ELISA 4PL Calculator

4-Parameter Logistic Curve Fit Tool

Enter your standard curve data, fit a 4PL model, and back-calculate unknown sample concentrations. Select an assay preset or enter custom standards.

How to use: 1) Choose your assay preset and units below, 2) enter your standard concentrations and OD values, 3) fit the 4PL curve, 4) enter your sample ODs and dilutions, 5) read the back-calculated concentrations. Steps 3-5 unlock once you fit the curve.
1Choose your assay
2Standard Curve Data

The concentration column is pre-filled with the standard dilution series for the selected assay preset — edit it for your own standards, or click Clear to start from a blank table. Enter OD values (comma-separated for replicates, e.g. 1.85, 1.92, 1.88).

# Concentration (pg/mL) OD Values (comma-separated replicates) Mean OD %CV
Frequently Asked Questions
An ELISA 4PL calculator fits a 4-parameter logistic curve to your standard curve and then back-calculates unknown sample concentrations from their measured OD values. Workflow on this tool: (1) pick an assay preset (or enter custom standards), (2) paste OD values for each standard concentration (comma-separated for replicates), (3) click Fit 4PL Curve to optimise A, B, C, D against your data using Levenberg-Marquardt. The tool then displays R², EC50, LLOQ, and ULOQ, validates each standard's back-calculated accuracy, and reports any sample with OD below LLOQ or above ULOQ. Sample concentrations and dilution corrections are tabulated and exportable as CSV.
Yes — 4PL and 4 parameter logistic refer to the same sigmoidal regression model: y = D + (A - D) / (1 + (x/C)^B). A 4PL calculator, 4PL curve calculator, and 4 parameter logistic curve calculator all fit the same four parameters (A min asymptote, B Hill slope, C EC50, D max asymptote) to dose-response data. The 4PL model is the FDA/EMA-recommended fit for immunoassay standard curves because it captures the natural sigmoidal saturation of antibody-antigen binding far better than linear or log-linear regression. For most ELISAs, R² should exceed 0.99 with each back-calculated standard within 80–120% of nominal.
A 4-parameter logistic (4PL) curve is a sigmoidal mathematical model used to fit dose-response data such as ELISA standard curves. The four parameters are: A (minimum asymptote, the response at zero concentration), B (Hill slope, describing the steepness of the curve), C (EC50/IC50, the concentration at the inflection point), and D (maximum asymptote, the response at infinite concentration). The equation is y = D + (A - D) / (1 + (x/C)^B). The 4PL model is preferred over linear regression for ELISA data because immunoassay dose-response curves are inherently sigmoidal, and linear fits only work over a narrow range.
A good ELISA standard curve should have an R-squared value above 0.99, ideally above 0.995. Each standard point should back-calculate to within 80-120% of its nominal concentration. The %CV between replicate wells should be below 20% for each standard. The curve should show a clear sigmoidal shape with well-defined upper and lower asymptotes. If more than one standard point fails acceptance criteria, the curve may need to be re-run.
LLOQ (Lower Limit of Quantification) is the lowest concentration of analyte that can be reliably measured with acceptable precision and accuracy. ULOQ (Upper Limit of Quantification) is the highest concentration that can be reliably measured. Together they define the quantifiable range or dynamic range of the assay. Samples with OD values outside this range should be flagged and re-assayed at a different dilution.
Samples are flagged when their OD values fall below the LLOQ or above the ULOQ of the standard curve. Below LLOQ means the analyte concentration is too low to quantify accurately. Above ULOQ means the response has saturated. To resolve this, dilute high-concentration samples further and re-assay, or use a more sensitive assay for low-abundance samples. Always report the dilution factor used.
For most ELISA applications, a 4PL fit is sufficient and recommended. The 5PL model adds an asymmetry parameter that can improve the fit when the sigmoidal curve is not symmetrical around the EC50. However, 5PL requires more data points and can overfit noisy data. Use 4PL as your default, and only switch to 5PL if you consistently see systematic deviations at the extremes of your curve with 7+ standard points.
A minimum of duplicate wells per standard concentration is standard practice, with triplicates recommended for critical assays or assay validation. Duplicates allow %CV calculation but provide limited statistical power. Triplicates give better precision estimates and allow outlier identification. For GLP/GMP-regulated assays, duplicates are the minimum requirement. The blank (zero standard) should always be run at least in duplicate.
The Hill slope B sets the steepness of the 4PL curve around its midpoint (EC50/C). A value near 1 gives a symmetric, moderately steep sigmoid; higher values (>1) give a steeper, more switch-like transition, while lower values (<1) give a shallower one. Typical ELISA Hill slopes fall in the ~0.5–3 range. A very steep slope narrows the usable dynamic range.
LLSCA/ULSCA (lower/upper limit of the standard curve, i.e. the lowest and highest calibrators) define the concentration range the curve actually spans. LLOQ/ULOQ (lower/upper limit of quantification) are the lowest and highest concentrations where back-calculated accuracy and precision meet acceptance criteria. The quantifiable range (LLOQ–ULOQ) always sits within the standard-curve range (LLSCA–ULSCA).
La curva patrón 4PL se construye ajustando las absorbancias de los estándares (calibradores) al modelo logístico de 4 parámetros y = D + (A-D)/(1+(x/C)^B), donde A y D son las asíntotas inferior y superior, C es la EC50 y B la pendiente de Hill. Después se calculan por interpolación inversa las concentraciones de las muestras desconocidas invirtiendo el ajuste; solo se aceptan los valores dentro del rango LLOQ–ULOQ y se comprueban el R² y la recuperación de los estándares recalculados.
Invert the fitted 4PL equation: x = C*((A-D)/(y-D) - 1)^(1/B), using the sample's absorbance y (the mean of its replicates, blank-subtracted), then multiply the result by the dilution factor. Only report concentrations that fall within the validated LLOQ–ULOQ range. Flag any out-of-range sample and re-assay it at a different dilution so its signal lands inside the quantifiable range.