Calculated Result
This section appears above the form after submission.
Interactive Plot
Sample Output Table
Showing the first 18 valid points.| # | X | Y | Z |
|---|---|---|---|
| Run a calculation to populate this table. | |||
Calculator
Enter a function of x and y. Supported examples include x^2 + y^2, sin(x) * cos(y), sqrt(x^2 + y^2), and exp(-(x^2 + y^2)).
Example Data Table
This example uses z = x² + y² for a small 3 × 3 grid. It shows how sampled points build the full surface.
| X | Y | Z = x² + y² |
|---|---|---|
| -1 | -1 | 2 |
| 0 | -1 | 1 |
| 1 | -1 | 2 |
| -1 | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 0 | 1 |
| -1 | 1 | 2 |
| 0 | 1 | 1 |
| 1 | 1 | 2 |
Formula Used
The calculator graphs a multivariable surface from the general relationship z = f(x, y). It samples the function across user-defined X and Y ranges.
Surface function: z = f(x, y)
X step size: Δx = (xmax - xmin) / (nx - 1)
Y step size: Δy = (ymax - ymin) / (ny - 1)
Grid points: xi = xmin + iΔx, yj = ymin + jΔy
Center value: zcenter = f((xmin + xmax)/2, (ymin + ymax)/2)
The graph is formed by evaluating the expression at every sampled coordinate pair. The calculator also reports the sampled minimum, maximum, mean, and valid point count.
How to Use This Calculator
- Enter a valid multivariable expression using
xandy. - Set the X and Y minimum and maximum values.
- Choose step counts for both directions.
- Select a graph style such as surface, contour, or heatmap.
- Click Generate Graph to calculate the grid.
- Review the result cards above the form.
- Inspect the plotted surface and output table.
- Use the CSV or PDF buttons to save your results.
FAQs
1. What functions can I enter?
You can enter expressions that use x and y, plus common functions like sin, cos, tan, sqrt, log, exp, and abs.
2. What does the graph show?
The graph shows the surface formed by z values across sampled x and y coordinates. Each point represents one evaluated function result.
3. Why do some points become undefined?
Certain functions fail for some inputs. Examples include square roots of negative numbers and division by zero. Those points are excluded.
4. How do more steps affect the graph?
More steps create a denser grid and smoother graph. They also increase calculation time because more points must be evaluated.
5. What is the center value?
The center value is the function output at the midpoint of the chosen x and y ranges. It gives a quick reference value.
6. Can I export the sampled data?
Yes. The CSV button downloads valid x, y, and z points. The PDF button saves the summary, chart, and visible table.
7. Which graph type should I use?
Use surface for depth, contour for level curves, heatmap for intensity, and wireframe when you want structure without a solid surface.
8. Is this useful for learning multivariable calculus?
Yes. It helps you connect formulas to shapes, compare domains, inspect symmetry, and see how changing ranges affects the surface.