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Enzyme Turnover Number

Reactions catalyzed per enzyme per second.

Formula

kcat=Vmax[E]k_{cat} = \frac{V_{max}}{[E]}

Variables

V_{max}Max rate
[E]Enzyme concentration

Example

Enzyme efficiency measure

How it works

The turnover number, or kcat, tells you how many substrate molecules one enzyme active site can convert into product each second when the enzyme is working at full capacity. It comes from dividing the maximum reaction rate, Vmax, by the total concentration of active enzyme, [E], because at saturation each enzyme molecule is assumed to be cycling as fast as it can. This makes kcat an intrinsic catalytic property of the enzyme under defined conditions, not a measure of how much enzyme is present.

When to use it

Use this when comparing how fast different enzymes work, or when converting a measured Vmax into a per-enzyme catalytic rate. It is especially useful in enzyme kinetics, biochemical assay analysis, and evaluating enzyme engineering or mutation effects.

Worked example, step by step

Given: Vmax = 18.0 μmol/s [E] = 3.0 nmol Step 1: Make the units compatible. 18.0 μmol/s = 18.0 × 10^-6 mol/s 3.0 nmol = 3.0 × 10^-9 mol Step 2: Apply the formula. kcat = Vmax / [E] kcat = (18.0 × 10^-6 mol/s) / (3.0 × 10^-9 mol) Step 3: Divide the numbers and powers of ten. kcat = 6.0 × 10^3 s^-1 Final answer: kcat = 6000 s^-1 This means each enzyme molecule converts 6000 substrate molecules per second at maximum rate.

Common mistakes to avoid

  • using Vmax without converting enzyme amount and rate units to match
  • confusing kcat with Km or kcat/Km, which describe different aspects of enzyme behavior
  • dividing by total protein concentration instead of the concentration of active enzyme molecules

Did You Know?

BMI was devised by a Belgian astronomer in the 1830s to study populations, never intended to judge individuals.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026