Use this chemistry calculator to reproduce a named relationship with explicit quantities and units for study, laboratory planning, or an independent numerical check.

Unit cell type

Packing of the unit cell.

Compute the percent of a unit cell volume filled by hard-sphere atoms for the common cubic and close-packed packings. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Packing efficiency (%)

Fraction of the cell volume occupied by spheres.

• Crystallographic calculations assume the stated ideal lattice, indexing, wavelength, occupancy, and unit-cell geometry. Defects, strain, texture, thermal expansion, mixed phases, and instrumental corrections are outside the compact model.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check units and significant figures, compare the result with limiting cases, and use measured or source-specific constants where available. Laboratory, safety, and regulatory decisions require validated methods and appropriate uncertainty analysis.

• Packing Fraction Calculator

  Calculate the hard-sphere packing fraction of a unit cell from atomic radius, atom count, and unit-cell volume.

• Coordination Number Calculator

  Look up the number of nearest neighbours around an atom for the common cubic and close-packed structures.

• Unit Cell Density Calculator

  Compute the theoretical crystal density rho = Z*M/(N_A*a^3) from the atoms per unit cell, molar mass, and cubic edge length.