Lineweaver–Burk plot calculator
Paste the substrate concentrations and the initial rates. The calculator converts them to 1/[S] and 1/v, fits a straight line, draws the plot and reads Vmax from the y intercept and Km from the slope or the x intercept.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the substrate concentrations and the initial rates in the same order; all must be above zero.
- Read the plot, the slope and the intercepts, and Vmax and Km derived from them.
- Copy the points to draw the plot in your own software if needed.
Taking reciprocals of v = Vmax[S] ÷ (Km + [S]) gives a straight line:
1/v = (Km ÷ Vmax) × 1/[S] + 1/Vmax
The calculator fits it by ordinary least squares on the points (1/[S], 1/v), then:
- Vmax = 1 ÷ intercept;
- Km = slope × Vmax;
- the line crosses the x axis at −1/Km.
Worked example
Default data: [S] = 0.5, 1, 2, 4, 8, 16 and v = 2.1, 3.4, 5.0, 6.6, 8.0, 8.9. The points run from (2, 0.4762) down to (0.0625, 0.1124).
- slope = 0.1874, y intercept = 0.1035, R² = 0.9996;
- Vmax = 1 ÷ 0.1035 = 9.659;
- Km = 0.1874 × 9.659 = 1.8104, and the x intercept is −1 ÷ 1.8104 = −0.5524.
When to use it
- To show data and the type of inhibition at a glance; it is the plot most textbooks use.
- To check a nonlinear fit: points should lie close to the line.
- Not as the only estimate of Vmax and Km when the low-concentration rates are noisy.
Frequently asked questions
What is a Lineweaver–Burk plot?
A straight-line form of the Michaelis–Menten equation: 1/v = (Km ÷ Vmax) × (1/[S]) + 1/Vmax. Plotting 1/v against 1/[S] gives a line whose y intercept is 1/Vmax, whose slope is Km/Vmax and which crosses the x axis at −1/Km.
How does it show the type of inhibition?
Plot the data with and without the inhibitor. Lines meeting on the y axis (same Vmax, higher Km) point to competitive inhibition; lines meeting on the x axis (same Km, lower Vmax) to non-competitive; parallel lines to uncompetitive. Run the calculator once for each data set and compare the intercepts.
Why do Vmax and Km differ from a direct fit?
Reciprocals stretch the scale: the lowest concentrations become the largest x values, and their small rates, which carry the largest relative error, pull the line. For the default data the line gives Km 1.8104 and Vmax 9.659, a direct nonlinear fit Km 1.9544 and Vmax 9.9436. For the best estimates use the Michaelis–Menten calculator.
Can I use zero as a concentration?
No: 1/0 has no value. Leave out blanks and points with no measurable rate.