Ki Calculator (Cheng-Prusoff Equation) — IC50 to Ki Conversion

Q: What value should I enter for substrate concentration [S]?

Enter the fixed substrate concentration prepared in the enzyme activity assay, not Km. If IC50 was measured at multiple substrate concentrations, the Ki values calculated from each should be consistent — if they differ substantially, the inhibition mode may not be purely competitive or noncompetitive and the mechanism should be re-evaluated.

Q: How large can the difference between IC50 and Ki be?

For competitive inhibition, IC50/Ki = 1 + [S]/Km. At [S] = Km the ratio is 2; at [S] = 10×Km it is 11. Many laboratories use substrate concentrations above Km to ensure adequate signal-to-noise, so reporting IC50 directly in place of Ki will systematically overestimate inhibitor potency.

Q: Why does pure noncompetitive inhibition not require [S] and Km?

A pure noncompetitive inhibitor binds free enzyme E and the enzyme–substrate complex ES with equal affinity (α = 1). Changes in substrate concentration do not affect inhibitor binding, so IC50 is independent of [S] and Ki = IC50.

Q: Can this tool be used when the Hill slope is not equal to 1?

Not recommended. The Cheng-Prusoff equation is derived under the assumption that Hill slope n = 1. If the fitted IC50 curve shows n substantially outside this range ( 1.3), cooperativity, multiple binding sites, or mixed-mode inhibition may be present; the appropriate mechanism-specific correction should be used instead.

Convert IC50 to Ki using the Cheng-Prusoff equation for competitive, uncompetitive, or pure noncompetitive enzyme inhibition.

IC50 IC50 unit

Substrate concentration [S] [S] unit

Km Km unit

Inhibition type

Formula origin

The Cheng-Prusoff equation was published by Cheng Y-C and Prusoff W-H in 1973 in Biochemical Pharmacology (PMID: 4202581; Biochem Pharmacol 1973;22(23):3099-108, DOI 10.1016/0006-2952(73)90196-2). Derived directly from steady-state enzyme kinetic rate equations, it remains the standard method for converting experimentally measured IC50 values to true inhibition constants Ki, with more than ten thousand citations to date.

IC50 (half-maximal inhibitory concentration) is the inhibitor concentration required to reduce enzyme activity by 50% under a specific set of experimental conditions; Ki (inhibition constant) is the intrinsic equilibrium dissociation constant for inhibitor–target binding, independent of substrate concentration.

Equations for the three inhibition modes

Competitive inhibition

Ki = IC50 / (1 + [S] / Km)

A competitive inhibitor competes with the substrate for the same active site. The higher the substrate concentration, the more inhibitor is needed to displace it, so IC50 increases; Ki corrects for this concentration dependence and recovers the true binding affinity.

Pure noncompetitive inhibition

Ki = IC50

The inhibitor binds free enzyme E and the enzyme–substrate complex ES with equal affinity and does not interfere with substrate binding. IC50 is unaffected by [S] and equals Ki directly.

Uncompetitive inhibition

Ki' = IC50 / (1 + Km / [S])

The inhibitor binds only the ES complex. As substrate concentration increases, more binding targets become available and IC50 decreases with rising [S]. Here Ki’ is the apparent inhibition constant.

Why Ki is more informative than IC50

IC50 is condition-dependent: for the same inhibitor under competitive inhibition, raising the substrate concentration from 0.5×Km to 10×Km drives IC50 from 1.5×Ki to 11×Ki — a 7-fold difference with no change in the drug itself. Ki does not vary with experimental conditions and can be compared directly across laboratories; it is the preferred value to report when publishing inhibition data.

Worked example (tool defaults): IC50 = 50 nM, [S] = 100 µM, Km = 200 µM, competitive inhibition. [S]/Km = 100/200 = 0.5, Ki = 50 ÷ (1 + 0.5) = 33.3 nM.

Scope and limitations

Applicable only to single-substrate steady-state enzyme kinetics where substrate concentration remains constant during the assay (reaction conversion < 10%).
Requires an IC50 derived from a concentration–inhibition curve with Hill slope n ≈ 1; the equation is not valid when n deviates substantially from 1.
Mixed noncompetitive inhibition (unequal affinity for E and ES, α ≠ 1) and radioligand binding assays (which require the radioligand binding version of the equation) are outside the scope of this tool.

Common mistakes

Entering Km in place of [S]: The substrate concentration [S] is the actual substrate amount prepared in the assay; Km is the Michaelis constant for that substrate. The two are usually not equal. Confusing them produces an incorrect result without triggering any error.

Mismatched units: [S] and Km must be converted to the same unit before computing their ratio; a mismatch introduces an order-of-magnitude error. This tool normalises both to nM before computing.

Reporting IC50 instead of Ki: When the assay substrate concentration is 10×Km, IC50 for a competitive inhibitor exceeds Ki by 11-fold — a gap large enough to affect hit calling in drug screening and to distort SAR (structure–activity relationship) analysis.

FAQ

What value should I enter for substrate concentration [S]?

Enter the fixed substrate concentration prepared in the enzyme activity assay, not Km. If IC50 was measured at multiple substrate concentrations, the Ki values calculated from each should be consistent — if they differ substantially, the inhibition mode may not be purely competitive or noncompetitive and the mechanism should be re-evaluated.

How large can the difference between IC50 and Ki be?

For competitive inhibition, IC50/Ki = 1 + [S]/Km. At [S] = Km the ratio is 2; at [S] = 10×Km it is 11. Many laboratories use substrate concentrations above Km to ensure adequate signal-to-noise, so reporting IC50 directly in place of Ki will systematically overestimate inhibitor potency.

Why does pure noncompetitive inhibition not require [S] and Km?

A pure noncompetitive inhibitor binds free enzyme E and the enzyme–substrate complex ES with equal affinity (α = 1). Changes in substrate concentration do not affect inhibitor binding, so IC50 is independent of [S] and Ki = IC50.

Can this tool be used when the Hill slope is not equal to 1?

Not recommended. The Cheng-Prusoff equation is derived under the assumption that Hill slope n = 1. If the fitted IC50 curve shows n substantially outside this range (< 0.7 or > 1.3), cooperativity, multiple binding sites, or mixed-mode inhibition may be present; the appropriate mechanism-specific correction should be used instead.