Michaelis-Menten Calculator
Reaction velocity from Vmax, Km, and substrate concentration.
What it does
The Michaelis-Menten equation describes how the initial rate of an enzyme-catalyzed reaction changes with substrate concentration. It turns a saturation curve into a compact formula with two parameters, Vmax and Km.
Vmax is the maximum velocity the enzyme can reach when substrate is plentiful. Km is the substrate concentration at half of Vmax and is often used as a rough inverse measure of enzyme affinity: a lower Km means the enzyme reaches half speed at a lower substrate level.
The tool above takes Vmax, Km, and the substrate concentration. It returns the predicted initial velocity, that velocity as a percentage of Vmax, and the ratio of substrate to Km, which makes the saturation behavior easier to read.
This is an idealized model. Real enzymes can show cooperativity, inhibition, multiple substrates, or diffusion limits, and the calculation uses the concentrations you enter rather than a full kinetic fit.
How to use
- Enter Vmax in the activity unit you want, such as micromoles per minute.
- Enter Km in the same concentration unit as the substrate.
- Enter the substrate concentration in that same unit.
- Read the predicted velocity and its percentage of Vmax.
- Check the [S]/Km ratio to see how close the reaction is to saturation.
- Change one input at a time to see how sensitive the rate is.
Formula
- v
- Initial reaction velocity in activity units per time.
- Vmax
- Maximum velocity at saturating substrate.
- Km
- Michaelis constant, the substrate concentration at half Vmax.
- [S]
- Substrate concentration, in the same unit as Km.
When [S] equals Km, the denominator becomes 2 x Km and the velocity is Vmax/2. When [S] is much smaller than Km, the rate is roughly proportional to [S]. When [S] is much larger, the rate approaches Vmax.
Worked example
Example: Vmax 100, Km 5, substrate 10
Vmax is 100 units/min, Km is 5 mM, and the substrate concentration is 10 mM.
- Substrate-to-Km ratio: 10 / 5 = 2.
- Denominator: Km + [S] = 5 + 10 = 15.
- Numerator: Vmax x [S] = 100 x 10 = 1,000.
- Velocity: 1,000 / 15 = 66.67 units/min.
- Percent of Vmax: 66.67 / 100 x 100 = 66.67%.
- Tool shows 66.67 units/min, 66.67%, and a ratio of 2.
Reference table
| [S] / Km | Velocity / Vmax | Behavior |
|---|---|---|
| 0.1 | 9.09% | Nearly first order |
| 0.25 | 20.00% | Well below saturation |
| 0.5 | 33.33% | Below half speed |
| 1 | 50.00% | Half Vmax at Km |
| 2 | 66.67% | Above half speed |
| 4 | 80.00% | Approaching saturation |
| 10 | 90.91% | Close to Vmax |
Limits
- Assumes a single-substrate reaction with rapid equilibrium or steady-state kinetics and no inhibition.
- Uses the Vmax and Km you enter. Real values must be fitted from initial-rate experiments, not read from a single endpoint.
- Does not model substrate depletion, product inhibition, cooperativity, or enzyme inactivation over time.
- Concentrations must use the same unit for Km and [S]. Mixing molar and millimolar values gives a wrong ratio.
Common mistakes
- Entering Km in mM and substrate in M without converting.
- Reporting velocity in the wrong activity unit because Vmax was entered in a different unit.
- Treating Km as a rate constant instead of a concentration.
- Assuming the equation applies when substrate is depleted or product accumulates.
- Using a linear fit through the entire curve instead of the Michaelis-Menten form.
Try it yourself
Quick checks. Answers sit tucked under each question.
Vmax 50 units/min, Km 2 mM, substrate 8 mM. What is the velocity?
v = 50 x 8 / (2 + 8) = 400 / 10 = 40 units/min, which is 80% of Vmax.
Vmax 120 units/min, Km 10 mM, substrate 2 mM. What is the percent of Vmax?
v = 120 x 2 / 12 = 20 units/min. That is 20 / 120 = 16.67% of Vmax.
Vmax 200 units/min, Km 4 mM, substrate 4 mM. What is the velocity?
Substrate equals Km, so the velocity is half of Vmax: 100 units/min, or 50%.
Questions
What does Km mean in simple terms?
Km is the substrate concentration that gives half of the maximum reaction rate. A smaller Km generally means the enzyme reaches half speed at a lower substrate level.
Is Km the same as Vmax?
No. Km is a concentration, while Vmax is a velocity. They have different units and describe different parts of the saturation curve.
Why does velocity level off at high substrate?
The enzyme molecules become saturated with substrate, so adding more substrate cannot increase the rate beyond Vmax.
Can I use this calculator for inhibition?
Only if you already have an adjusted apparent Vmax or Km for the inhibitor. The basic equation does not model inhibitor binding directly.
What units should I use?
Any consistent units work. Km and substrate must match, and the velocity uses the same activity unit as Vmax per unit time.
Does the result show the initial rate?
Yes, the equation describes the initial velocity before substrate depletion or product buildup becomes significant.