Example (preset)
Choose an example to fill inputs, then review the generated binding curve fit.
- Paste concentration and response (replicate columns supported) or import a CSV/TSV file.
- Select the model (auto/one site/Hill) and units.
- Kd, fitted curve, and fit metrics are shown.
Static sample: one-site binding
The default preset uses concentration in nM and response in percent. It estimates Kd ≈ 50.47 nM, pKd ≈ 7.297, and R² ≈ 0.99986 with the one-site model.
| Concentration | Mean response | What to check |
|---|---|---|
| 0 nM | ≈ 4.92% | Baseline; displayed with symlog handling when needed |
| 30 nM | ≈ 40.31% | Approaching the midpoint |
| 1000 nM | ≈ 95.63% | Upper binding plateau |
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.
Settings (minimum needed)
Results
Plots
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
Use this page to fit binding data and estimate Kd with a one-site or Hill-style curve while keeping the raw points visible.
How it works
The calculator fits the selected model to concentration and response pairs, then reports fitted parameters, residual behavior, and model comparison metrics. Keep concentration units consistent and inspect the curve before trusting a single Kd value.
When to use one site vs Hill
- Start with one site when the curve is a simple saturating binding response.
- Try Hill when the transition is unusually steep or shallow and you have enough points around the midpoint.
- Prefer the simpler model when AICc is similar or the Hill coefficient is unstable.
Common mistakes to avoid
- Mixing nM, uM, and mM concentrations in one table.
- Estimating Kd from data that never approaches saturation.
- Ignoring outliers or background correction before fitting.
- Interpreting a Hill coefficient without checking whether the model is justified.
Interpretation and worked example
Start with the example data, then replace points with your measured concentrations and responses. If residuals cluster on one side of the curve, revisit background, normalization, or the selected model.