# Michaelis-Menten Equation Calculator

Determines parameters of enzyme-controlled reactions, from rates of reaction to substrate concentration and Michaelis constant.

Refer to the text below the tool for more information about the parameters in the Michaelis-Menten equation.

The Michaelis Menten kinetic equation is used for determining the kinetics of enzyme-controlled reactions, where the biochemical reaction is assumed to be involving a single substrate.

Michaelis-Menten kinetics allows the computing of the rate of the reaction (V_{0}), substrate concentration [S], Michaelis constant (K_{m}), and the maximum rate of reaction (V_{max}).

### Formulas

`V`

_{0}= V_{max}x [S] / ([S] + K_{m})`V`

_{max }= V_{0 }x ([S] + K_{m}) / [S]`K`

_{m }= (V_{max}x [S] / V_{0}) – [S]`[S] = V`

_{0}x K_{m}/ (V_{max}– V_{0})

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## Michaelis-Menten Equation Explained

The Michaelis Menten kinetic equation is used for determining the kinetics of enzyme-controlled reactions, where the biochemical reaction is assumed to be involving a single substrate.

Michaelis-Menten kinetics allows the computing of:

- Reaction Rate (V
_{0}) – measured in 1/sec or 1/min; - Substrate concentration [S] – measured in M, mM, μM or nM;
- Maximum Rate (V
_{max}) – measured in 1/sec or 1/min; - Michaelis constant (K
_{m}) – measured in M, mM, μM or nM.

Each of the four parameters in the Michaelis-Menten equation can be extracted as follows:

`V`

_{0}= V_{max}x [S] / ([S] + K_{m})`V`

_{max }= V_{0 }x ([S] + K_{m}) / [S]`K`

_{m }= (V_{max}x [S] / V_{0}) – [S]`[S] = V`

_{0}x K_{m}/ (V_{max}– V_{0})

The Michaelis-Menten model is based on the enzyme equation: E + S ⇄ ES → E +P where E is the enzyme, S is the substrate and P is the product.

The enzyme binds with the substrate, and that connection results in the product and this reaction can happen multiple times and, in both directions, so essentially, the above equation describes three reactions:

- k1: E + S → ES
- k2: ES → E + S
- k3: ES → E + P

The amount of ES remains relatively stable during the course of a reaction, until the amount of substrate is close to 0, so the following two observations can be drawn:

- When the substrate concentration is low, the speed of equation is directly proportional to the substrate;
- When the level of substrate is high, the speed becomes independent and does not exceed a maximum rate.

The Michaelis constant describes the stability of the ES complex – in the same unit as the substrate.

## References

### Original reference

Michaelis L, Menten ML. Die Kinetik der Invertinwirkung. Biochem Z. 1913; 49: 333–369.

### Other references

Johnson KA and Goody RS. The Original Michaelis Constant: Translation of the 1913 Michaelis–Menten Paper. Biochemistry 2011, 50, 39, 8264–8269.

Reuveni S, Urbakh M, Klafter T. Role of Substrate Unbinding in Michaelis-Menten Enzymatic Reactions. Proc Natl Acad Sci U S A. 2014;111(12):4391-6.

Specialty: Miscellaneous

Year Of Study: 1913

Article By: Denise Nedea

Published On: June 5, 2020

Last Checked: June 5, 2020

Next Review: June 5, 2025