Cubic Cell Calculator

Calculate unit-cell volume, packing fraction, coordination number, and lattice relationships for SC, BCC, and FCC cells.

Last updated: June 2026 | By Patchworkr Team

Lattice Parameter

Atomic Radius Optional

Packing fraction is derived from the hard-sphere model for each cubic structure.

Live Results

Structure

Simple Cubic

Unit Cell Volume

66.430125 Å³

Atoms Per Cell

Coordination Number

Packing Fraction

52.35987756%

Radius from Lattice

2.025 Å

Atom Volume

34.78273211 Å³

Formulas

Volume: V = a^3

Simple cubic: r = a / 2, atoms = 1, coordination = 6

BCC: r = (sqrt(3) / 4) a, atoms = 2, coordination = 8

FCC: r = a / (2 sqrt(2)), atoms = 4, coordination = 12

Packing fractions: SC = π/6, BCC = sqrt(3)π/8, FCC = π/(3 sqrt(2))

Example: FCC copper with a = 3.615 Å

Volume: 3.615^3 ≈ 47.24 Å³

Radius: a / (2 sqrt(2)) ≈ 1.278 Å

Packing fraction: 74.05%

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