EC50 calculator
Fit a four-parameter logistic curve to agonist concentration-response data. Computed as you type.
Fit a four-parameter logistic curve to agonist concentration-response data. Computed as you type.
The EC50 is the half maximal effective concentration: the concentration of an agonist, hormone, growth factor or ligand that produces 50% of its maximal response. It is the standard measure of potency. A lower EC50 means less compound is needed for the same effect. Because it depends on receptor density, cell type and readout, an EC50 is only comparable between experiments run under the same conditions.
x is the concentration and y the response. Bottom is the baseline,Top is the maximal response (Emax), the EC50 is the midpoint on the log-concentration axis, and the Hill slope sets the steepness of the transition. This is the "log(agonist) vs. response – variable slope" model used in GraphPad Prism and most plate-reader software.
Responses are averaged per concentration, then all four parameters are estimated by non-linear least squares (Levenberg–Marquardt) on the log-concentration scale, starting from the data extremes and a log-logit line and refining until the sum of squared residuals stops improving.R² reports how much of the response variation the curve explains, and the per-point table shows each observed mean beside its fitted value so outliers stand out. For a deeper look at the fit parameters use the dose-response curve fitter, or the Hill slope calculator for the slope alone.
IC50 is the same midpoint for an inhibitor, where the response falls with concentration; use the IC50 calculator for that. If your responses fall here, the fit still works and the Hill slope comes out negative. Emax is the top plateau, a measure of efficacy rather than potency: two agonists can share an EC50 yet reach very different maximal responses, and a partial agonist has a lower Emax than a full agonist.
One concentration per line, followed by one or more response values. Separate columns with spaces, tabs or commas, so a paste straight from a spreadsheet works. Extra response columns are treated as replicates and averaged. Concentrations must be above zero; a "0" control cannot sit on a log axis, so leave it out or enter it as a very small value. Use at least four concentrations, with points on both the baseline and the maximal-response plateau.
By fitting a four-parameter logistic (4PL) curve to response versus log concentration. The fit estimates the bottom and top plateaus, the Hill slope, and the concentration halfway between the plateaus, which is the EC50. This calculator runs the full non-linear least-squares fit in the browser.
EC50 is the concentration of an agonist that produces half of its maximal effect; IC50 is the concentration of an inhibitor that produces half of its maximal inhibition. Both are midpoints of the same 4PL curve, one rising and one falling.
Emax is the maximal response an agonist can produce, the top plateau of the curve. EC50 is the concentration needed to reach half of that. Potency is about EC50; efficacy is about Emax. A drug can be very potent (low EC50) yet have low efficacy (low Emax).
At least four, and ideally six to ten spread evenly on a log scale so that both the baseline and the maximal response are defined. Replicates at each concentration improve the fit; enter them as extra columns and they are averaged.
How steep the transition is. A slope of 1 matches a simple one-site model. Values above 1 suggest positive cooperativity or a threshold response; values below 1 suggest negative cooperativity, receptor heterogeneity or a shallow, drawn-out response.