Coordination Number Calculator & Theory

What is Coordination Number (CN)?

The Coordination Number of a central metal atom in a complex is defined as the total number of ligand donor atoms to which the metal is directly bonded. It is not necessarily equal to the number of ligands, as some ligands (polydentate) can form multiple bonds.

Primary Mathematical Formula:

$$\text{CN} = \sum_{i=1}^{n} (\text{Number of Ligands}_i \times \text{Denticity}_i)$$

Ligand Binding Solver

Ligand Type

Quantity

Rules for Determination

Sigma Only: Only $\sigma$-bonds are counted. $\pi$-bonds in metal-carbonyls do not increase the CN.
Denticity Factor: A chelating ligand like ethylenediamine (en) counts as 2 because it has two donor sites.
Geometry Link: CN 4 usually implies Tetrahedral or Square Planar, while CN 6 implies Octahedral.

Solved Example:

Complex: $[Co(en)_2Cl_2]^+$
Ligands: 2 $\times$ en (Bidentate) + 2 $\times$ Cl (Monodentate)
Calculation: $(2 \times 2) + (2 \times 1) = 6$
Coordination Number = 6

Scientific Research & Industrial Uses

Coordination numbers are critical in Pharmacology. For instance, the anti-cancer drug Cisplatin has a CN of 4, allowing it to fit into the major groove of DNA to inhibit tumor growth.

Application	CN Range	Example Complex
Bio-imaging	CN 7-9	Lanthanide Probes
Catalysis	CN 4-5	Wilkinson’s Catalyst
Metalloproteins	CN 4-6	Hemoglobin (Fe-Heme)
Nuclear Chemistry	CN 8-12	Actinide Extractions

Top Coordination Compounds Reference

Zeise's Salt

Complex Name	Formula	CN	Geometry
Potassium Ferrocyanide	$[Fe(CN)_6]^{4-}$	6	Octahedral
Nickel Tetracarbonyl	$[Ni(CO)_4]$	4	Tetrahedral
$[PtCl_3(\eta^2-C_2H_4)]^-$	4	Square Planar
EDTA Complex	$[Ca(EDTA)]^{2-}$	6	Octahedral