Volume Calculator – Cube, Box, Cylinder

🔢 Volume Calculator – How It Works

This volume calculator helps you quickly calculate the volume of common 3D geometric shapes.
Choose a shape, enter the required dimensions, and get instant results in metric or imperial units.

All variables shown in the diagrams match the input fields below the calculator.

📦 Supported Shapes & Formulas

Cube

What: A cube with equal side length.
Variable:

• a – side length

Formula:
V = a³

Rectangular Box

What: A box with different length, width, and height.
Variables:

• l – length

• w – width

• h – height

Formula:
V = l · w · h

Cylinder

What: A cylinder with circular base.
Variables:

• r – radius

• h – height

Formula:
V = π · r² · h

Sphere

What: A perfect sphere.
Variable:

• r – radius

Formula:
V = 4/3 · π · r³

Cone

What: A cone with circular base tapering to a point.
Variables:

• r – base radius

• h – height

Formula:
V = 1/3 · π · r² · h

Capsule

What: A cylinder with two hemispherical ends.
Variables:

• r – radius

• h – height of the cylindrical part

Formula:
V = π · r² · h + 4/3 · π · r³

Hemisphere

What: Half of a sphere.
Variable:

• r – radius

Formula:
V = 2/3 · π · r³

Square Pyramid

What: A pyramid with a square base.
Variables:

• a – base side length

• h – vertical height (from base center to apex)

Formula:
V = 1/3 · a² · h

Rectangular Pyramid

What: A pyramid with a rectangular base.
Variables:

• l – base length

• w – base width

• h – vertical height

Formula:
V = 1/3 · l · w · h

Triangular Prism

What: A prism with a triangular cross-section.
Variables:

• b – triangle base

• ht – triangle height

• l – prism length

Formula:
V = 1/2 · b · ht · l

Spherical Cap

What: A portion (cap) cut from a sphere.
Variables:

• R – radius of the full sphere

• h – cap height (measured from the cut plane to the top of the sphere)

Valid for: 0 ≤ h ≤ 2R

Formula:
V = 1/3 · π · h² · (3R − h)

Conical Frustum

What: A cone with the top cut off.
Variables:

• R – bottom radius

• r – top radius

• h – height

Formula:
V = 1/3 · π · h · (r² + rR + R²)

Ellipsoid

What: A stretched or compressed sphere.
Variables:

• a, b, c – semi-axes in three perpendicular directions

⚠️ If you know the full diameters, enter half the value.

Formula:
V = 4/3 · π · a · b · c

Tube / Pipe

What: The material volume of a hollow cylinder.
Variables:

• d1 – outer diameter

• d2 – inner diameter

• l – length

Condition: d1 > d2

Formula:
V = π · (d1² − d2²) / 4 · l

Torus (Donut Shape)

What: A ring-shaped solid.
Variables:

• R – distance from center to tube center

• r – tube radius

Formula:
V = 2 · π² · R · r²