Understand the relationship
The reasoning behind the result
Kd is a concentration parameter in this model
Kd=RfreeLfree/Bcomplex
For a reversible one-to-one interaction under the stated concentration-based model, Kd relates free binding sites, free ligand and their complex at equilibrium. The numerator has concentration squared and the denominator has concentration, so Kd uses the same concentration unit.
This definition does not make every apparent affinity measurement interchangeable. Temperature, medium, molecular form, site class and assay conditions matter. Multivalent avidity and cooperative or heterogeneous interactions are outside the one-site interpretation.
A curve fit estimates capacity alongside affinity
For trial Kd, fᵢ=Lᵢ/(Kd+Lᵢ); Bmax=Σ(Bᵢfᵢ)/Σfᵢ²
The unweighted nonlinear fit minimizes squared differences between recorded specific binding and the one-site curve. It profiles a positive Bmax at each trial Kd, then searches the entered positive Kd interval. The fitted capacity remains in the response unit; ligand concentration and response units need not be the same.
A corrected response can include signed measurement scatter, but the fitted physical capacity and Kd must be positive. The model has a zero specific-binding baseline, no fitted nonspecific term and no ligand-depletion correction because its x values are free concentrations. A bounded optimum and limited concentration range are reported rather than treated as a precise affinity determination. No confidence interval, automatic weighting or outlier removal is supplied.
Kinetic and equilibrium constants connect only under the same mechanism
kon·Rfree·Lfree=koff·Bcomplex ⇒ Kd=koff/kon
At equilibrium, the forward and reverse fluxes of an elementary reversible one-to-one step are equal. With kon in L/(mol·s) and koff in s⁻¹, their ratio is mol/L. The calculator converts that result to the chosen concentration unit before reporting it.
The ratio is not a general way to interpret a composite observed relaxation rate, a transport-limited sensor trace or a multistep interaction. Both input rate constants must describe the same interaction and conditions. Positive finite constants are required here; irreversible and non-identifiable zero-rate boundaries need another model.
Follow the numbers
Checking the same Kd with two kinds of evidence
- At equilibrium, free sites=20 nM, free ligand=40 nM and complex=80 nM give Kd=20×40/80=10 nM.
- Total sites are 100 nM and total ligand is 120 nM, with 80% of sites occupied.
- For a matching elementary model, koff=0.01 s⁻¹ and kon=1,000,000 L/(mol·s) give Kd=10⁻⁸ mol/L=10 nM.
The equality illustrates the model; it does not establish that separately measured experiments share conditions or mechanism.
Quick guide
How to use this calculator
- Choose the evidence actually available; equilibrium concentrations, curve measurements and kinetic constants are distinct inputs.
- For fitting, use free ligand and already corrected specific binding, with an explicit positive Kd search interval.
- For concentration balance, enter independently measured positive free species and bound complex at equilibrium.
- Inspect units, residuals or balance reconciliation. Agreement between methods only has meaning when conditions and the underlying model match.
Calculation method
Calculation and interpretation
Make the evidence behind an affinity estimate explicit while preserving fitted capacity, residuals and molar-unit conversions.
B=Bmax·Lfree/(Kd+Lfree); Kd=RfreeLfree/Bcomplex; for the same elementary reversible model, Kd=koff/kon.
Worked example
Checking the same Kd with two kinds of evidence
The equality illustrates the model; it does not establish that separately measured experiments share conditions or mechanism.
B=Bmax·Lfree/(Kd+Lfree); Kd=RfreeLfree/Bcomplex; for the same elementary reversible model, Kd=koff/kon.
Supported inputs
Precision and limits
A one-to-one experimental model
Assumes one class of independent equivalent sites, reversible one-to-one binding and stated assay conditions. It does not establish affinity in an organism, immune protection, antibody performance, clinical effect or a treatment dose.
Specific binding and free concentration
Multivalent avidity, cooperativity, nonspecific binding, multiple site classes, transport limitation and rebinding require other models. An antigen–antibody system can use this arithmetic only when the stated one-to-one independent-site approximation is justified.
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