Utilnaro

Solid geometry formulas

Cube and cuboid volume and surface area

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

Formula

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

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.

Cube and cuboid volume and surface area calculator

Solid
What do you want to calculate?

Known values

The result updates automatically.

Cube diagram
aV ?
  • a · Edge: known value
  • V · Volume: value being calculated (?)
  • S · Surface area: related value

Result

27 m³

Substitution and calculation

V = a³ = 27 m³

Symbols and units

SymbolQuantitySISupported units
VvolumeSpace enclosed by the solid.m³m³, cm³, mm³, km³
Stotal surface areaSum of the areas of all faces.m²m², cm², mm², km²
acube edgeCommon length of every cube edge.mm, cm, mm, km
acuboid lengthFirst cuboid edge.mm, cm, mm, km
bcuboid widthSecond cuboid edge perpendicular to a.mm, cm, mm, km
ccuboid heightThird cuboid edge perpendicular to a and b.mm, cm, mm, km

Formula rearrangements

Cube volume

V = a³

Cube surface area

S = 6a²

Cuboid volume

V = a × b × c

Cuboid surface area

S = 2(ab + ac + bc)

Worked examples

Volume of a cube

A cube has an edge length of 4 cm. Calculate its volume.

  1. 1Step 1: Use V = a³.
  2. 2Step 2: Substitute a = 4 cm.
  3. 3Step 3: Calculate 4 × 4 × 4 to obtain 64 cm³.

Result: 64 cm³

Surface area of a cuboid

A cuboid has edges of 5 cm, 3 cm, and 2 cm. Calculate its total surface area.

  1. 1Step 1: Use S = 2(ab + ac + bc).
  2. 2Step 2: Calculate the three face areas: 15 cm², 10 cm², and 6 cm².
  3. 3Step 3: Add them and multiply by 2 to obtain 62 cm².

Result: 62 cm²

Sources and review