Calculator inputs
Example data table
These points yield a near-linear reciprocal fit.
| [S] (mM) | v (mM/s) | 1/[S] | 1/v |
|---|---|---|---|
| 0.50 | 0.105 | 2.0000 | 9.5238 |
| 1.00 | 0.170 | 1.0000 | 5.8824 |
| 2.00 | 0.250 | 0.5000 | 4.0000 |
| 4.00 | 0.330 | 0.2500 | 3.0303 |
| 8.00 | 0.400 | 0.1250 | 2.5000 |
Formula used
Start with Michaelis–Menten kinetics: v = (Vmax · [S]) / (Km + [S]).
Take reciprocals to obtain the Lineweaver–Burk form: 1/v = (Km/Vmax) · (1/[S]) + 1/Vmax.
The fitted line y = m x + b gives m = Km/Vmax and b = 1/Vmax. Then Vmax = 1/b and Km = m/b.
How to use this calculator
- Collect substrate concentrations and initial rates at matching conditions.
- Paste pairs as [S], v, one pair per line.
- Choose units for labeling and exports.
- Select a regression mode, then press Plot and calculate.
- Review slope, intercept, Km, Vmax, R², and the plot.
- Download CSV or PDF to keep a record.
Notes and safeguards
- Reciprocal plots amplify noise at small rates.
- Prefer initial-rate measurements and consistent temperature.
- If the intercept is near zero, Vmax becomes unstable.
- Consider alternative fits when data are strongly curved.
Professional article
1) Purpose of the reciprocal plot
Lineweaver–Burk plotting converts Michaelis–Menten data into a straight line by graphing 1/v versus 1/[S]. It is useful for quick parameter estimates and visual comparisons across conditions. This tool automates the transform, fits the line, and reports diagnostics. It also helps flag deviations from simple kinetics when lines shift between experiments.
2) Collecting suitable kinetic data
Reliable plots begin with initial‑rate measurements taken during the linear phase, before substrate depletion or product inhibition. Use 5–8 substrate levels spanning about 0.2×Km to 5×Km when feasible, and include replicates to gauge scatter. Keep temperature, pH, ionic strength, and enzyme concentration constant. Aim for at least two repeats at each concentration.
3) Transforming values for the plot
The calculator accepts concentration–rate pairs and computes x=1/[S] and y=1/v for each point. Because reciprocals amplify low‑rate noise, small errors at low v can cause large vertical shifts. Review outliers, average replicates at the same [S], and avoid mixing units.
4) Interpreting slope and intercept
Linear regression yields y = m x + b, where m = Km/Vmax and b = 1/Vmax. From the fitted slope and intercept, the calculator derives Vmax = 1/b, Km = m/b, and the x‑intercept −b/m, equal to −1/Km. Also sanity‑check saturation in the original v versus [S] curve.
5) Choosing a regression mode
Two regression modes are available. Unweighted least squares treats all reciprocal points equally. v²‑weighted least squares down‑weights small v values (large 1/v), often reducing distortion from noisy low‑rate measurements. If rate uncertainty is roughly proportional to v, weighting can stabilize Km and Vmax. Use unweighted mode for teaching or balanced datasets.
6) Reading R² and residual error
R² summarizes how closely points follow a line, while SSE captures absolute residual error. A high R² can still hide curvature if the substrate range is narrow. Inspect the plot for systematic residual patterns, and check whether one extreme point dominates the fitted slope before exporting results.
7) Avoiding common analysis pitfalls
Common pitfalls include using non‑initial rates, including zero or negative values, or clustering all substrates far above Km. If the intercept approaches zero, Vmax becomes unstable and Km can blow up. Add more low‑substrate points, increase replicates, or consider non‑linear fitting for confirmation.
8) Reporting and archiving outputs
Use the export buttons to archive inputs, transformed values, and fitted predictions for notebooks or reports. Record units, regression mode, and rounding settings, then report Km and Vmax with sensible significant figures. Compare against literature under matched conditions and document buffer and instrument settings.
FAQs
1) What data should I enter?
Enter positive substrate concentrations and initial rates from the same experiment. Provide one pair per line using commas, tabs, or spaces. Keep units consistent; the unit selectors only label outputs and do not convert values.
2) Why do small rates change the plot so much?
Because the plot uses 1/v, small absolute errors when v is small become large changes in 1/v. This can pull the fitted line strongly. Use replicates, verify initial-rate conditions, and consider weighting.
3) What does the weighting option do?
The v²-weighted fit down-weights points with very small v (very large 1/v), which often reduces distortion from noisy low-rate measurements. Choose it when uncertainty grows as signal decreases or when the unweighted line is dominated by one point.
4) How are Km and Vmax calculated?
After fitting y = m x + b in reciprocal space, Vmax is computed as 1/b and Km as m/b. The x-intercept is −b/m, equal to −1/Km. If b is near zero, derived values become unstable.
5) What if Km or Vmax becomes negative?
Negative values usually indicate a poor linear model in reciprocal space, strong noise, or incorrect inputs. Re-check units and signs, remove obvious outliers, expand the substrate range around Km, and confirm with a direct non-linear fit of v versus [S].
6) Does a high R² guarantee a good model?
No. R² only describes linearity in the transformed plot. Reciprocal transforms can hide curvature over limited ranges and overemphasize small rates. Always inspect the plot, check residual patterns, and interpret Km and Vmax alongside the raw saturation curve.
7) Can I export my results?
Yes. Use Download CSV for a spreadsheet-ready table including 1/[S], 1/v, and fitted predictions. Use Download PDF for a compact report of the fit and derived parameters. Exports reflect your chosen units, regression mode, and rounding settings.