Michaelis-Menten Rate Calculator
Enzymes do not speed up indefinitely as you add more substrate; they level off as their active sites fill, and the Michaelis-Menten equation describes exactly that. This calculator computes the reaction rate from three values using the standard form v equals Vmax times the substrate concentration, divided by Km plus the substrate concentration. Vmax is the maximum rate the enzyme can reach when fully saturated, Km is the Michaelis constant, the substrate concentration that produces half of Vmax, and the substrate concentration is how much is present. At low substrate the rate climbs almost in proportion to it; at high substrate the rate flattens toward Vmax as the enzyme saturates. A neat property follows: when the substrate concentration equals Km, the rate is exactly half of Vmax, a handy check on any calculation. With Vmax of 100, Km of 10 and a substrate concentration of 5, the rate is 100 times 5 divided by 15, which is 33.33. Keep Vmax and the rate in matching units, and Km and substrate in matching concentration units. Every figure is computed deterministically from the equation, never estimated, with the method and a worked example shown below for verification.
The reaction rate follows enzyme saturation kinetics: v = Vmax[S] / (Km + [S]). With Vmax = 100, Km = 10 and [S] = 5, the rate is 33.33.
Michaelis-Menten formula
v = Vmax x [S] / (Km + [S])
Vmax = maximum rate at saturation
Km = substrate concentration giving half of Vmax
[S] = substrate concentration
The rate rises with substrate and approaches Vmax as the enzyme saturates. When the substrate equals Km, the rate is exactly half of Vmax.
Worked example
An enzyme has Vmax 100 and Km 10, with a substrate concentration of 5.
- Numerator = Vmax x [S] = 100 x 5 = 500
- Denominator = Km + [S] = 10 + 5 = 15
- v = 500 / 15 = 33.33
- Check: at [S] = Km = 10, v would be 100 x 10 / 20 = 50, half of Vmax
The reaction rate is 33.33. These are the calculator's default inputs, so the result above matches the widget exactly.
Rate as a fraction of Vmax
The rate approaches Vmax as substrate rises far above Km.
| [S] relative to Km | Rate as % of Vmax |
|---|---|
| 0.5 Km | 33.3% |
| 1 Km | 50.0% |
| 2 Km | 66.7% |
| 10 Km | 90.9% |
Enzyme kinetics and biochemistry concepts: US Geological Survey (USGS).
Michaelis-Menten rate calculator: frequently asked questions
What is the Michaelis-Menten equation?
It describes the rate of an enzyme-catalyzed reaction as v equals Vmax times the substrate concentration, divided by Km plus the substrate concentration. The rate rises with substrate and approaches a maximum, Vmax, as the enzyme becomes saturated.
What do Vmax and Km mean?
Vmax is the maximum rate reached when the enzyme is fully saturated with substrate. Km, the Michaelis constant, is the substrate concentration at which the rate is exactly half of Vmax, and it reflects how tightly the enzyme binds its substrate.
What happens when substrate equals Km?
When the substrate concentration equals Km, the equation gives v equal to Vmax times Km divided by 2Km, which simplifies to half of Vmax. This is the defining property of Km and a useful check on the calculation.
What units should I use?
Vmax and the rate share the same units, such as micromoles per minute, and Km and the substrate concentration share the same concentration units, such as millimolar. As long as Km and the substrate match, the equation works in any consistent unit system.
Is the result computed automatically?
Yes. The page applies the Michaelis-Menten equation deterministically. No value is estimated or hard-coded, so changing Vmax, Km or the substrate concentration updates the rate instantly.
Official sources
- Enzyme kinetics and biochemistry concepts: US Geological Survey (USGS). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.