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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).

How to use this calculator effectively

This guide helps you use Kd calculator: binding curve fit (one site / Hill) in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

How it works

The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

When to use

Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

Common mistakes to avoid

Interpretation and worked example

Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

See also

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.