Calculator Inputs
Use the form below to solve velocity, substrate concentration, Vmax, or Km from the Michaelis-Menten equation.
Example Data Table
| Substrate [S] (mM) | Velocity v (µmol/min) | Fraction of Vmax | Percent of Vmax |
|---|---|---|---|
| 0.25 | 10.9091 | 0.0909 | 9.09% |
| 0.50 | 20.0000 | 0.1667 | 16.67% |
| 1.00 | 34.2857 | 0.2857 | 28.57% |
| 2.50 | 60.0000 | 0.5000 | 50.00% |
| 5.00 | 80.0000 | 0.6667 | 66.67% |
| 10.00 | 96.0000 | 0.8000 | 80.00% |
Formula Used
Primary equation
v = (Vmax × [S]) / (Km + [S])
Rearranged to solve substrate concentration
[S] = (v × Km) / (Vmax - v)
Rearranged to solve maximum velocity
Vmax = v × (Km + [S]) / [S]
Rearranged to solve Michaelis constant
Km = [S] × (Vmax - v) / v
Useful interpretation
When [S] = Km, the reaction runs at v = Vmax / 2. That makes Km a practical marker of substrate affinity and operating range.
How to Use This Calculator
Step 1
Choose the quantity you want to solve: velocity, substrate concentration, Vmax, or Km.
Step 2
Enter the known values in consistent units. Substrate and Km must use the same concentration unit.
Step 3
Pick a graph range and number of points. Larger ranges help show the saturation plateau more clearly.
Step 4
Press Calculate Now. The result appears above the form with summary metrics and a Plotly curve.
Step 5
Use the CSV or PDF buttons to save your results for reports, lab notes, or classroom review.
Frequently Asked Questions
1. What does Km represent?
Km is the substrate concentration at which velocity reaches half of Vmax. Lower Km generally suggests stronger effective substrate binding or faster saturation under comparable conditions.
2. Why does the curve level off at high substrate concentration?
At high substrate levels, most enzyme active sites are occupied. Adding more substrate produces only small gains, so velocity approaches the ceiling value defined by Vmax.
3. Can this calculator solve for substrate concentration directly?
Yes. Choose the substrate concentration mode, enter target velocity, Vmax, and Km, then the calculator rearranges the equation to solve the required [S].
4. Why must target velocity stay below Vmax?
In the Michaelis-Menten model, velocity approaches Vmax asymptotically. A target velocity equal to or larger than Vmax would require infinite or nonphysical substrate concentration.
5. What units should I use?
Use any consistent units. Substrate and Km must match concentration units, while velocity and Vmax must match rate units. The calculator only works correctly when units stay consistent.
6. What does the [S]/Km ratio tell me?
The ratio indicates how close the system is to saturation. Small ratios suggest first-order behavior, while very large ratios suggest a near-zero-order, saturated enzyme response.
7. When is the Michaelis-Menten model less reliable?
It becomes less reliable with strong cooperativity, allosteric enzymes, substrate inhibition, multi-substrate systems, or significant product inhibition. Those cases often need more detailed kinetic models.
8. What does the graph show?
The graph plots reaction velocity against substrate concentration using the solved parameters. It also highlights your calculated operating point, making saturation behavior easier to interpret visually.