Use of the Cheng-Prusoff equation for determination of the equilibrium dissociation constant, K B , is based on an assumption that simple bi-molecular interaction kinetics are strictly followed. Under such circumstances, the slope parameters of the agonist concentration-response curve (K) and that of the inhibition curve (n) are unity. New equations are needed for calculating K B when slope parameters (K and n) deviate from unity. In this article, the slope parameters K and n are used as indexes of cooperativity. Thus, the following new equations are derived: (1) For calculation of K B from IC 5 0 , the new equation which incorporates both cooperativity indexes is described as K B =(IC 5 0 ) n /(1+A K /K A )=(IC 5 0 ) n /[1+(A/EC 5 0 ) K ] where A is the concentration of the agonist against which the IC 5 0 is determined, and K A is the apparent equilibrium dissociation constant of the agonist. This new equation is applicable when the cooperativity indexes of K and n are less than, equal to, or greater than unity. This equation reduces to the Cheng-Prusoff equation when the cooperativity indexes K and n are unity. (2) For saturation binding assays, the enhanced Scatchard analysis is described by the equation: B/F m =-B/K D +B m a x /K D where B and F are the concentrations of the bound and free ligand, respectively, and m is the cooperativity index of the ligand. A plot of B/F m versus B yields a straight line with a negative slope that equals 1/K D , and an x-axis intercept that equals B m a x . When m equals unity, the above analysis reduces to the traditional Scatchard analysis. (3) The importance of the slope parameters (K and n) on Schild analysis is illustrated by the equation: log(x K -1)=logB n -logK B , where x is the concentration ratio, and B is the concentration of the antagonist. The modified pA 2 is now defined as the -logarithm of the molar concentration of the antagonist (B), power adjusted with the slope parameter (B n ), that causes a two-fold shift of the agonist concentration-response curve (x K =2), also power adjusted with the slope parameter K. When K and n equal unity, the above analysis reduces to the traditional Schild analysis. A total of six power equations are derived for estimating K B values covering situations with different cooperativity indexes of agonists and antagonists. These equations should yield more accurate estimations of K B values.