The Michaelis-Menten equation is the starting point for almost all quantitative enzyme kinetics. Published by Leonor Michaelis and Maud Menten in 1913, it describes how the rate of an enzyme-catalyzed reaction depends on substrate concentration, and it remains the standard model taught in biochemistry courses and used in lab reports today. This calculator runs the equation forward from Vmax, Km, and substrate concentration, or rearranges it to solve for any one of the three constants when you already have a measured velocity.
How the Michaelis-Menten Calculator works
The calculator implements v = Vmax·[S] / (Km + [S]) directly. At low substrate concentration ([S] much less than Km), velocity rises almost linearly with [S] — the enzyme has plenty of free active sites. As [S] increases toward and past Km, the curve bends: active sites start staying occupied, and each additional bit of substrate produces a smaller velocity gain. At very high [S] (well above Km), the enzyme approaches saturation and v flattens out toward Vmax. This shape — steep rise, then a bending plateau — is the classic Michaelis-Menten hyperbola shown on the Kinetics Curve tab.
Inputs and what they mean
Vmax (maximum velocity) is a property of the enzyme and its total concentration in the reaction — it's the ceiling the velocity approaches but never quite reaches. Km (the Michaelis constant) is a property of the enzyme-substrate pair; it's often described loosely as an inverse measure of affinity, since a lower Km means the enzyme reaches half-maximal speed with less substrate around. Substrate concentration [S] is the one variable you control most directly in an experiment. On the Solve tab, you instead supply a measured velocity v plus two of the three constants, and the calculator rearranges the equation to find the missing one — useful when you've run an assay and need to back out Km or Vmax from the data.
Limits and edge cases
The basic Michaelis-Menten model assumes a single substrate, no product inhibition, no cooperativity between active sites, and steady-state conditions (substrate is in large excess relative to enzyme, so [S] doesn't change appreciably during measurement). Enzymes with multiple binding sites that show cooperative behavior (like hemoglobin's oxygen binding) follow a sigmoidal curve instead and need the Hill equation, not this model. When solving for Km or [S] on the Solve tab, the known velocity v must be strictly less than Vmax — at or above Vmax the rearranged equation has no finite solution, since v only approaches Vmax asymptotically and never equals or exceeds it. This calculator computes the non-linear Michaelis-Menten curve directly; it does not perform the linearized Lineweaver-Burk transformation (1/v vs 1/[S]), which is a separate curve-fitting technique some labs use for parameter estimation from noisy data.