AAT Bioquest

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.

For technical assistance on using this calculator, please contact websupport@aatbio.com.

This tool has recently been updated.

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 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:

ConcentrationResponse 1Response 2...

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.

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

3. Press the "Calculate X50" button to display results, including calculations and graph.

Data Entry

Load Data
Save Data

Process data


Have a question or a feature request about this tool? Feel free to reach out to us and let us know! We're always looking for ways to improve!

Submit request


This online tool may be cited as follows


"Quest Graph™ Four Parameter Logistic (4PL) Curve Calculator." AAT Bioquest, Inc.9 Dec2023https://www.aatbio.com/tools/four-parameter-logistic-4pl-curve-regression-online-calculator.


AAT Bioquest, Inc. (2023December 9). Quest Graph™ Four Parameter Logistic (4PL) Curve Calculator. AAT Bioquest. https://www.aatbio.com/tools/four-parameter-logistic-4pl-curve-regression-online-calculator.

This online tool has been cited in 27 publications, including

Parallelized immunomagnetic nanopore sorting: modeling, scaling, and optimization of surface marker specific isolation of extracellular vesicles from complex media
Authors: Lin, Andrew A and Shen, Hanfei and Spychalski, Griffin and Carpenter, Erica L and Issadore, David
Journal: (2023)
Modeling and optimization of parallelized immunomagnetic nanopore sorting for surface marker specific isolation of extracellular vesicles from complex media
Authors: Lin, Andrew A and Shen, Hanfei and Spychalski, Griffin and Carpenter, Erica L and Issadore, David
Journal: Scientific Reports (2023): 13292
Improved Therapeutic Delivery Targeting Clinically Relevant Orthotopic Human Pancreatic Tumors Engrafted in Immunocompromised Pigs Using Ultrasound-Induced Cavitation: A Pilot Study
Authors: Imran, Khan Mohammad and Tintera, Benjamin and Morrison, Holly A and Tupik, Juselyn D and Nagai-Singer, Margaret A and Ivester, Hannah and Council-Troche, McAlister and Edwards, Michael and Coutermarsh-Ott, Sheryl and Byron, Christopher and others,
Journal: Pharmaceutics (2023): 1585
Identification of the brain areas that mediate insulin action
Authors: Wang, Niannian
Journal: (2023)
High performance aptasensing platform development through in silico aptamer engineering for aflatoxin B1 monitoring
Authors: Mousivand, Maryam and Javan-Nikkhah, Mohammad and Anfossi, Laura and Di Nardo, Fabio and Salina, Matteo and Bagherzadeh, Kowsar
Journal: Food Control (2023): 109418
Effects on serum protein levels from one bout of high intensity interval training in individuals with axial spondyloarthritis and controls
Authors: Andersson, {\AA}sa and Olsson, M Charlotte and Torell, Anna and Mogard, Elisabeth and Haglund, Emma
Journal: (2023)
Development of tandem antigen capture ELISAs measuring QSOX1 isoforms in plasma and serum
Authors: Koelbel, Calvin and Ruiz, Yvette and Wan, Zijian and Wang, Shaopeng and Ho, Thai and Lake, Douglas
Journal: Free Radical Biology and Medicine (2023)
Adulteration of Bread with Potassium Bromate: A Comparative Study between Nigeria and Finland
Authors: Osemwowa, Etinosa Usiosefe and Pohjanvirta, Raimo
Journal: Journal of Food and Nutrition Research (2023): 109--114
Trypanocidal and cell swelling activity of 20-deoxysalinomycin
Authors: Steverding, Dietmar and Strand, Daniel and Huczy{\'n}ski, Adam
Journal: Experimental Parasitology (2022): 108414
T-Cell Response against Varicella Zoster Virus in Patients with Multiple Sclerosis during Relapse and Remission
Authors: P{\'e}rez-Sald{\'\i}var, Miriam and Ordo{\~n}ez, Graciela and Pineda, Benjam{\'\i}n and Sotelo, Julio and Mart{\'\i}nez-Palomo, Adolfo and Flores-Rivera, Jos{\'e} and Espinosa-Cantellano, Martha
Journal: International journal of molecular sciences (2022): 298
Recombinant Protein Micelles to Block Transduction by SARS-CoV-2 Pseudovirus
Authors: Chattaraj, Rajarshi and Kim, Christina Y and Lee, Daeyeon and Hammer, Daniel A
Journal: ACS nano (2022): 17466--17477
Q-TOF LC-MS compounds evaluation of propolis extract derived from Malaysian stingless bees, Tetrigona apicalis, and their bioactivities in breast cancer cell, MCF7
Authors: Mohamed, Wan Ahmad Syazani and Ismail, Noor Zafirah and Muhamad, Musthahimah and Omar, Eshaifol Azam and Samad, Nozlena Abdul and Ooi, Jer Ping and Mohamad, Sharlina
Journal: Saudi Journal of Biological Sciences (2022): 103403
Insights into the direct anti-influenza virus mode of action of Rhodiola rosea
Authors: D{\"o}ring, Kristin and Langeder, Julia and Duwe, Susanne and Tahir, Ammar and Grienke, Ulrike and Rollinger, Judith M and Schmidtke, Michaela
Journal: Phytomedicine (2022): 153895
Evaluation of hepatotoxic effects of acetaminophen on HepG2 cells by parallel real-time monitoring in a multi-sensor analysis platform for automated cell-based assays
Authors: Heichler, Christina and Nagy, M{\'a}rton and Wolf, Peter
Journal: Bioenergetics Communications (2022): 6--6
The evolution of life history strategies in plants and its relationship to the evolution of protective cellular mechanisms against reactive oxygen species
Authors: Zakhary, Abraam and Nagarajan, Aashika and Ngo, Charlotte and Saidajan, Marwa and Babbar, Supreet and Brown, Jason
Journal: (2021)
Quantum Optical Immunoassay: Upconversion Nanoparticle-based Neutralizing Assay for COVID-19
Authors: Rajil, Navid and Esmaeili, Shahriar and Neuman, Benjamin W and Nessler, Reed and Wu, Hung-Jen and Yi, Zhenhuan and Brick, Robert W and Sokolov, Alexei V and Hemmer, Philip R and Scully, Marlan O
Journal: arXiv preprint arXiv:2110.06755 (2021)
Modulation of steroid hormone synthesis by methanolic extracts of Boerhavia diffusa
Authors: Dhanusha, G and Sujith, S and Nisha, AR and Kariyil, Bibu John and Raji, K and Aathira, KK and Haima, JS
Journal: Journal of Pharmacognosy and Phytochemistry (2021): 1260--1264
Folic acid enhances proinflammatory and antiviral molecular pathways in chicken B-lymphocytes infected with a mild infectious bursal disease virus
Authors: Uribe-Diaz, Santiago and Nazeer, Nauman and Jaime, J and Vargas-Berm{\'u}dez, DS and Yitbarek, A and Ahmed, Marya and Rodr{\'\i}guez-Lecompte, JC
Journal: British Poultry Science (2021): 1--13
Cortisol concentration affects fat and muscle mass among Polish children aged 6--13 years
Authors: Pruszkowska-Przybylska, Paulina and Sitek, Aneta and Rosset, Iwona and Sobalska-Kwapis, Marta and S{\l}omka, Marcin and Strapagiel, Dominik and {\.Z}{\k{a}}dzi{\'n}ska, El{\.z}bieta and Morling, Niels
Journal: BMC pediatrics (2021): 1--8
Associations between second to fourth digit ratio, cortisol, vitamin D, and body composition among Polish children
Authors: Pruszkowska-Przybylska, Paulina and Sitek, Aneta and Rosset, Iwona and Sobalska-Kwapis, Marta and S{\l}omka, Marcin and Strapagiel, Dominik and {\.Z}{\k{a}}dzi{\'n}ska, El{\.z}bieta and Morling, Niels
Journal: Scientific Reports (2021): 1--9
A purified inactivated vaccine derived from Vero cell-adapted zika virus elicits protection in mice
Authors: Oh, Hyun-Seok and Yoon, Jong Won and Lee, Sanghyun and Kim, Soo-Ok and Hong, Sun Pyo
Journal: Virology (2021): 124--130
N, O-Nucleoside Analogues: Metabolic and Apoptotic Activity
Authors: Marraffa, Andrea and Presenti, Piero and Macchi, Beatrice and Marino-Merlo, Francesca and Mella, Mariella and Quadrelli, Paolo
Journal: ChemistryOpen (2020)
High-performance countercurrent chromatography to access Rhodiola rosea influenza virus inhibiting constituents
Authors: Langeder, Julia and Grienke, Ulrike and D{\"o}ring, Kristin and Jafari, Mahtab and Ehrhardt, Christina and Schmidtke, Michaela and Rollinger, Judith M
Journal: Planta Medica (2020)
Dietary emulsifiers alter composition and activity of the human gut microbiota in vitro, irrespective of chemical or natural emulsifier origin
Authors: Miclotte, Lisa and De Paepe, Kim and Rymenans, Leen and Callewaert, Chris and Raes, Jeroen and Rajkovic, Andreja and Van Camp, John and Van de Wiele, Tom
Journal: Frontiers in microbiology (2020): 577474
Association of saliva 25 (OH) D concentration with body composition and proportion among pre-pubertal and pubertal Polish children
Authors: Pruszkowska-Przybylska, Paulina and Sitek, Aneta and Rosset, Iwona and Sobalska-Kwapis, Marta and S{\l}omka, Marcin and Strapagiel, Dominik and {\.Z}{\k{a}}dzi{\'n}ska, El{\.z}bieta and Morling, Niels
Journal: American Journal of Human Biology (2020): e23397
Anticancer potential of dihydrocaffeic acid: a chlorogenic acid metabolite
Authors: Santana-G{\'a}lvez, Jes{\'u}s and Villela Castrej{\'o}n, Javier and Serna-Sald{\'\i}var, Sergio O and Jacobo-Vel{\'a}zquez, Daniel A
Journal: CyTA-Journal of Food (2020): 245--248