How do you calculate the volume of a sphere?

The volume of a sphere is calculated using the formula V = (4/3) * π * r³, where 'r' is the radius of the sphere. For example, if a sphere has a radius of 3 cm, its volume is (4/3) * π * 27 ≈ 113.1 cm³.

What is the formula for cylinder volume?

A cylinder's volume is found using the formula V = π * r² * h, where 'r' is the radius of the circular base and 'h' is the height of the cylinder.

What is the difference between a cone and a cylinder of the same size?

The volume of a cone is exactly one-third of the volume of a cylinder with the same base radius and height. The formula is V = (1/3) * π * r² * h.

How do you calculate the volume of a rectangular prism?

For a box or rectangular prism, simply multiply the three dimensions together: Volume = Length * Width * Height. Make sure all three dimensions are in the same unit system before multiplying.

What is an ellipsoid and how is its volume calculated?

An ellipsoid is a 3D shape similar to a squashed sphere or an egg. Its volume is calculated as V = (4/3) * π * a * b * c, where 'a', 'b', and 'c' are the semi-axes lengths in the three perpendicular directions.

Volume Calculator | 3D Shape Volume Tool

3D Volume Calculator

Select a shape, input its dimensions, and convert calculated volume to all units instantly.

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Provide positive values for the selected shape's dimensions to compute the volume instantly.

Mathematical Formulas of 3D Volumes

**Volume** measures the three-dimensional space occupied by an object. Calculations convert all measurements to a standardized baseline unit before evaluating the geometric equations.

The standard equations utilized by our engine include:

Sphere: V = (4/3) * pi * r³
Cylinder: V = pi * r² * h
Cone: V = (1/3) * pi * r² * h
Cube: V = s³

Rectangular Prism: V = l * w * h
Capsule: V = pi * r² * (4/3 * r + h)
Square Pyramid: V = (1/3) * a² * h
Ellipsoid: V = (4/3) * pi * a * b * c

Our engine automatically handles conversions between metric centimeters, millimeters, meters, and imperial inches, feet, and yards, yielding exact outputs instantly.

Volume Calculation FAQs

Answering common questions about 3D shapes, standard formulas, and capacity conversions.