The estimation of the antagonist equilibrium dissociation constant by the Schild plot is based on the assumption that when the same magnitude response is produced by an agonist in presense and absence of an antagonist then the following relationship holds: Where:
[A] = agonist concentration to produce a given effect in the absence of antagonist.
[A'] = agonist concentration to produce a given effect in the presence of antagonist.
[B] = antagonist concentration.
K_D = the equilibrium dissociation constant for A
K_B = the equilibrium dissociation constant for B
This equation rearranges to:

Logging both sides yields:

When ([A']/[A]) = 2, then the left side of the equation is equal to 0 and log [B] = log K_B.
Since it is difficult to antisipate which concentration of antagonist will shift the dose-effect curve 2-fold to the right, a series of experiments are conducted using several different antagonist doses. These data are plotted as shown in the figure, where the regression line is used to estimate the x-intercept as the the K_B.