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Kd calculator: binding curve fit (one site / Hill)

Estimate Kd (dissociation constant) from binding data. Fit one site (standard) or Hill (cooperativity), compare models (AICc), show mean±SD and residuals, and exclude outliers if needed.

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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 the model (auto/one site/Hill) and units.
  3. Kd, fitted curve, and fit metrics are shown.

This is an analysis tool. Model definitions can differ across software, so check the equation and the Kd definition (50% point) used in your workflow.

Input (paste / CSV)

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

Point exclusion (optional)
Click points on the plot to exclude/restore (Undo available)
Excluded
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Actions

Settings (minimum needed)

Advanced (optional)

If you include 0 concentration, it cannot be drawn on a log10 axis. The tool switches the display (e.g., symlog) when needed.

Results

Kd (50% point)
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pKd (M)
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Model—
Points—
R²—
RMSE—
AIC / AICc / BIC— / — / —
Bmax (Top−Bottom)—
Hill n (Hill only)—
Model comparison (auto)—

Plots

Click points to exclude/restore (Undo available)

Table (mean±SD, predicted, residuals)

Concentration mean SD y_hat resid Excluded

Parameters

Item Estimate 95% CI (when enabled)

The 95% CI is an approximation (linearization). Do not over-trust it when you have few points or outliers.

One site / Hill and Kd (50% point)

This tool fits a binding curve using a one-site (standard) or Hill (cooperativity) model and reports the concentration corresponding to the midpoint between top and bottom (the 50% point) as Kd.

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

Equations (reference)

Here, concentration x is ≥ 0.

  • one site（Langmuir）: y = bottom + (top-bottom) * x / (Kd + x)
  • Hill: y = bottom + (top-bottom) * x^n / (Kd^n + x^n)（n>0）

With this definition, x = Kd corresponds to the 50% point (midpoint between top and bottom).

If you include 0 concentration (control), 0 cannot be drawn on a log10 axis, so the tool adjusts the display (e.g., symlog).

FAQ

What is Kd (dissociation constant)?
In this tool, Kd is defined as the concentration corresponding to the 50% point of the binding curve (midpoint between top and bottom). A smaller Kd is often interpreted as higher affinity.
What is the difference between one site and Hill?
One site assumes standard saturable binding without cooperativity. The Hill model can capture cooperativity and is useful when the Hill coefficient n deviates from 1.
How does auto model selection work?
The tool fits both one site and Hill and compares metrics such as AICc. If the difference is small, preferring the simpler one-site model is often safer (shown in the results).
Can I include a zero concentration (control)?
Yes. The fit can handle it, but 0 cannot be drawn on a log x-axis, so the tool adjusts the display (e.g., symlog) when needed.
How are replicates handled?
By default, the fit uses the mean at each concentration. SD is used for error bars, and you can optionally weight points by 1/SD².
My Hill coefficient is extreme. Is that OK?
It can become unstable when you have few points, a narrow concentration range, or outliers. Consider excluding points, widening the range, or using constraints.
How is pKd calculated?
If your x unit can be converted to molar (M), pKd = -log10(Kd[M]). For mass concentration units (e.g., ng/mL), you can convert if molecular weight is known.