In biochemistry, Michaelis–Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions involving the transformation of one substrate into one product. It takes the form of a differential equation describing the reaction rate ${\displaystyle v}$ (rate of formation of product P, with concentration ${\displaystyle p}$) as a function of ${\displaystyle a}$, the concentration of the substrate  A (using the symbols recommended by the IUBMB). Its formula is given by the Michaelis–Menten equation:

${\displaystyle V}$, which is often written as ${\displaystyle V_{\max }}$, represents the limiting rate approached by the system at saturating substrate concentration for a given enzyme concentration. The Michaelis constant ${\displaystyle K_{\mathrm {m} }}$ has units of concentration, and for a given reaction is equal to the concentration of substrate at which the reaction rate is half of ${\displaystyle V}$. Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions. Only a small proportion of enzyme-catalysed reactions have just one substrate, but the equation still often applies if only one substrate concentration is varied.

The plot of ${\displaystyle v}$ against ${\displaystyle a}$ has often been called a "Michaelis–Menten plot", even recently, but this is misleading, because Michaelis and Menten did not use such a plot. Instead, they plotted ${\displaystyle v}$ against ${\displaystyle \log a}$, which has some advantages over the usual ways of plotting Michaelis–Menten data. It has ${\displaystyle v}$ as the dependent variable, and thus does not distort the experimental errors in ${\displaystyle v}$. Michaelis and Menten did not attempt to estimate ${\displaystyle V}$ directly from the limit approached at high ${\displaystyle \log a}$, something difficult to do accurately with data obtained with modern techniques, and almost impossible with their data. Instead they took advantage of the fact that the curve is almost straight in the middle range and has a maximum slope of ${\displaystyle 0.576V}$ i.e. ${\displaystyle 0.25\ln 10\cdot V}$. With an accurate value of ${\displaystyle V}$ it was easy to determine ${\displaystyle \log K_{\mathrm {m} }}$ from the point on the curve corresponding to ${\displaystyle 0.5V}$.

This plot is virtually never used today for estimating ${\displaystyle V}$ and ${\displaystyle K_{\mathrm {m} }}$, but it remains of major interest because it has another valuable property: it allows the properties of isoenzymes catalysing the same reaction, but active in very different ranges of substrate concentration, to be compared on a single plot. For example, the four mammalian isoenzymes of hexokinase are half-saturated by glucose at concentrations ranging from about 0.02 mM for hexokinase A (brain hexokinase) to about 50 mM for hexokinase D ("glucokinase", liver hexokinase), more than a 2000-fold range. It would be impossible to show a kinetic comparison between the four isoenzymes on one of the usual plots, but it is easily done on a semi-logarithmic plot.

A decade before Michaelis and Menten, Victor Henri found that enzyme reactions could be explained by assuming a binding interaction between the enzyme and the substrate. His work was taken up by Michaelis and Menten, who investigated the kinetics of invertase, an enzyme that catalyzes the hydrolysis of sucrose into glucose and fructose. In 1913 they proposed a mathematical model of the reaction. It involves an enzyme E binding to a substrate A to form a complex EA that releases a product P regenerating the original form of the enzyme. This may be represented schematically as

where ${\displaystyle k_{\mathrm {+1} }}$ (forward rate constant), ${\displaystyle k_{\mathrm {-1} }}$ (reverse rate constant), and ${\displaystyle k_{\mathrm {cat} }}$ (catalytic rate constant) denote the rate constants, the double arrows between A (substrate) and EA (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).

Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by

in which ${\displaystyle e_{0}}$ is the initial enzyme concentration. The reaction order depends on the relative size of the two terms in the denominator. At low substrate concentration ${\displaystyle a\ll K_{\mathrm {m} }}$, so that the rate ${\displaystyle v={\frac {k_{\mathrm {cat} }e_{0}a}{K_{\mathrm {m} }}}}$ varies linearly with substrate concentration ${\displaystyle a}$ (first-order kinetics in ${\displaystyle a}$). However at higher ${\displaystyle a}$, with ${\displaystyle a\gg K_{\mathrm {m} }}$, the reaction approaches independence of ${\displaystyle a}$ (zero-order kinetics in ${\displaystyle a}$), asymptotically approaching the limiting rate ${\displaystyle V_{\mathrm {max} }=k_{\mathrm {cat} }e_{0}}$. This rate, which is never attained, refers to the hypothetical case in which all enzyme molecules are bound to substrate. ${\displaystyle k_{\mathrm {cat} }}$, known as the turnover number or catalytic constant, normally expressed in s ^–1, is the limiting number of substrate molecules converted to product per enzyme molecule per unit of time. Further addition of substrate would not increase the rate, and the enzyme is said to be saturated.