IC50 and EC50 calculator

What the IC50 and EC50 are

The IC50 is the concentration of an inhibitor that gives half of its maximum effect. The EC50 is the same idea for something that increases a response, such as an agonist. Both are read from a sigmoidal dose–response curve fitted to your data, and both are measures of potency: the lower the value, the more potent the compound.

The model

y = D + (A − D) ÷ (1 + (x ÷ C)^B)

This is the four-parameter logistic (4PL), also called the variable-slope or Hill model. A and D are the plateaus at low and high concentration, so the top and bottom of the curve. C is the midpoint, which is the IC50 or EC50, and B sets how steep the curve is. The Hill slope is shown with GraphPad Prism's sign convention: negative for a falling curve, positive for a rising one. A Hill slope near ±1 is typical of simple one-site binding.

The 5PL model adds an asymmetry term for curves that bend more sharply at one end. Its C parameter is not the IC50, so the calculator works out the true midpoint from the fitted curve. Reporting C instead is a common mistake: on one of our test datasets it would have given 0.34 instead of 0.90, nearly threefold out.

Relative and absolute IC50

• Relative IC50 is halfway between the fitted top and bottom. It's the usual definition, and the one this calculator reports first.
• Absolute IC50 is where the curve crosses 50% of your controls. It only makes sense once responses are normalised to % of control, and it can differ from the relative IC50 when the curve doesn't run all the way from 100% to 0%.

Worked example

The example loaded on this page is an inhibitor tested in triplicate at ten 1:3 dilutions from 30 µM, with responses as % activity. A 4PL fit gives an IC50 of 0.4381 µM (95% confidence interval 0.3902 to 0.4918 µM), a pIC50 of 6.36, and an absolute IC50 of 0.4276 µM.

Getting a reliable IC50

• Test a range wide enough to show both plateaus, ideally with two or three concentrations on each.
• Use 8 to 12 concentrations spaced evenly on a log scale, such as half-log or 1:3 dilutions, with replicates.
• Normalise with control wells on the same plate: vehicle for 100%, and full inhibition or background for 0%.
• Treat an IC50 outside the tested range, or one with a confidence interval spanning more than tenfold, as an estimate only. The calculator flags both.

Fixing the top or bottom

If your highest or lowest concentrations don't reach a plateau, the fit has to guess where the curve levels off, and the IC50 becomes unreliable. When your controls define that level, you can fix it: with responses as % of control, set the top to 100 and the bottom to 0. The remaining parameters are then fitted, and the confidence intervals and degrees of freedom allow for the fixed values, in the same way as constraints in GraphPad Prism.

Only fix a plateau you have measured independently, such as with vehicle or full-inhibition controls on the same plate. Fixing it to a value the data disagree with pulls the IC50 with it.

How the confidence interval is calculated

The 95% confidence interval is worked out on a log scale, as if log IC50 were fitted directly, which is how GraphPad Prism reports it. That's why the interval is asymmetric around the IC50 and can never go below zero. pIC50 is −log₁₀ of the IC50 in mol/L, and is shown when the concentration unit is molar (M, mM, µM, nM, pM).

Accuracy

Every IC50, absolute IC50 and confidence interval is compared with an independent calculation in SciPy on 11 datasets, covering 4PL and 5PL, rising and falling curves, raw and normalised responses, fixed tops and bottoms, and concentrations in molar units. They agree to within 0.1%.

This calculator is checked against independent calculations before every release. How we check our calculators.

References

• Motulsky H, Christopoulos A (2004). Fitting Models to Biological Data Using Linear and Nonlinear Regression. Oxford University Press.
• Sebaugh JL (2011). Guidelines for accurate EC50/IC50 estimation. Pharmaceutical Statistics 10: 128–134.
• Gottschalk PG, Dunn JR (2005). The five-parameter logistic: a characterization and comparison with the four-parameter logistic. Analytical Biochemistry 343: 54–65.