in crystallography, the number of identical neighboring atoms or ions closest to a given atom or ion in a crystal. Straight lines connecting the centers of nearest atoms or ions in a crystal form the coordination polyhedron, with the given atom in its center.

Different polyhedrons may correspond to the same coordination number. The coordination number in the structures of diamond, silicon, germanium, and sphalerite is 4, and the coordination polyhedron is a tetrahedron. Each sodium ion in sodium chloride, NaCl, is surrounded by six chlorine ions, and each chlorine ion is surrounded by six sodium ions, meaning that the coordination numbers are 6 for both types of ions and the corresponding polyhedron is an octahedron. The coordination number of calcium ions in fluorite, CaF₂, is 8 and the corresponding polyhedron is a cube, whereas the coordination number for F ions is 4 and the coordination polyhedron is a tetrahedron. The highest possible coordination number is 12, which is typical of metals with cubic or hexagonal close-packed structure. Metals with a body-centered lattice have a coordination number of 8. Semiconductor crystals, which do not have close packing of atoms, have coordination numbers of 4 or 6.

In chemistry, the coordination number is the number of atoms or atomic groups directly bonded to a given atom in complex compounds. The concept of coordination numbers is also used in descriptions of fluids and amorphous bodies. In this case, the coordination number is the average number of the nearest neighbors of the atom; it may be fractional. The coordination number is a measure of short-range order in liquids and amorphous bodies.