Cubic Unit Cell Calculator

A cubic unit cell is the smallest repeating cubic volume used to describe several important crystal structures. Simple cubic, body-centered cubic, and face-centered cubic arrangements differ in where atoms are positioned and how many atomic portions belong to one cell. Corner atoms are shared by eight neighboring cells, face atoms by two, and a body-center atom belongs completely to its own cell. These sharing rules give one atom per simple cubic cell, two per body-centered cell, and four per face-centered cell. Geometry links lattice edge length to atomic radius when atoms are modeled as touching hard spheres. In simple cubic crystals, atoms touch along an edge, so the radius is half the edge length. In body-centered cubic crystals they touch along the body diagonal, giving radius equal to the edge times the square root of three divided by four. In face-centered cubic crystals contact occurs along a face diagonal, giving radius equal to the edge times the square root of two divided by four. Crystal density is mass per unit-cell volume. The cell mass equals the number of atoms per cell multiplied by molar mass and divided by Avogadro's constant. An edge entered in angstroms is converted through the fact that one cubic angstrom equals 10 to the negative twenty-four cubic centimeters. Dividing cell mass by the cube of the edge then gives density in grams per cubic centimeter. Atomic packing factor is the fraction of cell volume occupied by the hard-sphere atoms. Its ideal value is about 0.5236 for simple cubic, 0.6802 for body-centered cubic, and 0.7405 for face-centered cubic. A larger factor indicates more efficient packing, although real electron density is not bounded by rigid spherical surfaces. The ideal model remains useful for comparing structures and checking crystallography exercises. Use a lattice parameter and molar mass belonging to the same pure crystalline phase. Temperature, pressure, alloy composition, defects, and phase transformations can change measured dimensions and density. The calculator assumes one chemical species with the ideal selected geometry and uses the current exact Avogadro constant. It is suitable for educational work and preliminary materials checks; detailed crystallographic interpretation should use measured diffraction data, uncertainty estimates, and the actual basis of the crystal structure.