Lineweaver-Burk Plot & Michaelis-Menten Calculator
Paste [S] and v. Get Km, Vmax, kcat and both plots.
Paste substrate concentrations and initial rates. The calculator fits v = Vmax·[S]/(Km + [S]) by nonlinear least squares and reports Km and Vmax with standard errors. It also fits the Lineweaver-Burk line 1/v = (Km/Vmax)(1/[S]) + 1/Vmax, where the y-intercept is 1/Vmax and the x-intercept is -1/Km. Enter the enzyme concentration to get kcat and kcat/Km.
Free, runs in your browser. Nothing you enter is uploaded.
What you enter
- Substrate concentration [S] and initial rate v for each point (at least 3)
- Units for [S] and v
- Total enzyme concentration (optional, for kcat)
What you get
- Km and Vmax with standard errors
- R² of the nonlinear fit
- Lineweaver-Burk slope, intercept, Km, Vmax and R²
- kcat and kcat/Km
- Michaelis-Menten and Lineweaver-Burk plots as SVG or PNG
Formula
v = Vmax·[S] / (Km + [S]) | 1/v = (Km/Vmax)·(1/[S]) + 1/Vmax | kcat = Vmax / [E]total
The nonlinear fit uses the Levenberg-Marquardt method on the untransformed rates, with standard errors from the residual variance and the Jacobian (the same method as SciPy curve_fit). The Lineweaver-Burk line is an ordinary least-squares fit of 1/v against 1/[S]: slope = Km/Vmax, y-intercept = 1/Vmax, x-intercept = -1/Km.
Questions
How do you find Km and Vmax from a Lineweaver-Burk plot?
Plot 1/v against 1/[S] and fit a straight line. The y-intercept equals 1/Vmax, so Vmax = 1/intercept. The x-intercept equals -1/Km, and the slope equals Km/Vmax, so Km = slope × Vmax.
Why do Km and Vmax differ between the Lineweaver-Burk plot and the nonlinear fit?
Taking reciprocals magnifies the error in the slowest rates, measured at low [S], so those points pull the line more than they should. The nonlinear fit weights all points on the original scale and gives more reliable estimates. Report the nonlinear values and use the Lineweaver-Burk plot for display or for spotting inhibition type.
What does Km tell you?
Km is the substrate concentration at which the rate is half of Vmax. A lower Km means the enzyme reaches half its maximum rate at a lower substrate concentration. Km equals the dissociation constant of the enzyme-substrate complex only when product formation is much slower than substrate release.
How do I calculate kcat?
Divide Vmax by the total active enzyme concentration in the same concentration units. With Vmax in µM/min and [E] in µM, kcat comes out in min⁻¹; divide by 60 for s⁻¹. The calculator does the unit conversion and also gives kcat/Km in M⁻¹ s⁻¹.
How many substrate concentrations do I need?
At least 3 for a fit, but 6 to 10 is better. Spread them from about 0.2 × Km to 5 × Km or higher so both the rising part and the plateau of the curve are covered.
How does the Lineweaver-Burk plot show the type of inhibition?
Run the assay with and without inhibitor and compare the lines. Competitive inhibitors give lines that cross on the y-axis (same Vmax). Noncompetitive inhibitors give lines that cross on the x-axis (same Km). Uncompetitive inhibitors give parallel lines.
References
- Lineweaver H, Burk D (1934). The determination of enzyme dissociation constants. J Am Chem Soc 56:658-666.
- Johnson KA, Goody RS (2011). The original Michaelis constant: translation of the 1913 Michaelis-Menten paper. Biochemistry 50:8264-8269.
- Cornish-Bowden A (2012). Fundamentals of Enzyme Kinetics, 4th ed. Wiley-Blackwell.
More Laboratory Calculators
All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.