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
- Enter Vmax (maximum reaction rate in μmol/min).
- Enter Km (Michaelis constant in mM).
- Enter substrate concentration [S] to get reaction rate v.
- Use Find Km tab to back-calculate Km from an observed rate.
- 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) ▾
- Berg, Tymoczko & Stryer — Biochemistry, 9th Ed., Chapter 8: Enzymes — Macmillan / W.H. Freeman
- Lehninger Principles of Biochemistry, 8th Ed. — Chapter 6: Enzyme Kinetics — Macmillan
- NCBI Bookshelf — Enzyme Kinetics — NCBI / W.H. Freeman
- Khan Academy — Enzyme Kinetics (AP Biology) — Khan Academy
- BRENDA — The Comprehensive Enzyme Information System — TU Braunschweig