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IC50 Calculator

Estimate an IC50 from dose-response data by four-parameter logistic fit, with the Hill slope, a 95% interval, the curve, and Ki by Cheng-Prusoff for competitive inhibitors.

Formula

response=bottom+top−bottom1+(doseIC50)h\text{response} = \text{bottom} + \dfrac{\text{top} - \text{bottom}}{1 + \left(\dfrac{\text{dose}}{\mathrm{IC}_{50}}\right)^{h}}
Ki=IC501+[S]/Km(competitive inhibitor)K_{\mathrm{i}} = \dfrac{\mathrm{IC}_{50}}{1 + [S]/K_{\mathrm{m}}}\quad(\text{competitive inhibitor})
IC50\mathrm{IC}_{50}
dose giving a response half-way between the top and the bottom
hh
steepness of the curve; 1 for simple one-site binding
KiK_{\mathrm{i}}
inhibition constant, independent of the substrate concentration

How it works

An IC50 is the concentration of an inhibitor that reduces a response by half. It is estimated by fitting a sigmoidal curve, most often the four-parameter logistic, to responses measured over a range of doses spaced evenly on a log scale. The fit gives the IC50, the slope, and the top and bottom of the curve; the page can also fix the top and bottom, for data expressed as percent of a control.

An IC50 is a property of the assay and not of the inhibitor alone: it changes with incubation time, cell type and, for an enzyme, with the substrate concentration. For a competitive inhibitor, the Cheng-Prusoff relationship converts it to the inhibition constant Ki, which is independent of the substrate concentration.

Worked example

Nine doses from 0.001 to 10 with responses falling from 99 to 3 (illustrative).

  1. The fit gives a response of 99.2 at zero dose and 1.2 at high dose, a Hill slope of 1.05, and an IC50 of 0.2203.
  2. The 95% interval is 0.211 to 0.230.

IC50 = 0.220 (0.211 to 0.230), a steepness near 1 that is consistent with simple binding.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • A symmetric sigmoidal dose-response on a log dose scale.
  • Doses are accurate and the response is measured with similar error at every dose.
  • For Ki, a competitive inhibitor of a single-substrate enzyme at steady state, with [S] and Km in the same unit.

Common mistakes

  • Fitting too few doses, or doses that do not reach the top and bottom of the curve.
  • Reporting an IC50 outside the tested doses as though it were measured.
  • Treating an IC50 from one assay as a constant, and comparing it to one measured under other conditions.

Related tools

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Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.