Volume CalculatorFree online math calculator — instant results, no sign-up

Volume of common 3D shapes.

Inputs

Volume
27

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About the Volume Calculator

This calculator computes the volume of six standard three-dimensional geometric figures: cubes, rectangular boxes, spheres, cylinders, cones, and square pyramids. It is used by students, designers, carpenters, and engineers to find the enclosed space or capacity of solids based on their linear dimensions.

Shape
The 3D shape selected from the dropdown: Cube, Box, Sphere, Cylinder, Cone, or Pyramid (square).
a (side/length/radius)
Side length for a cube or square pyramid base, length for a box, or radius for a sphere, cylinder, or cone (any consistent unit of length > 0).
b (width)
Base width for a rectangular box (used only when Shape is Box; consistent linear units).
Height
Perpendicular height for a box, cylinder, cone, or square pyramid (ignored for Cube and Sphere; consistent linear units).

Formula and method

Cube: V = a^3
Box: V = a × b × h
Sphere: V = (4/3) × π × a^3
Cylinder: V = π × a^2 × h
Cone: V = (π × a^2 × h) / 3
Pyramid (square): V = (a^2 × h) / 3
  • VVolume of the solid
  • aPrimary linear dimension: side length (Cube, Pyramid), length (Box), or radius (Sphere, Cylinder, Cone)
  • bWidth of the rectangular box
  • hPerpendicular vertical height
  • πMathematical constant pi (~3.14159265)

The tool reads the selected geometric shape and applies its corresponding standard geometric volume formula using dimensions a, b, and h. Dimensions not relevant to the chosen shape (such as width and height for a cube or sphere) are ignored in the calculation. The final volume is displayed rounded to up to 6 decimal places.

Worked example

These are the calculator's starting values and the results it actually produces for them.

Inputs

  • ShapeCube
  • a (side/length/radius)3
  • b (width)4
  • Height5

Results

  • Volume27

How to use the Volume Calculator

  1. 1Select the target geometric solid from the Shape dropdown.
  2. 2Enter dimension a (side length, box length, or radius depending on the solid).
  3. 3Enter width b if calculating a rectangular box, and perpendicular height for shapes requiring height.
  4. 4Read the computed total volume in cubic units matching your input measurements.

Reading your result

The result represents the total three-dimensional cubic capacity enclosed by the shape. The units of the volume correspond directly to the cube of the input units (for example, cubic centimeters if measured in centimeters, or cubic meters if measured in meters).

Limitations

The calculator does not convert between different measurement units, requiring all input dimensions to share the same unit of length. It only supports square bases for pyramids and circular bases for cones and cylinders, excluding oblique figures, truncated solids (frustums), or non-square pyramids.

Common questions

What units are used for the resulting volume?+

The calculator is unit-agnostic; it outputs cubic units corresponding to the length units entered. For instance, dimensions entered in inches produce cubic inches, and dimensions in meters yield cubic meters.

Which inputs are needed for a sphere or cube?+

A cube and a sphere only use the dimension 'a' (side length for a cube, radius for a sphere). The width 'b' and 'Height' inputs have no effect on their calculations.

Does height refer to slant height or vertical height?+

Height must always be the perpendicular vertical height from the base to the apex or top plane, not the diagonal slant height along the outer surface.

Does the calculator save my information?+

Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.

Further reading

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Results are estimates for informational purposes and are not financial, medical or legal advice.