# Half maximal effective concentration

The term half maximal effective concentration (EC50) refers to the concentration of a drug which induces a response halfway between the baseline and maximum.[1] It is commonly used as a measure of drug potency.

The EC50 of a graded dose response curve therefore represents the concentration of a compound where 50% of its maximal effect is observed[2]. The EC50 of a quantal dose response curve represents the concentration of a compound where 50% of the population exhibit a response[3].

It is also related to IC50 which is a measure of a compound's inhibition (50% inhibition). For competition binding assays and functional antagonist assays IC50 is the most common summary measure of the dose-response curve. For agonist/stimulator assays the most common summary measure is the EC50.[4]

According to the FDA, IC50 represents the concentration of a drug that is required for 50% inhibition in vitro whereas EC50 represents the plasma concentration required for obtaining 50% of a maximum effect in vivo.[5]

Concentration measures typically follow an S-shaped curve, increasing rapidly over a relatively small change in concentration. The point at which the effectiveness slows with increasing concentration is the IC50. This can be determined mathematically by derivation of the best-fit line. However, it is more easily observed from a graph and estimated rather than through complex calculus equations.

## Equation

The equation used to fit the EC50 is:

Y = Bottom + (Top - Bottom)/(1 + (X/EC50)(Hill slope))

where Y is the observed value, Bottom is the lowest observed value, Top is the highest observed value, and the Hill slope gives the largest absolute value of the slope of the curve.

And an alternate form of the equation is:

Y = Bottom + (Top - Bottom)/(1+ 10((Log(EC50)-X) * (Hill slope)))