At half saturation, ligand concentration equals
When half of the available receptors are occupied, fractional saturation equals 0.5. Substitution into the binding equation shows that the free ligand concentration at this point must equal the dissociation constant Kd. Measurement of the ligand concentration that produces half-maximal occupancy therefore yields Kd directly, provided nonspecific binding has been subtracted and equilibrium has been reached.
Ref: NCERT Biology Class 11–12 Alberts et al Molecular Biology of the Cell Lodish et al, Molecular Cell Biology Cooper & Hausman, The Cell Abbas et al., Cellular and Molecular Immunology (for immunology sections)