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Michaelis-Menten Calculator

Calculate the rate of a Michaelis-Menten enzyme at a substrate concentration, or the substrate for a target rate, with the saturation curve and rates at multiples of Km.

Formula

v=Vmax⁡ [S]Km+[S]v = \dfrac{V_{\max}\,[S]}{K_{\mathrm{m}} + [S]}
[S]=Km vVmax⁡−v[S] = \dfrac{K_{\mathrm{m}}\,v}{V_{\max} - v}
at [S]=Km:v=Vmax⁡2\text{at } [S] = K_{\mathrm{m}}:\quad v = \dfrac{V_{\max}}{2}
Vmax⁡V_{\max}
the maximum rate, reached at saturating substrate
KmK_{\mathrm{m}}
the substrate concentration at which the rate is half of Vmax
[S][S]
substrate concentration, in the same unit as Km

How it works

For a single-substrate enzyme at steady state, the rate rises with substrate concentration and levels off at Vmax. The Michaelis constant Km is the concentration that gives half of it, and is a rough measure of how tightly the enzyme binds its substrate: a smaller Km means half-saturation at a lower concentration.

The table shows how the rate climbs with multiples of Km: at Km the enzyme is 50% saturated, at ten times Km about 91%, and getting near Vmax takes much more. That is why assays designed to measure Vmax use a substrate concentration of at least ten times Km.

Worked example

An enzyme with Vmax = 100 and Km = 2.5 (any consistent units) at [S] = 5.

  1. v = 100 × 5 / (2.5 + 5) = 66.67.
  2. [S] is 2 × Km, so the enzyme is 66.7% saturated.

v = 66.67, which is 66.7% of Vmax. To reach v = 75 would need [S] = 7.5.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • One substrate, no inhibition, cooperativity or product inhibition.
  • The substrate is in large excess over the enzyme, so its concentration is unchanged during the measurement.
  • Steady state: the enzyme-substrate complex forms and breaks down at the same rate.

Common mistakes

  • Using the equation for an allosteric or cooperative enzyme, whose curve is sigmoidal.
  • Mixing units for [S] and Km.
  • Expecting to reach Vmax at a finite concentration. The rate only approaches it.

Related tools

Enzyme Kinetics Calculator (Km, Vmax Fit)Nonlinear Michaelis-Menten fit, with Lineweaver-Burk for comparisonOpen calculatorEnzyme Activity Calculator (Units, Specific Activity)U/mL from an absorbance rate, specific activity and unit conversionOpen calculatorIC50 CalculatorFour-parameter logistic fit, with Ki by Cheng-PrusoffOpen calculatorProtein Binding Affinity (Kd) CalculatorKd and Bmax from a saturation curve, and fraction boundOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.