What is the Cheng-Prusoff equation?

The Cheng-Prusoff equation is Ki = IC50 / (1 + [S] / Km). It converts the half-maximal inhibitory concentration IC50 — which depends on substrate concentration — into the true dissociation constant Ki, which is an intrinsic property of the inhibitor-enzyme interaction.

Why is Ki preferred over IC50?

IC50 varies with assay conditions, especially substrate concentration. Running the same assay at [S] = Km gives IC50 = 2×Ki, while at [S] = 0.1×Km, IC50 ≈ Ki. Ki is a condition-independent constant, making potency comparisons valid across different labs and assay protocols.

Does the Cheng-Prusoff equation apply to non-competitive inhibitors?

No. The standard Cheng-Prusoff equation Ki = IC50 / (1 + [S]/Km) applies only to competitive inhibitors. Non-competitive and uncompetitive inhibitors have different correction factors; for non-competitive inhibition, Ki = IC50 is often used directly since the IC50 of a non-competitive inhibitor does not depend on [S].

What units should I use?

IC50, [S], and Km must all use the same concentration unit (e.g., all in µM or all in nM). The resulting Ki will be in the same unit. The calculator is unit-agnostic — just keep all three inputs consistent.

What happens when [S] is much larger than Km?

When [S] >> Km the correction factor (1 + [S]/Km) is large, so IC50 is much larger than Ki. This means IC50 significantly overestimates how potent the inhibitor actually is. Running assays at [S] ≈ Km minimizes this bias.

Can I reverse-calculate IC50 from Ki?

Yes. Rearranging the Cheng-Prusoff equation gives IC50 = Ki × (1 + [S]/Km). This tool shows both directions: enter any two known values and leave IC50 or Ki blank to solve for the unknown (use the reverse mode button).

Ki Inhibition Calculator

Name: Ki Inhibition Calculator
Availability: InStock
Author: Nham Vu

Enter IC50, substrate concentration, and Km to calculate Ki using the Cheng-Prusoff equation for competitive enzyme inhibitors.

Inhibitor Parameters

IC50 — Half-maximal inhibitory concentration

Measured concentration that inhibits 50% of enzyme activity.

[S] — Substrate concentration in assay

Substrate concentration used when measuring IC50.

K_m — Michaelis constant

Substrate concentration at which v = ½V_max.

Concentration unit (same for all values)

Result

K_i

—

Correction factor

—

1 + [S]/K_m

Ki = IC50 / (1 + [S]/K_m)
Ki = — / (1 + — / —)
Ki = — / — = —

IC50 —

K_i —

[S] / K_m ratio —

Correction factor —

IC50 / Ki ratio —

Assay Bias

[S] = 0 → IC50 = Ki [S] = Km → IC50 = 2×Ki

No bias — High bias

Run a calculation to see how much your assay's [S]/Km ratio inflates IC50 relative to Ki.

Summary

Enter IC50, substrate concentration, and Km to calculate Ki using the Cheng-Prusoff equation for competitive enzyme inhibitors.

How it works

Enter the IC50 value measured in your inhibition assay.
Enter [S], the substrate concentration used during the assay.
Enter Km, the Michaelis constant of the enzyme for that substrate.
Select consistent concentration units for all three values.
Click Calculate; the tool applies Ki = IC50 / (1 + [S]/Km) and displays Ki with the correction factor.
The correction factor panel shows how much [S]/Km shifts IC50 away from Ki.

Use cases

Convert IC50 measurements to the condition-independent Ki for competitive inhibitors.
Compare inhibitor potency across experiments run at different substrate concentrations.
Validate that a measured IC50 is reasonable given known Km and [S].
Calculate the correction factor when [S] is much larger than Km.
Teach the Cheng-Prusoff relationship in biochemistry or pharmacology courses.
Determine Ki from dose-response curves in drug discovery screening campaigns.
Estimate IC50 from a known Ki when designing a new assay at a target [S].
Assess how assay substrate concentration biases apparent IC50 relative to true Ki.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu