Michaelis-Menten Calculator
The Michaelis-Menten model is the foundation of enzyme kinetics. It describes how reaction velocity (v) depends on substrate concentration ([S]): v = Vmax x [S] / (Km + [S]). Vmax is the maximum velocity (same units as v, e.g., umol/min) and Km is the Michaelis constant (same units as [S], e.g., mM). This calculator computes reaction velocity at a given substrate concentration, the percentage of Vmax achieved, and the ratio [S]/Km for context. Use consistent units throughout. The model assumes steady-state conditions and no product inhibition.
Michaelis-Menten equation
v = Vmax x [S] / (Km + [S])
When [S] = Km: v = Vmax / 2
When [S] is much greater than Km: v approaches Vmax
The equation assumes: (1) steady-state conditions, (2) [S] is much greater than [E]total, (3) no product inhibition, and (4) a single substrate binding site per enzyme molecule.
Key kinetic relationships
- At [S] = Km: v = 0.5 x Vmax (50% of maximum).
- At [S] = 0.1 x Km: v = approximately 0.09 x Vmax (9%).
- At [S] = 10 x Km: v = approximately 0.91 x Vmax (91%).
- Catalytic efficiency = kcat / Km (requires knowing [E]total to compute kcat from Vmax).
- A Lineweaver-Burk double-reciprocal plot (1/v vs 1/[S]) linearises the hyperbola for graphical Km and Vmax estimation.
Frequently asked questions
What is the Michaelis-Menten equation?
The Michaelis-Menten equation v = Vmax[S] / (Km + [S]) describes the relationship between enzyme reaction velocity (v) and substrate concentration ([S]). Vmax is the maximum velocity and Km is the Michaelis constant, the substrate concentration at which v = Vmax / 2.
What does Km mean biologically?
Km (Michaelis constant) is the substrate concentration that produces half-maximal velocity. A low Km means the enzyme has high affinity for its substrate (reaches half-maximal rate at low [S]). A high Km means low affinity. Km is approximately equal to the dissociation constant of the enzyme-substrate complex when kcat is much smaller than k-1.
What is Vmax?
Vmax is the maximum reaction velocity achieved when all enzyme active sites are saturated with substrate. It equals kcat x [E]total, where kcat is the catalytic constant (turnover number). Vmax increases when you add more enzyme; Km does not change with enzyme concentration.
What happens at [S] equal to Km?
When [S] = Km, the equation simplifies to v = Vmax x Km / (Km + Km) = Vmax / 2. So the reaction runs at exactly half the maximum velocity. This is the defining property of Km.
What is catalytic efficiency?
Catalytic efficiency (kcat/Km) combines turnover number and substrate affinity into a single figure of merit. It describes how efficiently an enzyme converts substrate to product at low [S]. Values near 10^8 to 10^9 M^-1 s^-1 approach the diffusion limit and are considered catalytically perfect.
Official sources
- NCBI Bookshelf (Stryer Biochemistry): Enzyme kinetics and Michaelis-Menten.
- NIH/NCBI: Original Michaelis-Menten 1913 paper translation.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.