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Biochemistry Curve fitting

IC50/EC50 calculator (dose–response curve fit: 4PL/5PL)

Estimate IC50/EC50 (the 50% point) from concentration–response data. Compare 4PL vs 5PL, choose inhibition vs activation, show mean±SD and residuals, exclude outliers, and review fit metrics (R², RMSE, AIC).

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Example (preset)

Choose an example to fill inputs and see results immediately.

Description
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How to use (3 steps)
  1. Paste concentration and response (replicate columns supported) or import a CSV/TSV file.
  2. Select direction (inhibition/activation) and model (auto/4PL/5PL).
  3. IC50/EC50 (50% point), fitted curve, and fit metrics are shown.

This is an analysis tool. 4PL/5PL definitions can differ across software. Check the equation and the definition of the “50% point”. In 5PL, the inflection parameter may differ from the 50% point.

Input (paste / CSV)

Format: col 1 = concentration, col 2+ = response (rep1, rep2, …). TSV/CSV supported.

Point exclusion (optional)
Excluded
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Actions

Settings (minimum needed)

Advanced (optional)
Note
In 5PL, the inflection parameter may differ from the 50% point. See the description in the result cards.

Results

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pIC50 (M)
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Model—
Direction—
Points (conc > 0)—
R²—
RMSE—
AIC / AICc / BIC— / — / —
Model comparison (auto)—

Plots

To exclude points, turn on “Point exclusion” in the Input section.

Table (mean±SD, predicted, residuals)

Concentration mean SD Predicted Residual Excluded

Parameters

Parameter Estimate 95% CI (when enabled)

The 95% CI is an approximation (linearization). Do not over-trust it when you have few points or outliers. In 5PL, the 50% point may differ from the inflection-parameter EC50, so interpret results with the notes in the result cards.

4PL/5PL and the 50% point

This tool fits a dose–response curve with 4PL (symmetric) or 5PL (asymmetric) and calculates the midpoint between top and bottom (the 50% point) as IC50/EC50.

Fitting uses Levenberg–Marquardt (nonlinear least squares). With SD weighting enabled, each point is weighted by 1/SD2.

Equations (reference)

Here, concentration x is positive.

  • 4PL: y = bottom + (top-bottom) / (1 + (x/EC50)^hill)
  • 5PL: y = bottom + (top-bottom) / (1 + (x/EC50_param)^hill)^asym

In 5PL, EC50_param is not always the “50% point”. This tool computes the 50% point separately and shows it explicitly.

A zero concentration (control) can help for normalization, but it cannot be used on a log x-axis, so excluding it from fitting is usually safer.

How to use this calculator effectively

Use this page to estimate the 50% point from dose-response data, compare 4PL with 5PL, and review fit quality before you export or share results.

1. Prepare the table first

Put concentration in the first column and replicate responses in the following columns. Keep concentration units consistent across all rows, and decide whether zero-concentration controls should be used only for normalization or also shown in the raw table.

2. Choose the simplest model that explains the curve

Start with auto or 4PL. Move to 5PL only when the left and right sides of the sigmoid are clearly asymmetric. A lower AIC can help, but do not rely on a small numerical difference alone.

3. Use point exclusion sparingly

Exclude a point only when you have an experimental reason, such as a failed well or a pipetting error. Check whether the direction, IC50/EC50, and residual pattern remain plausible after exclusion.

4. Interpret the 50% point and pIC50 together

This tool shows the 50% point explicitly. In 5PL, it may differ from the inflection parameter. If the concentration unit can be converted to molar, pIC50/pEC50 helps compare potency across datasets.

See also

FAQ

What is the difference between IC50 and EC50?
Often, IC50 is used for inhibition (response decreases with higher concentration) and EC50 for activation (response increases). This tool computes the 50% point and labels it based on the selected direction.
What is the difference between 4PL and 5PL?
4PL assumes a symmetric sigmoidal curve. 5PL can model asymmetric sigmoids and may fit better when the left and right sides differ.
Is the 5PL EC50 parameter the same as the 50% point?
Not always. In 5PL, the inflection parameter can differ from the midpoint between top and bottom. This tool computes and shows the 50% point explicitly.
Can I include a zero concentration (control)?
You can use it for normalization, but 0 cannot be used on a log x-axis. Excluding it from fitting is usually safer (this tool follows that approach).
How are replicates handled?
The fit uses the mean at each concentration. SD is used for error bars, and you can optionally weight points by 1/SD².
How is pIC50 calculated?
If your x unit can be converted to molar (M), pIC50 = -log10(IC50[M]). For mass concentration units (e.g., ng/mL), you can convert if molecular weight is known.