The negative base-10 logarithm of the dissociation constant Kd expressed in molar units. A Kd of 1 nM is pKd 9; 10 nM is pKd 8. Working in pKd keeps affinities that span six orders of magnitude on one comparable, roughly linear scale.

Why is ΔG = RT ln Kd?

At equilibrium the standard free energy of a reaction is −RT ln K for its equilibrium constant K. For binding, the association constant Ka = 1/Kd, so ΔG° = −RT ln Ka = RT ln Kd, with Kd in molar units relative to the 1 M standard state. A negative ΔG° means binding is favorable.

Is Ki the same as Kd?

No. Ki is an inhibition constant from a competition experiment and Kd a dissociation constant from a direct binding experiment. For a competitive inhibitor at equilibrium they coincide, and Cheng–Prusoff converts an IC50 into Ki; IC50 itself depends on assay conditions and is not interchangeable with either.

Does temperature change pKd?

Not in this converter: pKd is defined from Kd alone. The temperature enters through RT, so ΔG° computed from the same Kd is larger in magnitude at 37 °C than at 25 °C. A measured Kd does itself change with temperature, by the van 't Hoff relation, but that is a property of the system, not of the conversion.

Kd to pKd and ΔG binding affinity calculator

Results

pKd: 7.921
Kd: 12 nM
ΔG°, kcal/mol: −10.81
ΔG°, kJ/mol: −45.21
Ka = 1/Kd: 8.333e7 M⁻¹
RT at this temperature: 2.479 kJ/mol0.5925 kcal/mol

Ki from IC50 · an approximation

Cheng and Prusoff, 1973

Cheng–Prusoff: IC50 to Ki

For a competitive inhibitor measured at equilibrium, Ki = IC50 / (1 + [S]/Km) in an enzyme assay, or Ki = IC50 / (1 + [L]/Kd) in a competition binding assay. The result holds only under those conditions; it is not a Kd, and it shifts with the concentration of substrate or tracer used.

Cheng and Prusoff, 1973. Valid for competitive inhibition at equilibrium and when the inhibitor is not depleted; not valid for tight binding, irreversible or non-competitive inhibitors.

The formulas

Three numbers, one equilibrium

Kd: Kd = [A][B] / [AB] = koff / kon; The equilibrium dissociation constant, in molar units. It is the concentration of free ligand at which half the target sites are occupied.
pKd: pKd = −log₁₀(Kd / M); A dimensionless logarithm: 1 nM is pKd 9, 1 µM is pKd 6. One pKd unit is a tenfold change in Kd and 1.364 kcal/mol at 25 °C.
ΔG°: ΔG° = RT ln Kd = −RT ln Ka = −2.303 RT · pKd; The standard binding free energy, taking Kd relative to the 1 M standard state. R = 8.314 462 618 J·mol⁻¹·K⁻¹ (CODATA 2018, exact); 1 kcal = 4.184 kJ (thermochemical calorie).
RT: RT(298.15 K) = 2.479 kJ/mol = 0.5925 kcal/mol; So at 25 °C, ΔG° in kcal/mol is about −1.364 × pKd; at 37 °C the factor is −1.419.

Worked examples

R = 8.314 462 618 J·mol⁻¹·K⁻¹

By hand, at 298.15 K

Each row is computed from the formulas above; the calculator reproduces every value.

Worked examples: Kd, pKd and ΔG° at 298.15 K unless stated.
Kd	pKd	ΔG°, kcal/mol	ΔG°, kJ/mol	Note
12 nM	7.921	−10.81	−45.21	ln(1.2 × 10⁻⁸) = −18.238; × 2.4790 kJ/mol
3.2 nM	8.495	−11.59	−48.49	a low-nanomolar binder
250 pM	9.602	−13.10	−54.81	one log unit tighter than 2.5 nM: −1.364 kcal/mol more
1.5 µM	5.824	−7.945	−33.24	a typical fragment-screening hit
1 mM	3.000	−4.093	−17.12	the weak end of the scale
12 nM at 310.15 K	7.921	−11.24	−47.03	the same Kd at 37 °C; pKd does not change, ΔG° does

Questions

What the numbers mean

What is pKd?: The negative base-10 logarithm of the dissociation constant Kd expressed in molar units. A Kd of 1 nM is pKd 9; 10 nM is pKd 8. Working in pKd keeps affinities that span six orders of magnitude on one comparable, roughly linear scale.
Why is ΔG = RT ln Kd?: At equilibrium the standard free energy of a reaction is −RT ln K for its equilibrium constant K. For binding, the association constant Ka = 1/Kd, so ΔG° = −RT ln Ka = RT ln Kd, with Kd in molar units relative to the 1 M standard state. A negative ΔG° means binding is favorable.
Is Ki the same as Kd?: No. Ki is an inhibition constant from a competition experiment and Kd a dissociation constant from a direct binding experiment. For a competitive inhibitor at equilibrium they coincide, and Cheng–Prusoff converts an IC50 into Ki; IC50 itself depends on assay conditions and is not interchangeable with either.
Does temperature change pKd?: Not in this converter: pKd is defined from Kd alone. The temperature enters through RT, so ΔG° computed from the same Kd is larger in magnitude at 37 °C than at 25 °C. A measured Kd does itself change with temperature, by the van 't Hoff relation, but that is a property of the system, not of the conversion.

Sources

CODATA 2018 — molar gas constant R (NIST) (opens in a new tab) — R = 8.314 462 618 J·mol⁻¹·K⁻¹, exact
NIST Special Publication 811 — Guide for the Use of the International System of Units (opens in a new tab) — thermochemical calorie, 4.184 J
Cheng Y, Prusoff WH. Biochem Pharmacol 1973;22:3099–3108 (opens in a new tab) — the Ki–IC50 relationship
Gilson MK, Zhou H-X. Calculation of protein–ligand binding affinities. Annu Rev Biophys Biomol Struct 2007 (opens in a new tab) — ΔG°, standard state and Kd
IUPAC Gold Book (opens in a new tab) — dissociation constant, equilibrium constant

A reference tool. It performs a unit conversion and does not predict, measure or rank anything; nothing here is an Epitorix performance figure.

Kd to pKd and ΔG, converted.

Converter

Results

Cheng–Prusoff: IC50 to Ki

Three numbers, one equilibrium

By hand, at 298.15 K

What the numbers mean

Sources

Converter

Results

Cheng–Prusoff: IC50 to Ki

Three numbers, one equilibrium

By hand, at 298.15 K

What the numbers mean

The other six, open in the browser.