Unit Cell Volume Calculator

Calculate Crystal Unit Cell Volumes with Precision

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Cubic System Calculator

Calculate unit cell volume for cubic crystal systems (a = b = c, α = β = γ = 90°)

Volume: - ų

Tetragonal System Calculator

Calculate unit cell volume for tetragonal crystal systems (a = b ≠ c, α = β = γ = 90°)

Volume: - ų

Orthorhombic System Calculator

Calculate unit cell volume for orthorhombic crystal systems (a ≠ b ≠ c, α = β = γ = 90°)

Volume: - ų

Understanding Unit Cell Volume

What is a Unit Cell?

A unit cell is the smallest repeating unit in a crystal structure that shows the full symmetry of the crystal pattern. It is characterized by:

  • Three lattice parameters (a, b, c)
  • Three angles (α, β, γ)
  • A specific arrangement of atoms

Crystal Systems

There are seven crystal systems:

  • Cubic: a = b = c, α = β = γ = 90°
  • Tetragonal: a = b ≠ c, α = β = γ = 90°
  • Orthorhombic: a ≠ b ≠ c, α = β = γ = 90°
  • Hexagonal: a = b ≠ c, α = β = 90°, γ = 120°
  • Trigonal: a = b = c, α = β = γ ≠ 90°
  • Monoclinic: a ≠ b ≠ c, α = γ = 90° ≠ β
  • Triclinic: a ≠ b ≠ c, α ≠ β ≠ γ

Volume Calculations

The volume of a unit cell depends on its crystal system:

  • Cubic: V = a³
  • Tetragonal: V = a²c
  • Orthorhombic: V = abc
  • More complex systems involve trigonometric functions of the angles

Essential Unit Cell Volume Formulas

Cubic System

V = a³

Tetragonal System

V = a²c

Orthorhombic System

V = abc