Michaelis-Menten Equation Calculator

The Michaelis-Menten equation, v = (Vmax x [S]) / (Km + [S]), describes how the initial velocity v of an enzyme-catalyzed reaction depends on substrate concentration [S]. Vmax is the maximum possible velocity at saturating substrate, and Km (the Michaelis constant) is the substrate concentration at which v equals half of Vmax. It is the foundational equation of enzyme kinetics, derived by Leonor Michaelis and Maud Menten in 1913.

Km is the substrate concentration at which reaction velocity is exactly half-maximal (v = Vmax/2). It reflects the balance between how fast the enzyme-substrate complex forms and how fast it breaks down (back to enzyme and substrate, or forward to product). A low Km generally indicates the enzyme reaches significant activity at low substrate concentrations, often interpreted as higher apparent affinity for the substrate.

Vmax is the theoretical maximum reaction velocity, reached only when the enzyme is fully saturated with substrate (every active site occupied) so that adding more substrate can no longer increase the rate. Vmax depends on the total enzyme concentration and the enzyme's catalytic turnover rate (kcat), specifically Vmax = kcat x [E]total.

At high [S], essentially all enzyme molecules are already bound to substrate (saturated), so adding more substrate cannot create more enzyme-substrate complexes to react. The reaction becomes limited by how fast the enzyme itself can process substrate (turnover rate), not by substrate availability, which is exactly what produces the characteristic hyperbolic plateau near Vmax.

Rearranging the Michaelis-Menten equation for [S] gives [S] = (Km x v) / (Vmax - v). This only works for v strictly less than Vmax, since v can approach but never reach or exceed Vmax; as v gets closer to Vmax, the required [S] grows without bound.

When [S] = Km, the equation simplifies to v = Vmax x Km / (Km + Km) = Vmax / 2 exactly. This is precisely how Km is defined and measured experimentally: it is the substrate concentration that produces half-maximal velocity.

Km and [S] share the same concentration units, commonly molar (M), millimolar (mM), or micromolar (μM). Vmax and v share the same rate units, commonly micromoles of product per minute, or moles per second per unit of enzyme. As long as [S] and Km use matching units, and Vmax and v use matching units, the equation works with any consistent unit choice.

Km and Vmax are typically found by measuring initial reaction velocity at several different substrate concentrations, then fitting the Michaelis-Menten curve to the data (nonlinear regression), or using a linearization method like the Lineweaver-Burk double-reciprocal plot (1/v vs 1/[S]), though modern practice favours direct nonlinear fitting for statistical accuracy.

Not necessarily. A low Km means the enzyme reaches half-maximal activity at low substrate, which is advantageous when substrate is scarce, but the overall catalytic efficiency of an enzyme is better judged by the ratio kcat/Km (specificity constant), which accounts for both binding affinity and how fast the enzyme actually converts bound substrate to product.

The classic derivation assumes a single substrate, a steady-state concentration of the enzyme-substrate complex (its formation and breakdown rates are equal and roughly constant over the measurement period), substrate in large excess over enzyme, and that the reverse reaction (product back to substrate) is negligible during the initial-velocity measurement window.

Competitive inhibitors increase the apparent Km (more substrate is needed to reach the same velocity) but do not change Vmax, since enough substrate can still outcompete the inhibitor. Noncompetitive inhibitors decrease Vmax but leave Km unchanged, since they block catalysis regardless of substrate binding. Uncompetitive inhibitors decrease both Km and Vmax proportionally. Comparing shifted curves is a standard way to classify inhibitor type.