Contour Plot Generator Calculator
Example data table
This sample illustrates a small grid for quick validation. Your generated grids can be much larger.
| x | y | z |
|---|---|---|
| -1 | -1 | 0.159155 |
| 0 | -1 | 0.096532 |
| 1 | -1 | 0.159155 |
| -1 | 0 | 0.096532 |
| 0 | 0 | 0.159155 |
| 1 | 0 | 0.096532 |
| -1 | 1 | 0.159155 |
| 0 | 1 | 0.096532 |
| 1 | 1 | 0.159155 |
How to use this calculator
- Select Generate from formula or upload a CSV grid.
- Set x and y ranges and choose a grid size that fits your detail needs.
- Pick a function and adjust its parameters to shape the surface.
- Choose plot style, contour levels, smoothing, and a color scale.
- Press Generate Plot, then export CSV or PDF if needed.
Formula used
A contour plot visualizes level sets of a surface z = f(x, y), where each contour line satisfies f(x, y) = k for a constant level k.
For probability surfaces, the bivariate normal option computes the joint density from μx, μy, σx, σy and correlation ρ. For regression surfaces, the quadratic option models curvature using ax² + by² + cxy plus linear and intercept terms.
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Grid resolution and statistical fidelity
Contour accuracy depends on how finely you sample x and y. A 50×50 grid yields 2,500 points and supports quick exploration, while 150×150 yields 22,500 points and captures sharper ridges. For smooth densities, increasing nx and ny reduces stair‑step artifacts and improves level placement. For noisy surfaces, fewer points can hide local spikes and emphasize broader structure.
Choosing levels for interpretation
Contour levels translate numeric z values into interpretable bands. Using 10–15 levels is often readable for reports, while 20–30 levels helps detect subtle gradients. Probability contours are commonly compared by relative height near the mean, whereas response surfaces are compared by curvature and slope direction. If min and max differ by several orders, fewer levels prevent overly dense lines.
Correlation effects in bivariate normal models
In the bivariate normal option, ρ controls contour tilt and elongation. With ρ≈0, contours are axis‑aligned ellipses (or circles when σx=σy). As |ρ| increases toward 0.8, ellipses rotate and stretch along a diagonal, indicating stronger linear association. This calculator also reports mean and standard deviation of z, letting you confirm expected concentration and dispersion across the grid.
Smoothing as a presentation control
Smoothing does not change the underlying function values; it changes how gradients render between sampled points. Values near 0.85 provide a clean look for dashboards, while values near 0.30 preserve sharper transitions for diagnostic work. If your audience needs exact boundaries, reduce smoothing and increase grid size instead. When communicating uncertainty, pair moderate smoothing with fewer levels for clarity.
Comparing contour, heatmap, and surface views
Contour lines show equal‑value structure, heatmaps show continuous intensity, and 3D surfaces show height and saddle direction. In exploratory statistics, switching views helps validate findings: a heatmap can reveal plateau regions that contour spacing may mask, while a surface can expose sign changes and inflection points. Keeping the same color scale across views supports consistent interpretation of z magnitude.
Export workflows for analysis and reporting
CSV export is ideal for downstream modeling and reproducibility. A full grid can be pivoted into matrices, used for interpolation, or compared to observed outcomes. PDF export supports shareable summaries. For team reviews, include the note field as a run identifier and align contour settings across experiments.
FAQs
1) What CSV format is accepted?
The file must have headers x,y,z and represent a complete grid. Each unique x combines with each unique y exactly once, so the tool can build a rectangular z matrix.
2) How do I choose nx and ny?
Start with 50×50 for fast iteration. Increase toward 120×120 when contours look blocky or when you need sharper boundaries. Larger grids increase compute time and file size.
3) Why do my contours look too crowded?
Reduce the contour levels to 10–15, or narrow the x and y ranges around the region of interest. Crowding often happens when z varies rapidly across a wide domain.
4) What does smoothing change?
Smoothing affects rendering between grid points, not the underlying computed z values. Lower smoothing preserves sharp transitions. Higher smoothing produces cleaner gradients for presentations.
5) When should I use the quadratic surface?
Use it for response surface exploration, curvature checks, and simple regression‑like shapes. The cross term cxy rotates contours, while ax² and by² control bowl or ridge intensity.
6) Can I share the plot in a report?
Yes. Use Download PDF for a single-page export that includes the plot and summary blocks. You can also print to PDF from your browser for a quick shareable version.