Sphere Packing Density Calculator

Packing Density: -

Number of Spheres per Unit Cell: -

Coordination Number: -

Understanding Sphere Packing

What is Sphere Packing?

Sphere packing studies the arrangement of spheres in space to achieve optimal density.

Packing Density = (Volume of spheres) / (Total volume)

Common Densities:

  • SC: π/6 ≈ 0.524
  • BCC: π√3/8 ≈ 0.680
  • FCC/HCP: π√2/6 ≈ 0.740

Advanced Concepts

  • Crystallographic Systems:
    • Bravais Lattices
    • Miller Indices
    • Point Groups
    • Space Groups
  • Theoretical Bounds:
    • Kepler Conjecture
    • Random Close Packing
    • Kissing Numbers
    • Voronoi Cells
  • Applications:
    • Crystal Structure
    • Material Properties
    • Molecular Modeling
    • Granular Materials

Properties and Applications

Coordination Numbers

SC: 6, BCC: 8, FCC: 12

Void Spaces

Tetrahedral and Octahedral

Crystal Systems

7 Basic Systems

Phase Transitions

Density-driven changes