IC50 / EC50 Four-Parameter Logistic Fit Calculator (with Data Reliability Checks)

The standard approach for dose–response curves is the four-parameter logistic (4PL) model:

Y = Bottom + (Top − Bottom) / (1 + 10^((logIC50 − logC) × Hill))

The four parameters are the upper plateau, lower plateau, half-maximal effective concentration, and the steepness of the curve (Hill slope). Fitting an IC50 is straightforward; the hard part is deciding whether that number is trustworthy.

I. If concentrations don’t reach both plateaus, you have extrapolation, not an IC50

IC50 is defined as the concentration at which the response falls exactly halfway between the upper and lower plateaus. If the highest concentration hasn’t driven the response to the lower plateau, or the lowest concentration hasn’t recovered to the upper plateau, both plateaus are extrapolated by the fitting algorithm, and so is the IC50—it may lie entirely outside the concentration range you actually tested.

Results like this often look convincing on a graph: smooth curve, high R². A high R² only means the model passes through your measured points; it says nothing about whether the extrapolated plateaus are real. This tool tells you explicitly whether the fitted IC50 falls within your tested concentration range and how far each end is from reaching a plateau.

As a rule of thumb, your concentration range should span at least two orders of magnitude above and below the IC50, with 8–10 points on a semi-log scale (3-fold or 10-fold dilution steps).

II. Don’t casually fix the Hill slope to 1

Many off-the-shelf tools default to fixing the slope at 1. A slope of 1 implies a single binding site and no cooperativity—this is an assumption, not a fact. Real data may have slopes of 0.5 or 2; forcing slope = 1 distorts the curve shape and shifts the IC50 systematically.

This tool reports both results side by side: the free-fit slope and the slope fixed at 1. The difference between them is exactly what that assumption costs you on your particular dataset.

Conversely, if the fitted slope is far from 1 (e.g., greater than 3 or less than 0.3), this usually doesn’t mean you’ve discovered strong cooperativity. It’s more likely a signal that something else is wrong: too few concentration points, plateaus not reached, an outlier, or more than one mechanism operating in the system.

III. IC50 is condition-dependent; comparing values across conditions is meaningless

The same compound against the same target will give different IC50 values if you change the substrate concentration—competitive inhibition is especially sensitive to this: the more substrate present, the more inhibitor you need to displace it. This is exactly what the Cheng–Prusoff relationship describes: IC50 rises with substrate or ligand concentration, while Ki does not.

Therefore:

• Always report IC50 together with the assay conditions (substrate or ligand concentration, enzyme amount, incubation time, readout method). Writing “IC50 = 1.2 µM” alone gives readers no way to tell whether any discrepancy with their own data reflects the compound or the experimental design.
• For cross-laboratory comparisons, use Ki, not IC50.
• EC50/IC50 values from cell-based assays are further confounded by permeability, efflux, and serum binding; they are not directly comparable to cell-free biochemical values.

IV. IC50 and EC50 use the same mathematics

The only difference is direction: when response decreases with concentration, the effect is inhibition (IC50, negative Hill slope); when response increases, it is activation (EC50, positive slope). This tool detects the sign of the fitted slope and labels the result automatically—no need to choose in advance.

Related tools

For Michaelis–Menten Km and Vmax fitting (the same nonlinear fitting approach), see Enzyme Kinetics; for linear standard curves and back-calculation of unknowns, see Standard Curve; for serial dilution planning, see Dilution Calculator; for two-group comparison sample sizing, see Sample Size Estimator.