Math formulas

Solid geometry formulas

Calculate volumes, surface areas, and dimensions of common three-dimensional solids.

Formulas and calculators

Calculate volume, total surface area, or a missing edge of a cube or rectangular cuboid.

Cuboid: V = abc, S = 2(ab + ac + bc); cube: V = a³, S = 6a²

Calculated quantities

V - volume · S - total surface area · a - cube edge · a - cuboid length · b - cuboid width · c - cuboid height

Cuboid: V = abc, S = 2(ab + ac + bc); cube: V = a³, S = 6a²

When to use it: Cuboid volume is the product of its three edges, and its surface area is the sum of the six rectangular faces. A cube is the special case with equal edges.
Calculated quantities: V - volume (m³) · S - total surface area (m²) · a - cube edge (m) · a - cuboid length (m) · b - cuboid width (m) · c - cuboid height (m)
Worked example: Volume of a cube: A cube has an edge length of 4 cm. Calculate its volume.

The cuboid has rectangular faces and three mutually perpendicular edge directions.
All cube edges are equal; cuboid edges may differ.
Every edge length must be positive.
Volume uses cubic units, surface area uses squared units, and edges use linear units.