Enzyme Kinetics (Michaelis-Menten)

The Michaelis-Menten equation, v = Vmax × [S] ÷ (Km + [S]), describes how an enzyme's reaction velocity rises with substrate concentration and then plateaus once the enzyme's active sites are saturated — this calculator plugs your Vmax, Km, and current substrate concentration directly into that formula to return the instantaneous velocity. Km, the Michaelis constant, is the substrate concentration at which velocity reaches exactly half of Vmax; a lower Km means the enzyme reaches significant activity at lower substrate concentrations, which is interpreted as higher apparent affinity for that substrate. The calculator also reports percent of Vmax and percent saturation (both derived from the same v/Vmax and [S]/(Km+[S]) ratios), which together flag whether you're operating in the steep, substrate-limited part of the curve (low [S] relative to Km) or the flat, enzyme-limited plateau (high [S] relative to Km) — the accompanying curve, plotted from 0 to 5×Km, makes that saturation visually obvious.

Vmax/Km is reported as "catalytic efficiency," but this is only a true efficiency proxy when normalized by enzyme concentration (the real specificity constant is kcat/Km); as computed here it's a simpler ratio useful for comparing runs at the same enzyme concentration. The 1/v and 1/[S] values support a Lineweaver-Burk double-reciprocal plot, a classic linearization trick that turns the hyperbolic Michaelis-Menten curve into a straight line, making Km and Vmax easier to extract graphically — though it's known to weight low-substrate, low-velocity data points disproportionately and is used less than nonlinear regression in modern practice.