³ · Box: l·w·h · Sphere: (4/3)πr³ · Cylinder: πr²h · Cone: (1/3)πr²h

Each shape uses its own formula: a cube is side³; a rectangular box is length × width × height; a sphere is (4/3)πr³; a cylinder is πr²h; and a cone is one third of a cylinder's volume, (1/3)πr²h, because a cone tapers to a point instead of keeping a constant cross-section.

TermMeaning
VolumeThe amount of three-dimensional space a shape encloses, in cubic units.
Surface areaThe total area of every face or curved surface of the shape, in square units.
RadiusThe distance from the centre to the edge, used for spheres, cylinders and cones instead of a side length.

The inputs explained

FieldWhat to enter
ShapeThe shape whose volume you want to calculate.
Side length, or radius for sphere/cylinder/coneFor a cube this is the side length; for a box, the length; for sphere, cylinder or cone, the radius.
Width (box only)The width of the box, only used when the shape is a rectangular box.
Height (box, cylinder & cone only)The height, only used for a box, cylinder or cone.

When to use it

Working out how to calculate volume for a container

A box, tank or tube with known dimensions gives its capacity directly in cubic units, which converts to litres by dividing by 1,000 if the dimensions were entered in centimetres.

Checking a volume formula for schoolwork

Switching between shapes with the same calculator makes the pattern easier to see: a cylinder and a cone with the same radius and height differ by exactly a factor of three.

Estimating material for a spherical or conical object

A dome, ball or funnel-shaped part is rarely a rectangular box, and using the matching sphere or cone formula avoids the common mistake of treating every shape like a box.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How much does volume grow as a cube's side length increases?

A cube, with its side length stepped up across a range of sizes.

Cube, side length varied
Side lengthVolumeSurface area
28.00024.000
464.00096.000
6216.000216.000
8512.000384.000
101,000.00600.000
208,000.002,400.00
Doubling a cube's side length multiplies its volume by eight (2³), not two, which is why a cube twice as tall as another holds eight times as much, not twice as much.

Volume of a cylinder at a fixed height, as the radius increases

A cylinder of height 10, with its radius stepped up across a range of sizes.

Cylinder, height 10, radius varied
RadiusVolumeSurface area
131.41669.115
2125.664150.796
3282.743245.044
4502.655351.858
5785.398471.239
61,130.97603.186
Volume grows with the square of the radius, so doubling the radius from 2 to 4 roughly quadruples the volume, while the height stays the same.

Questions

What is the formula for volume?

It depends on the shape: a cube is side³, a box is length × width × height, a sphere is (4/3)πr³, a cylinder is πr²h and a cone is (1/3)πr²h. There is no single volume formula that covers every shape.

How do I calculate the volume of an irregular object?

This calculator only handles the five regular shapes listed. An irregular object is usually measured by displacement, submerging it in a known volume of water and reading the rise, since there is no simple formula for an arbitrary shape.

Why is a cone's volume a third of a cylinder's?

A cone with the same base radius and height as a cylinder tapers steadily to a point rather than keeping a constant cross-section all the way up, and integrating that taper gives exactly one third of the cylinder's volume, a result that holds for any cone or pyramid against its matching prism.

How do I convert volume in cubic centimetres to litres?

Divide by 1,000: one litre is exactly 1,000 cubic centimetres. This calculator shows that conversion automatically underneath the main volume figure whenever the dimensions are entered in centimetres.

For a full ladder of volume and capacity units, litres, gallons, cups and more, see the volume & capacity converter. For the perimeter of a flat, two-dimensional shape instead, use the perimeter calculator.