Michaelis-Menten Equation Calculator

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Calculate an enzyme's reaction rate, substrate concentration, Km, or Vmax when you know the other three Michaelis-Menten values.

Choose the calculation
Enter the known values
Initial reaction rate (v)

The rate predicted by the one-substrate Michaelis-Menten equation.

Rate as a percent of Vmax
%

At a substrate concentration equal to Km, this value is 50%.

Fraction of Vmax

A value of 0.75 means the rate is 75% of Vmax.

Substrate-to-Km ratio

A ratio of 1 corresponds to half of Vmax in this model.

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How to use our Michaelis-Menten Equation Calculator

  1. Choose the value you need in "Solve for." Leave "Reaction rate" selected to predict the initial reaction rate.
  2. Choose "Rate unit for v and Vmax," then enter every rate value in that same assay-rate unit.
  3. Choose the unit printed with Km in "Km concentration unit" and the unit printed with substrate in "Substrate concentration unit." These units can be different.
  4. Enter the three values required for the selected calculation and select "Calculate." Scientific notation such as 1e-9 is accepted.
  5. Read the first result as the requested value. Check "Rate as a percent of Vmax" and "Substrate-to-Km ratio" to see how close the modeled reaction is to Vmax.
  6. If you selected a concentration unit after entering its number, re-enter the source number. Changing a unit treats the existing number as being in the newly selected unit.
Example inputs for Michaelis-Menten Equation Calculator
Example inputs for Michaelis-Menten Equation Calculator

Definitions

Michaelis-Menten equation: A model that relates an enzyme's initial reaction rate to substrate concentration in a simple one-substrate reaction.

Initial reaction rate (v): The reaction rate measured early enough that major substrate depletion and product buildup have not changed it much.

Maximum reaction rate (Vmax): The limiting rate predicted by the model when substrate is very abundant.

Michaelis constant (Km): The substrate concentration at which the model predicts a rate equal to one-half of Vmax.

Substrate concentration ([S]): The substrate amount per volume in the reaction mixture.

Fraction of Vmax: The initial rate divided by Vmax. For example, 0.75 means the rate is 75% of Vmax.

Rate at common substrate-to-Km ratiosSimple Michaelis-Menten model: predicted initial rate as a share of Vmax. At [S] = Km, the predicted rate is 50% of Vmax; higher substrate approaches Vmax without reaching it.Rate at common substrate-to-Km ratiosSimple Michaelis-Menten model: predicted initial rate as a share of Vmax.0.25 x Km20 %0.5 x Km33.3 %1 x Km50 %2 x Km66.7 %4 x Km80 %Substrate concentration relative to Km
Rate at common substrate-to-Km ratios
At [S] = Km, the predicted rate is 50% of Vmax; higher substrate approaches Vmax without reaching it.

Common mistakes and quick fixes

Mistake: Using different assay-rate bases for "Initial reaction rate (v)" and "Maximum reaction rate (Vmax)," such as umol/min for one and absorbance units/min for the other.
Fix: Use values measured on the same assay basis and select that shared basis in "Rate unit for v and Vmax."

Mistake: Entering the stock-solution concentration instead of the concentration in the final reaction mixture.
Fix: Enter the substrate concentration after dilution in the assay mixture.

Mistake: Treating Km as a reaction rate.
Fix: Enter Km as a substrate concentration and choose its concentration unit separately.

Mistake: Trying to solve for substrate concentration or Km when the initial rate equals or exceeds Vmax.
Fix: Check the source values. A finite positive answer in these modes requires an initial rate greater than zero and lower than Vmax.

Limitations & Key Assumptions / Boundary Conditions

  • This calculator uses a simple one-substrate initial-rate Michaelis-Menten model. It does not model inhibition, allosteric behavior, cooperativity, multiple substrates, or changing enzyme activity.
  • Vmax and the initial rate must use the same assay basis. The calculator does not convert between amount rates, concentration rates, and absorbance rates.
  • Km and substrate concentration can be entered in M, mM, uM, or nM, but they must describe the same reaction conditions.
  • When a target rate is close to Vmax, the solved substrate concentration becomes very large and is highly sensitive to small changes in the entered values.
  • A calculated value follows from the entered measurements or fitted values. It does not prove that an enzyme system follows this model under every laboratory condition.

Methodology

Equation and units

The calculator converts Km and substrate concentration to M before calculation, so their source units may differ. It leaves v and Vmax in the selected shared rate unit.

v = Vmax[S] / (Km + [S])

In this equation, v is the initial reaction rate, Vmax is the maximum reaction rate, Km is the Michaelis constant, and [S] is substrate concentration.

Inverse calculations

When you select another unknown, the calculator rearranges the same equation and converts a solved concentration into the selected answer unit.

[S] = vKm / (Vmax - v)

Km = [S](Vmax - v) / v

Vmax = v(Km + [S]) / [S]

A finite positive substrate concentration or Km requires 0 < v < Vmax. Solving for Vmax requires [S] to be greater than zero.

Supporting values

After finding the requested value, the calculator uses the complete set of values to calculate the fraction of Vmax, percent of Vmax, and substrate-to-Km ratio.

fraction of Vmax = v / Vmax

percent of Vmax = 100v / Vmax

substrate-to-Km ratio = [S] / Km

Example:

with Vmax = 100 umol/min, Km = 2 mM, and [S] = 6 mM, the predicted rate is 100 x 6 / (2 + 6) = 75 umol/min. That is 75% of Vmax, and the substrate-to-Km ratio is 3.