Four Parameter Logistic (4PL) Curve Calculator

Four parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "s", shaped curve. This type of curve is particularly useful for characterizing bioassays because bioassays are often only linear across a specific range of concentration magnitudes. Beyond this linear range, the responses quickly plateau and approach the minimum and maximum.

Four parameter logistic curve refers to the following four parameters:
  1. Minimum: the point of smallest response; can be baseline response, control or response when treatment concentration is zero.
  2. Maximum: the point of greatest response
  3. Inflection point: the dose at which the curvature of the response line changes; where the rate of change switches signs; often referred to as the IC50 or EC50
  4. Hill coefficient: the slope of the curve at the inflection point

Note that four parameter logistic (4PL) curves are symmetric in nature around the inflection point. For asymmetric logistic curves, a five parameter logistic (5PL) curve is required.

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How to use this tool:
1. Paste experimental data into the box on the right. Data can be copied directly from Excel columns. Data can also be comma-separated, tab-separated or space-separated values. If entering data manually, only enter one concentration per line.

Replicates can be graphed simultaneously. Graph will generated error bars based on the standard error of the mean (SEM). Simply paste or enter all data columns to begin. Format should be as follows:

ConcentrationResponse 1Response 2...

NEW! Plot up to three data sets!
Users can now graph up to three data sets on the same graph for comparison purposes. To add a new data set, press the "+" tab above the data entry area. Data sets can be renamed by double clicking the tab. Each dataset will generate a corresponding 4PL value as well as the equation for the best fit line.

2. Verify your data is accurate in the table that appears.

3. Press the "Calculate 4PL" button to display results, including calculations and graph.

Process Data