Michaelis-Menten Equation Calculator
Km is a concentration, not a rate — it is where the enzyme runs at exactly half its maximum.
The formula
v = Vmax [S] / (Km + [S])
Km is a concentration, not a rate
The Michaelis constant is the substrate concentration at which the enzyme runs at half its maximum speed. That falls straight out of the equation: set [S] equal to Km and the fraction becomes Km/2Km, which is a half. It is measured in molar, and a low Km means the enzyme saturates at low substrate — loosely, that it binds tightly.
Saturation is the whole shape
At low substrate the rate rises almost linearly, because nearly every enzyme molecule is free and waiting. At high substrate it flattens, because every active site is already occupied and adding more substrate changes nothing. Reaching 90 % of Vmax takes nine times Km; reaching 99 % takes ninety-nine times. The last few per cent are effectively unreachable.
Catalytic perfection
Dividing the turnover number by Km gives the catalytic efficiency, and it has a ceiling: an enzyme cannot process a substrate faster than the substrate arrives. That diffusion limit is around 10⁸ to 10⁹ M⁻¹s⁻¹, and a handful of enzymes — catalase, carbonic anhydrase, triose phosphate isomerase — sit at it. They cannot be improved by any further evolution, because the limit is physics rather than chemistry.
Where these models stop
Michaelis-Menten assumes a single substrate and a steady state; Langmuir assumes one layer on identical sites with no interaction between them; Stokes-Einstein assumes a hard sphere much larger than the solvent molecules around it. Each is an idealisation that happens to describe real systems well over a useful range, and each fails predictably outside it. Knowing which assumption a number rests on is usually more valuable than the number.