EC50 Calculator (Dose–Response Curve Fit)

Fit a four-parameter logistic agonist dose–response curve and get the EC50, Hill slope, Emax and R² from concentration–response data.

The EC50 Calculator fits a variable-slope four-parameter logistic curve to concentration–response data by least squares and reports the EC50 (concentration producing half-maximal effect), log EC50, Hill slope, baseline and Emax plateaus and R².

Free, runs in your browser. Nothing you enter is uploaded.

How to use it

Paste concentrations and responses.
Read EC50, Hill slope and Emax.
Constrain to 0–100 % for normalised data.

What you enter

≥ 4 concentrations
Response per concentration

What you get

EC50 and log EC50
Hill slope
Baseline and Emax
R²

Formula

y = Bottom + (Top − Bottom) / (1 + 10^((logEC50 − log₁₀x) · Hill))

Identical to the IC50 model; for an increasing response the fitted Hill slope is positive and the EC50 is the midpoint between baseline and Emax.

Worked example

Input: 1–3000 nM; response 3 8 22 48 71 88 96 99 %

Result: EC50 = 34.8 nM, Hill slope 0.91, Emax 100.5 %, R² > 0.999

Half-maximal activation at ~35 nM with a near-unity slope.

Questions

What is the difference between EC50 and Kd?

EC50 is a functional potency measure from a response curve; Kd is the equilibrium binding affinity. They coincide only under specific assumptions (no receptor reserve, direct proportionality of response to occupancy).

How many concentrations do I need?

At least 6–8 spanning about two log units on either side of the EC50 so both plateaus are defined.

Limitations

Both plateaus should be defined by data.
Relative EC50 unless plateaus are constrained to 0–100 %.

References

Sebaugh JL (2011). Guidelines for accurate EC50/IC50 estimation. Pharm Stat 10:128-134.

More Cell Biology

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.