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:

Minimum: the point of smallest response; can be baseline response, control or response when treatment concentration is zero.
Maximum: the point of greatest response
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
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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This online resource may be cited as follows

MLA	"Quest Graph™ Four Parameter Logistic (4PL) Curve Calculator." AAT Bioquest, Inc., 29 Aug. 2026, https://www.aatbio.com/tools/four-parameter-logistic-4pl-curve-regression-online-calculator.
APA	AAT Bioquest, Inc. (2026, August 29). Quest Graph™ Four Parameter Logistic (4PL) Curve Calculator. AAT Bioquest. https://www.aatbio.com/tools/four-parameter-logistic-4pl-curve-regression-online-calculator.
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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 X-Value per line. Replicates can be graphed simultaneously. Graph will generate 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:
Concentration Response 1 Response 2 …
C₁ R1₁ R2₁ …
C₂ R1₂ R2₂ …
C₃ R1₃ R2₃ …
… … … …
Users can 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 X₅₀ value as well as the equation for the best fit line.
Verify your data is accurate in the table that appears.
Press the "Calculate X₅₀" button to display results, including calculations and graph.

Four Parameter Logistic (4PL) Regression
Calculate a best fit line with minimum, maximum, Hill coefficient and inflection point
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Polynomial Regression
Determine the best fit line using linear, quadratic, cubic and quartic equations

Concentration	Response 1	Response 2	…
C₁	R1₁	R2₁	…
C₂	R1₂	R2₂	…
C₃	R1₃	R2₃	…
…	…	…	…

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