IC50 to Ki calculator

How do I convert IC50 to Ki?

Enter the IC50 with its unit, the substrate concentration used in the assay, and the substrate's Km. The calculator returns the pIC50, then applies the Cheng-Prusoff equation for the inhibition mechanism you choose and shows the Ki, the pKi and the equation with your values substituted. For a competitive inhibitor measured with substrate at its Km, Ki is half the IC50.

A kinase inhibitor with an IC50 of 100 nM, measured at 10 µM ATP against a Km for ATP of 10 µM:

IC50: 100 nM (1.0000e-7 M)
pIC50: 7.000

Mechanism: Competitive
[S]: 10 µM
Km: 10 µM
Equation: Ki = IC50 / (1 + [S]/Km)
Ki = 100 nM / (1 + 10 µM/10 µM) = 50 nM
pKi: 7.301

The same equation converts a radioligand displacement IC50, with the radioligand concentration in place of [S] and its Kd in place of Km. A competitor with an IC50 of 45 nM against 2 nM of a radioligand whose Kd is 0.5 nM:

IC50: 45 nM (4.5000e-8 M)
pIC50: 7.347

Mechanism: Competitive
[S]: 2 nM
Km: 500 pM
Ki = 45 nM / (1 + 2 nM/500 pM) = 9 nM
pKi: 8.046

How do I convert IC50 to pIC50?

pIC50 is the negative base-10 logarithm of the IC50 in moles per liter, so convert the IC50 to molar first and then take $-\log_{10}$. An IC50 of 100 nM is $10^{-7}$ M, which is a pIC50 of 7.0; 1 µM is 6.0 and 10 nM is 8.0. Each unit of pIC50 is a tenfold change in potency, and a higher pIC50 means a more potent compound.

To go the other way, set Start from to pIC50. The IC50 is $10^{-\text{pIC50}}$ M:

IC50: 50.12 nM (5.0119e-8 M)
pIC50: 7.300

Turn off Calculate Ki when you only need the conversion. The IC50 vs Ki guide explains why potency is compared and averaged as pIC50 rather than as a concentration.

Settings

The calculator takes no file. Every input is a setting.

Each concentration has its own unit, so an IC50 in nM, ATP in mM and Km in µM can be entered as they appear in a paper. A field left empty is reported as an error rather than replaced with its default.

Results

The Result tab shows the values and the substituted equation. Data lists IC50 in nM, µM and M, pIC50, Ki in the same units, pKi and the shift factor. Files has that table as CSV, the full calculation as JSON, and a run log.

The Cheng-Prusoff equations

Yung-Chi Cheng and William Prusoff derived how the IC50 of a reversible inhibitor relates to its inhibition constant for each classic mechanism of a single-substrate enzyme (Cheng and Prusoff, 1973):

A competitive inhibitor competes with substrate for the free enzyme, so more substrate raises the IC50; at [S] = 10 Km the IC50 is 11 times Ki. An uncompetitive inhibitor binds only the enzyme-substrate complex and behaves the opposite way, appearing more potent as substrate rises. A pure noncompetitive inhibitor binds the free enzyme and the complex equally well, so its IC50 equals Ki at any substrate concentration.

Mixed inhibition, where the two binding constants differ, needs both constants and cannot be recovered from one IC50. Measure inhibition at several substrate concentrations and fit the mixed model instead.

Tight-binding correction

Cheng-Prusoff assumes the free inhibitor concentration equals the amount added. When an inhibitor is potent enough that its IC50 approaches the enzyme concentration, a meaningful share of it is bound and the IC50 can never fall below half the enzyme concentration. Solving the Morrison equation for tight-binding inhibitors at 50% activity gives $IC_{50} = K_i^{app} + [E]/2$ (Morrison, 1969; Copeland et al., 1995). With the correction on, the calculator subtracts [E]/2 before applying Cheng-Prusoff:

IC50: 8 nM (8.0000e-9 M)
[E]: 5 nM
IC50 − [E]/2: 5.5 nM
Equation: Ki = (IC50 − [E]/2) / (1 + [S]/Km)
Ki = (8 nM − 5 nM/2) / (1 + 10 µM/10 µM) = 2.75 nM
pKi: 8.561

That example also gets a warning, because an IC50 within 10-fold of [E] leaves Ki poorly determined. An IC50 at or below [E]/2 returns an error: the assay is titrating the enzyme, and only a repeat with less enzyme can measure Ki.

When the result is not a true Ki

The calculation is only as good as the assay behind it. Cheng-Prusoff assumes reversible binding at equilibrium, a Hill slope close to 1, a Km measured under the same buffer and temperature, and an inhibitor whose mechanism you have confirmed. A time-dependent or covalent inhibitor has an IC50 that drifts with preincubation time and no single Ki. A cell-based IC50 includes permeability, protein binding and the cell's own substrate levels, which the equation knows nothing about.

Functional assays are a separate case. An IC50 from inhibiting an agonist response depends on the agonist's efficacy and the shape of its concentration-response curve, and applying the binding form of Cheng-Prusoff there can misstate antagonist affinity (Leff and Dougall, 1993). Schild analysis is the standard method for those data.

Which tool should I use?

Boltz-2 reports predicted affinity as $\log_{10}$ of an IC50 in µM, so a value of −1 is 0.1 µM. Its pIC50 is 6 minus that value, and you can enter it here with Start from set to pIC50.

FAQ

What is the Cheng-Prusoff equation?

It converts an IC50 into an inhibition constant by removing the effect of substrate or radioligand concentration. For a competitive inhibitor, $K_i = IC_{50}/(1 + [S]/K_m)$.

Is Ki always smaller than IC50?

For competitive and uncompetitive inhibitors measured with any substrate present, yes; the IC50 is shifted upward by the factor in the denominator. For a pure noncompetitive inhibitor the two are equal.

What is a good pIC50?

It depends on the stage of a project. Screening hits often sit around pIC50 5 to 6 (1 to 10 µM), and optimized leads and drug candidates are usually above 7 (100 nM), commonly 8 to 9.

Can I convert a Kd into a Ki?

For simple one-site reversible binding, Ki is the equilibrium dissociation constant of the inhibitor, so a Kd measured directly for the same complex under the same conditions is the same quantity. No conversion is needed.

Why does the calculator refuse my IC50?

With the tight-binding correction on, an IC50 at or below half the enzyme concentration has no Ki that the equation can recover. Check that [E] is the active enzyme concentration in the well, and repeat the assay with less enzyme if it is.