Enzyme Kinetics Calculator — Km from Michaelis-Menten
This enzyme kinetics calculator estimates the Michaelis constant (Km) using the observed reaction rate (v), substrate concentration ([S]), and the maximum velocity (Vmax). It uses the classic Michaelis-Menten relationship:
v = (Vmax × [S]) / (Km + [S])Rearranged to solve for Km:
Km = (Vmax × [S] / v) − [S]Enter your substrate concentration (in M), the observed reaction rate, and the known or estimated Vmax. The calculator will automatically compute Km and show a Michaelis-Menten curve based on the estimated Km and provided Vmax.
Example
Suppose you measure a reaction rate of 0.5 (in your rate units) at a substrate concentration of 0.1 M and you estimate Vmax to be 1. The calculator computes Km as:
Km = (1 × 0.1 / 0.5) − 0.1 = (0.2) − 0.1 = 0.1 M
The Michaelis-Menten curve will then be plotted to help visualize how velocity changes with substrate concentration given the estimated Km and Vmax.
How to Use
- Enter the substrate concentration [S] in molar units (M).
- Enter the observed initial reaction rate (v) under those substrate conditions.
- Enter the estimated Vmax for the enzyme under your assay conditions.
- The calculator auto-updates Km and shows a predicted curve. If inputs are invalid (for example, v ≤ 0 or v ≥ Vmax), an error message will be shown because Km cannot be computed reliably.
Tips and Considerations
- Ensure that rates are initial velocities measured under steady-state conditions.
- Units must be consistent: if Vmax is expressed in per-second units, reaction rate should be in the same units.
- If the observed reaction rate equals or exceeds Vmax, Km from this simple rearrangement is not meaningful.
- For more robust Km and Vmax estimation, consider fitting multiple [S], v pairs to the Michaelis-Menten equation using nonlinear regression.
Frequently Asked Questions
What is Km?
Km (Michaelis constant) is the substrate concentration at which the reaction rate is half of Vmax for a simple Michaelis-Menten enzyme system. It provides insight into the affinity of the enzyme for the substrate: a lower Km indicates higher affinity.
Can I calculate Vmax from a single measurement?
No — Vmax is best determined by analyzing multiple measurements across a range of substrate concentrations and fitting the data to the Michaelis-Menten model. This tool assumes you provide an estimated Vmax.
Why does the calculator require v < Vmax?
Mathematically, solving for Km from the rearranged Michaelis-Menten equation requires v to be greater than 0 and less than Vmax to produce a positive, finite Km. If v ≥ Vmax, the formula would produce zero or negative Km values which are biologically implausible for normal Michaelis-Menten kinetics.