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Michaelis-Menten Equation Calculator

Calculate enzyme reaction rate using the classic Michaelis–Menten model: v = (Vmax[S])/(Km + [S]). Solve for v, Vmax, Km, or [S]. Includes quick picks, step-by-step, a mini saturation curve, and interpretation (low substrate vs saturation).

Background

The Michaelis–Menten equation describes how reaction velocity (v) changes with substrate concentration ([S]) for many enzyme-catalyzed reactions. Vmax is the maximum rate at saturation, and Km is the substrate concentration where v = Vmax/2.

Enter values

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

[S] and Km must use the same type of concentration unit (we convert internally).

At [S] = Km, the rate is half of Vmax.

This unit also applies to v.

If you solve for v, you can leave this blank.

v uses the same unit as Vmax (locked to avoid mismatched units).

Quick intuition

Low [S] → rate rises almost linearly. High [S] → saturation (v approaches Vmax). At [S]=Km, v=Vmax/2.

Options

Comparison curve (optional)

Enter an alternative Km₂ and Vmax₂ (same units as the main selections). We’ll overlay it on the same plot.

If blank, comparison overlay is ignored.

Uses the same time basis (per s / per min) as your main rate unit.

Rounding affects display only.

Chips prefill and calculate immediately.

Result

No results yet. Enter values and click Calculate.

How to use this calculator

  • Choose what to solve for: v, Vmax, Km, or [S].
  • Enter the other values (units can be different; we convert internally), then click Calculate.
  • Use the curve: it shows saturation, marks Km, and plots your current [S] point.

How this calculator works

  • Unit conversions: concentrations convert internally to M, rates to M/s.
  • Michaelis–Menten: v = (Vmax[S])/(Km + [S]).
  • Rearrangements: solves algebraically for the chosen variable (with checks like Vmax > v when solving for [S]).

Formulas & Equations Used

Michaelis–Menten equation: v = (Vmax[S])/(Km + [S])

Solve for Vmax: Vmax = v(Km + [S])/[S]

Solve for Km: Km = (Vmax[S]/v) − [S]

Solve for [S]: [S] = (vKm)/(Vmax − v)

Example Problem & Step-by-Step Solution

Example 1 — Compute v

Vmax=120 µM/s, Km=30 µM, [S]=30 µM. Find v.

  1. Use v = (Vmax[S])/(Km + [S]).
  2. Compute: v = 120×30/(30+30) = 60 µM/s.

Example 2 — Solve for Km

Vmax=120 µM/s, v=60 µM/s, [S]=30 µM. Find Km.

  1. Rearrange: Km = (Vmax[S]/v) − [S].
  2. Km = (120×30/60) − 30 = 60 − 30 = 30 µM.

Example 3 — Solve for [S]

Vmax=120 µM/s, Km=30 µM, v=80 µM/s. Find [S].

  1. Rearrange: [S] = (vKm)/(Vmax − v).
  2. [S] = (80×30)/(120−80) = 2400/40 = 60 µM.

Frequently Asked Questions

Q: What does Km mean?

Km is the substrate concentration where the rate is half of Vmax: v=Vmax/2.

Q: What happens at very high [S]?

The enzyme saturates and v approaches Vmax (adding more substrate barely increases rate).

Q: Can v be bigger than Vmax?

Not in the Michaelis–Menten model. If v ≥ Vmax, check inputs or units.