Advanced Multivariable Function Plotter Calculator

Enter Function and Plot Settings

Function z = f(x, y)

Plot Type

Color Scale

x Minimum

x Maximum

x Grid Points

y Minimum

y Maximum

y Grid Points

Evaluation Point x₀

Evaluation Point y₀

Derivative Step h

Supported functions: sin, cos, tan, exp, log, sqrt Use variables: x, y Example: exp(-(x^2+y^2)/8) * sin(x*y)

Enter any valid expression using x and y. The calculator samples the domain, computes summary statistics, and renders an interactive Plotly chart.

Function	x Range	y Range	Grid	Point (x₀, y₀)	Sample Result f(x₀, y₀)
sin(x)*cos(y) + x^2/8 - y^2/10	-5 to 5	-5 to 5	41 × 41	(1, 1)	0.5796
exp(-(x^2+y^2)/8) * sin(x*y)	-4 to 4	-4 to 4	51 × 51	(1.5, 0.5)	0.5277
x^2 + y^2	-3 to 3	-3 to 3	31 × 31	(1, -2)	5.0000

Formula Used

This calculator evaluates a multivariable function written as z = f(x, y) across a rectangular grid. For each grid point, it computes z_ij = f(x_i, y_j).

Numerical partial derivatives at the selected point use central differences:

∂f/∂x ≈ [f(x₀+h, y₀) − f(x₀−h, y₀)] / (2h)

∂f/∂y ≈ [f(x₀, y₀+h) − f(x₀, y₀−h)] / (2h)

The gradient magnitude is:

|∇f| = √[(∂f/∂x)² + (∂f/∂y)²]

The calculator also estimates the sampled minimum, sampled maximum, sampled mean, and grid size from all valid evaluated points.

How to Use This Calculator

Enter a function using variables x and y.
Choose a plot type such as surface, contour, or heatmap.
Set x and y minimums, maximums, and grid points.
Provide the evaluation point (x₀, y₀) for local analysis.
Set a small derivative step h for numerical partial derivatives.
Click Plot Function to render the chart and summary results.
Use Download CSV for sampled points or Download PDF for a report.

FAQs

1. What does this multivariable function plotter do?

It graphs z = f(x, y) over a chosen domain. It also calculates sampled statistics, evaluates the function at a selected point, and estimates partial derivatives numerically.

2. Which variables can I use in the function?

Use x and y as the independent variables. You can combine them with supported functions such as sin, cos, tan, exp, log, sqrt, and powers.

3. Why are some values missing or invalid?

If your expression becomes undefined at certain points, those samples are skipped. Common reasons include division by zero, square roots of negatives, or logarithms of nonpositive values.

4. What is the difference between surface and contour plots?

A surface plot shows the three-dimensional shape of the function. A contour plot shows constant-value curves on a flat plane, which helps reveal level sets and gradients clearly.

5. Are the derivatives exact?

No. They are numerical approximations using central differences. Smaller h values often improve accuracy, but very tiny steps may introduce rounding effects.

6. How many grid points should I use?

Higher grid counts produce smoother visuals and better sampled statistics, but they require more computation. Values between 31 and 81 per axis work well for most cases.

7. What does the CSV export contain?

The CSV file contains sampled x, y, and z values for every valid grid point. You can open it in spreadsheet tools for further analysis or archiving.

8. What does the PDF export include?

The PDF report includes the expression, domain settings, evaluation point, summary metrics, and an image of the generated plot for documentation or sharing.