Volume Calculator

How it works

Matching dimensions to a solid shape

Volume measures the space inside the modeled solid. Select the correct shape and distinguish radius, diameter, height, and slant-related measurements using the field labels. All dimensions must use compatible units before combining them. The result uses cubic units and describes the idealized shape; wall thickness, openings, or irregular geometry need a mode or separate calculation that accounts for them.

Sphere: formula and assumptions

V = 4πr³/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cone: formula and assumptions

V = πr²h/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cube: formula and assumptions

V = a³.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Cylinder: formula and assumptions

V = πr²h.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Rectangular prism: formula and assumptions

V = length × width × height.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Capsule: formula and assumptions

V = πr²h + 4πr³/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Spherical cap: formula and assumptions

V = πh²(3r−h)/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Conical frustum: formula and assumptions

V = πh(r²+rr₂+r₂²)/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Ellipsoid: formula and assumptions

V = 4πabc/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Rectangular pyramid: formula and assumptions

V = abh/3.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Hollow cylinder: formula and assumptions

V = π(r²−r₂²)h.

Use consistent length units. Dimensions must be positive. A spherical cap includes its flat base; ellipsoid surface area is an approximation. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Spherical cap alternate dimensions: formula and assumptions

R=(base radius²+h²)/(2h); h=R±√(R²−base radius²).

Sphere radius and base radius can describe a minor and a major cap; both are shown. Each dimension can use its own unit. Results use the selected output unit with the appropriate square or cube.

Worked example

Using the Sphere example:

Radius

5

Radius unit

Meters

Result length unit (squared for area, cubed for volume)

Meters

V = 4πr³/3.

Example result

These are illustrative inputs. Change the values to explore a different scenario.

Formula references

• OpenStax: Algebra and Trigonometry (opens in a new tab)

References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.

Common questions