Michaelis-Menten Equation Calculator — Enzyme Kinetics
Enter the maximum velocity (Vmax), Michaelis constant (Km) and substrate concentration [S] to calculate the reaction rate v, enzyme saturation, and see the full velocity-versus-concentration curve.
µmol/min
µM
µM
v = Vmax × [S] / (Km + [S])
- 1
Denominator (Km + [S])
5 + 5 = 10 - 2
Reaction rate v
10 × 5 ÷ 10 = 5
How does this calculator work?
v = Vmax × [S] / (Km + [S]). Vmax is the maximum rate; Km is the substrate concentration at half-saturation. At [S] = Km the enzyme is 50% saturated. The curve rises hyperbolically, approaching Vmax asymptotically. Vmax/Km is a useful proxy for catalytic efficiency when substrate is limiting.
Formula
How this is calculated
The Michaelis-Menten model describes how the rate of an enzyme-catalysed reaction varies with substrate concentration under steady-state conditions. The model assumes a simple two-step mechanism: the enzyme (E) binds substrate (S) reversibly to form the enzyme–substrate complex (ES), which breaks down to release product (P) and regenerate E. Under steady state — when [ES] is not changing — the velocity follows v = Vmax × [S] / (Km + [S]).
Vmax is the theoretical maximum rate reached when every active site is occupied. Km (the Michaelis constant) is the substrate concentration at which v = Vmax/2; a lower Km indicates higher apparent affinity. The saturation fraction v/Vmax shows what fraction of maximum capacity is in use at the given [S]. The ratio Vmax/Km acts as a proxy for catalytic efficiency when substrate is limiting (comparable to kcat/Km when Vmax = kcat × [E]total).
The model assumes: a single substrate and product, constant enzyme concentration, negligible product inhibition, and no cooperative or allosteric effects. Real enzymes often deviate: allosteric regulation gives sigmoidal kinetics, multisubstrate reactions require more complex rate laws, and product inhibition alters the apparent Km. Units must be consistent — if Km is in µM, [S] must also be in µM; v and Vmax share whatever rate unit you choose.
Frequently asked questions
Km is the substrate concentration at which the reaction rate equals half of Vmax. It reflects the apparent affinity of the enzyme for its substrate — a lower Km means the enzyme reaches half-saturation at a lower concentration, indicating higher affinity. Km equals the true dissociation constant Kd only when the catalytic step is much slower than the dissociation step (the Briggs-Haldane limit).
By measuring reaction rates at several substrate concentrations and fitting the Michaelis-Menten equation by non-linear regression. Historically, the Lineweaver-Burk double-reciprocal plot (1/v vs 1/[S]) was used — the y-intercept is 1/Vmax and the x-intercept is −1/Km — but it amplifies errors at low [S] and is now mainly used for teaching.
The Michaelis-Menten equation is a rectangular hyperbola — v asymptotically approaches Vmax as [S] → ∞. In practice, increasing [S] tenfold above Km raises v to Vmax × 10/11 ≈ 91%, and a hundredfold above Km gives 99/100 ≈ 99%. True saturation would require infinitely concentrated substrate, which is physically impossible.
Also known as
TG we-Calculate Editorial Team. (2026). Michaelis-Menten Equation Calculator — Enzyme Kinetics [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/michaelis-menten-equation-calculator
TG we-Calculate Editorial Team. "Michaelis-Menten Equation Calculator — Enzyme Kinetics." TG we-Calculate. 2026. https://we-calculate.com/calculator/michaelis-menten-equation-calculator.
TG we-Calculate Editorial Team, "Michaelis-Menten Equation Calculator — Enzyme Kinetics," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/michaelis-menten-equation-calculator
@misc{wecalculate_michaelis_menten_equation_calculator, title = {Michaelis-Menten Equation Calculator — Enzyme Kinetics}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/michaelis-menten-equation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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