Tools›Statistics

Michaelis-Menten Km and Vmax Calculator (Nonlinear Fit + Three Linearization Methods)

Nonlinear fit for Km and Vmax with Lineweaver-Burk, Hanes-Woolf, and Eadie-Hofstee linearizations shown in parallel—their spread directly reports data quality.

1/v = (Km/Vmax)·(1/[S]) + 1/Vmax

FAQ

Why is the Lineweaver-Burk double-reciprocal plot not recommended for estimating Km?

Because the reciprocal transformation distorts the error structure. Low-substrate-concentration points are already the least precise (small rates, poor signal-to-noise). Taking the reciprocal pushes their 1/[S] values to the far right of the plot, where they dominate the regression slope—the least reliable data carry the most weight, and their errors are amplified by the transformation. Conversely, the high-concentration points that are measured most accurately cluster near the origin and contribute almost nothing to the fit. The double-reciprocal plot is still useful today, but for diagnosing deviations (e.g., identifying inhibition types), not for reading parameter values.

Which method should I use then?

Use nonlinear regression whenever possible—fit the raw (concentration, rate) pairs by least-squares with no transformation, so the error structure is preserved as-is. That is also the recommended value this tool reports. If a linearization is required, Hanes-Woolf ([S]/v vs [S]) is the most stable of the three; Eadie-Hofstee is problematic because v appears on both axes, so measurement error enters both sides.

The four methods give different Km values. Which one is correct?

With noise-free data, all four agree exactly—the default example in this tool uses such ideal data, so all four results are identical. Once noise is present they diverge, and **the magnitude of that divergence is itself a readout of whether the dataset can withstand linearization**. When the spread exceeds 10%, report the nonlinear fit value and state the method clearly in your methods section.

What information must be included when reporting Km?

Reporting "Km = 0.34 mM" alone is incomplete. With noisy data, the four algorithms commonly disagree by tens of percent, so you must state: which fitting method was used, how many concentration points, the concentration range, and the number of replicates. Without this, anyone comparing your value to theirs cannot tell whether the difference is biological or algorithmic.

How should I choose substrate concentrations?

The concentrations should bracket Km. The practical guideline is 0.2 × Km to 5 × Km, with at least five points. The reason follows directly from the equation: if you measure only where [S] ≪ Km, the equation reduces to v ≈ (Vmax/Km)·[S]—a straight line—and only the ratio Vmax/Km is identifiable; if you measure only where [S] ≫ Km, the curve is flat and you can estimate Vmax but get no information about Km. This tool checks your range against the fitted Km.

I don't know Km yet—how can I choose concentrations based on it?

Start with a coarse screen: space concentrations in 10-fold steps across three or four orders of magnitude and look for where the rate begins to curve noticeably—that region indicates the order of magnitude of Km. Then design a finer series around that range for the definitive experiment. This tool works on pilot data too—it will tell you the range does not cover Km, which is exactly the information you need.

Are there requirements for the rate or concentration units?

No. The tool does not convert units; it only requires that you use them consistently. Km takes the unit of your substrate concentration, Vmax takes the unit of your rate, and the output labels are taken directly from what you enter. To convert substrate concentrations between % and mol/L, use the percent concentration converter.

Related tools