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EC50 Calculator

Estimate an EC50 from dose-response data by four-parameter logistic fit, with the Hill slope, a 95% interval and the fitted curve, for agonists and stimulatory responses.

Formula

response=R∞+R0−R∞1+(doseEC50)h\text{response} = R_\infty + \dfrac{R_0 - R_\infty}{1 + \left(\dfrac{\text{dose}}{\mathrm{EC}_{50}}\right)^{h}}
EC50: the dose giving a half-maximal response\mathrm{EC}_{50}:\ \text{the dose giving a half-maximal response}
EC50\mathrm{EC}_{50}
dose giving a response half-way between the response at zero dose and at saturation
hh
steepness of the curve

How it works

An EC50 is the concentration of an agonist or stimulus that gives half of its maximal effect, and measures potency. As for an IC50, it is estimated by fitting a four-parameter logistic curve to responses over a log-spaced range of doses. The curve rises from a low response at zero dose to a plateau at saturating dose.

A good EC50 needs doses that reach both ends of the curve, at least seven or so of them, evenly spaced on a log scale. The tool warns when the EC50 lies outside the doses tested, when the interval is very wide, and when the fit has not converged.

Worked example

Nine doses from 0.001 to 10 with responses rising from 2 to 97 (illustrative).

  1. The fit gives a response of 1.6 at zero dose and 99.4 at saturation.
  2. The Hill slope is 1.00 and the EC50 is 0.2474, with a 95% interval of 0.240 to 0.255.

EC50 = 0.247 (0.240 to 0.255), with a slope of 1 as expected for a simple hyperbolic response.

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

Assumptions

  • A symmetric sigmoidal curve on a log dose scale.
  • Doses and responses are measured with similar error across the range.
  • The response is expressed on a consistent scale, such as percent of maximum.

Common mistakes

  • Fitting a curve that has not reached a plateau, which leaves the top and the EC50 undetermined.
  • Using linear, not logarithmic, dose spacing, which crowds all points at the top of the curve.
  • Confusing EC50 with the affinity of the agonist. Potency depends on receptor reserve and on the response measured.

Related tools

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Related equipment

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