Michaelis-Menten Calculator

Calculate enzyme reaction rates using the Michaelis-Menten equation. Find Km, Vmax, kcat, and catalytic efficiency. Includes Lineweaver-Burk double-reciprocal plot parameters.

μmol/min
mM
mM
Reaction Rate v (μmol/min)
Fractional Saturation (v/Vmax)
% of Maximum Rate
Extended More scenarios, charts & detailed breakdown
μmol/min
mM
mM
Rate v
Fractional Saturation
% of Vmax
Professional Full parameters & maximum detail
μmol/min
mM
μM
mM
mM
mM
mM
mM
kcat (Turnover Number, s⁻¹)
Catalytic Efficiency kcat/Km (M⁻¹s⁻¹)
v at [S]₁
v at [S]₂
v at [S]₃
v at [S]₄
v at [S]₅

How to Use This Calculator

  1. Enter Vmax (maximum reaction rate in μmol/min).
  2. Enter Km (Michaelis constant in mM).
  3. Enter substrate concentration [S] to get reaction rate v.
  4. Use Find Km tab to back-calculate Km from an observed rate.
  5. Use Professional for kcat, catalytic efficiency, and saturation curves.

Formula

v = Vmax × [S] / (Km + [S])

kcat = Vmax / [E]_total  |  Catalytic efficiency = kcat / Km

Lineweaver-Burk: 1/v = (Km/Vmax) × (1/[S]) + 1/Vmax

Example

Example: Vmax = 100 μmol/min, Km = 10 mM, [S] = 10 mM. v = 100 × 10 / (10 + 10) = 50 μmol/min (50% of Vmax, since [S] = Km).

Frequently Asked Questions

  • The Michaelis-Menten equation describes enzyme reaction kinetics: v = Vmax × [S] / (Km + [S]). Here v is the reaction rate, Vmax is the maximum rate, [S] is substrate concentration, and Km is the Michaelis constant (the [S] at half-maximal rate).
  • Km (Michaelis constant) equals the substrate concentration at which reaction rate is exactly half of Vmax. A lower Km indicates higher enzyme affinity for the substrate. Km ≈ Kd (dissociation constant) when the catalytic step is slow.
  • kcat is the number of substrate molecules converted to product per enzyme molecule per second. kcat = Vmax / [E]_total. Typical enzymes: catalase kcat ~4×10⁷ s⁻¹, carbonic anhydrase ~10⁶ s⁻¹, typical enzyme ~10²-10³ s⁻¹.
  • kcat/Km measures how efficiently an enzyme converts substrate to product at low [S]. The theoretical maximum is ~10⁸-10⁹ M⁻¹s⁻¹ (diffusion limit). Enzymes near this limit are called "catalytically perfect."
  • The Lineweaver-Burk (double-reciprocal) plot graphs 1/v vs 1/[S]. The y-intercept = 1/Vmax, x-intercept = −1/Km, and slope = Km/Vmax. It linearizes the hyperbolic Michaelis-Menten curve for graphical analysis.

Related Calculators

Sources & References (5)
  1. Berg, Tymoczko & Stryer — Biochemistry, 9th Ed., Chapter 8: Enzymes — Macmillan / W.H. Freeman
  2. Lehninger Principles of Biochemistry, 8th Ed. — Chapter 6: Enzyme Kinetics — Macmillan
  3. NCBI Bookshelf — Enzyme Kinetics — NCBI / W.H. Freeman
  4. Khan Academy — Enzyme Kinetics (AP Biology) — Khan Academy
  5. BRENDA — The Comprehensive Enzyme Information System — TU Braunschweig