Coordination Number Calculator
Calculate coordination number with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Formula
Radius Ratio = r(cation) / r(anion)
The radius ratio rule predicts coordination number based on the ratio of cation to anion radii. Specific ratio ranges correspond to stable geometries: below 0.155 = linear (CN=2), 0.155-0.225 = trigonal planar (CN=3), 0.225-0.414 = tetrahedral (CN=4), 0.414-0.732 = octahedral (CN=6), 0.732-1.0 = cubic (CN=8), and above 1.0 = cuboctahedral (CN=12).
Worked Examples
Example 1: NaCl Crystal Structure
Problem: Determine the coordination number of Na+ (radius 102 pm) with Cl- (radius 181 pm).
Solution: Radius ratio = r(Na+) / r(Cl-) = 102 / 181 = 0.5636\nRatio falls in range 0.414 - 0.732\nPredicted CN = 6 (octahedral)\nBond length = 102 + 181 = 283 pm\nThis matches the known NaCl rock salt structure
Result: CN = 6 | Geometry = Octahedral | Bond length = 283 pm
Example 2: CsCl Crystal Structure
Problem: Find the coordination number of Cs+ (radius 170 pm) with Cl- (radius 181 pm).
Solution: Radius ratio = r(Cs+) / r(Cl-) = 170 / 181 = 0.9392\nRatio falls in range 0.732 - 1.0\nPredicted CN = 8 (cubic)\nBond length = 170 + 181 = 351 pm\nCsCl adopts the body-centered cubic structure
Result: CN = 8 | Geometry = Cubic | Bond length = 351 pm
Frequently Asked Questions
What is the coordination number in chemistry?
The coordination number is the number of atoms, ions, or molecules (ligands) directly bonded to a central atom in a complex or crystal structure. It describes the immediate environment around a metal center and determines the geometry of the complex. For example, in the complex ion [Co(NH3)6]3+, cobalt has a coordination number of 6 because six ammonia molecules surround it. Coordination numbers typically range from 2 to 12, with 4 and 6 being the most common in transition metal chemistry. The coordination number affects properties like color, magnetism, and reactivity of the compound.
How does the radius ratio predict coordination number?
The radius ratio rule uses the ratio of the cation radius to the anion radius (r+/r-) to predict the coordination number and geometry in ionic crystals. When the cation is very small relative to the anion (ratio below 0.155), only 2 anions can fit around it in a linear arrangement. As the ratio increases, more anions can pack around the cation: 0.155-0.225 gives CN=3 (trigonal planar), 0.225-0.414 gives CN=4 (tetrahedral), 0.414-0.732 gives CN=6 (octahedral), and 0.732-1.0 gives CN=8 (cubic). While this rule provides good approximations, real crystal structures can deviate due to covalent bonding character and orbital effects.
What factors affect coordination number besides size?
Several factors beyond ionic radii influence coordination number. Electronic configuration plays a major role because certain d-electron counts favor specific geometries due to crystal field stabilization energy. Ligand properties matter too, as bulky ligands like triphenylphosphine reduce coordination numbers through steric effects, while small ligands like CO allow higher numbers. Charge and electronegativity affect the degree of covalent versus ionic bonding, shifting preferred geometries. Temperature and pressure can also change coordination numbers, as seen in the high-pressure transformation of NaCl from 6-coordinate to 8-coordinate CsCl-type structure.
What is the relationship between coordination number and hybridization?
Coordination number directly determines the hybridization of the central atom according to valence bond theory. A coordination number of 2 corresponds to sp hybridization with linear geometry, 3 to sp2 with trigonal planar geometry, 4 to sp3 (tetrahedral) or dsp2 (square planar), 5 to sp3d (trigonal bipyramidal) or dsp3, and 6 to sp3d2 (octahedral). For transition metals, d orbitals participate in hybridization, enabling higher coordination numbers. This relationship is essential for predicting molecular shapes, bond angles, and understanding reaction mechanisms in coordination chemistry and organometallic compounds.
How do you experimentally determine coordination numbers?
Coordination numbers are determined experimentally through several techniques. X-ray crystallography is the gold standard, directly revealing the three-dimensional arrangement of atoms around the central metal with sub-angstrom precision. Extended X-ray absorption fine structure (EXAFS) measures coordination numbers in both solid and solution states by analyzing oscillations in X-ray absorption spectra. Nuclear magnetic resonance (NMR) spectroscopy can reveal coordination numbers through chemical shifts and coupling patterns. Other methods include neutron diffraction for light atoms, pair distribution function analysis for amorphous materials, and computational methods like density functional theory to predict and validate experimental findings.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.