Contents
What this calculator does Formula Worked example How to use it When to use it Key takeaways Frequently asked questions
What this calculator does
The 3D graphing calculator plots surfaces defined by z = f(x, y) on a WebGL grid with orbit controls, labeled axes, and optional multiple expressions.
Formula
Surface evaluation on a grid:
z_{i,j} = f(x_i, y_j) for x in [x_min, x_max], y in [y_min, y_max]
The mesh samples n steps along each axis (tool default grid). Each vertex is (x_i, y_j, z_{i,j}). Supported expression bodies use the site math parser with variables x and y (and any named parameters you define).
Common surfaces:
| Name | Expression |
|---|---|
| Plane | z = ax + by + c |
| Paraboloid | z = x^2 + y^2 |
| Saddle | z = x^2 - y^2 |
| Wave | z = sin(x) * cos(y) |
Reduced-motion preferences disable auto-spin; orbit still works by drag.
Worked example
Plot z = x^2 + y^2 on x, y ∈ [-2, 2].
At (0, 0): z = 0. At (1, 1): z = 1 + 1 = 2. At (2, 0): z = 4. At (-2, -2): z = 4 + 4 = 8.
The mesh rises as a circular paraboloid bowl centered on the origin. Cross-section at y = 0 is the familiar 2D parabola z = x^2.
How to use it
- Enter a surface expression in terms of
xandy. - Set axis bounds for the domain you want to view.
- Add another expression if you need overlapping surfaces.
- Toggle colour or visibility per surface in the list.
- Drag to orbit; scroll to zoom the WebGL scene.
- Disable auto-spin when you need a fixed camera for screenshots.
When to use it
Use 3D surface plots to inspect multivariable functions from calculus, physics potentials, or empirical response surfaces. A contour sketch on paper shows level sets; the mesh shows height directly so local minima and ridges are visible.
Keep domains finite. Expressions with singularities (division by zero, log of non-positive values) produce gaps or spikes at bad samples. Tighten bounds around the region of interest when the surface grows without limit.
This tool owns interactive z = f(x, y) viewing. Matrix algebra, eigenvalues, and linear-system solve steps belong on the matrix calculator, not here.
Key takeaways
- Evaluate
z = f(x, y)on a rectangular(x, y)sample grid. - Read height from the vertical axis in the WebGL scene.
- Orbit and zoom to inspect minima, ridges, and saddles.
- Limit the domain when the function diverges.
- Stack multiple expressions only when comparing surfaces.
Frequently asked questions
What functions can I plot?
Enter any expression the parser accepts in x and y: polynomials, trig, exp, logs on valid domains, and combinations with parentheses. Named parameters work when you define them in the expression list. Implicit surfaces F(x,y,z)=0 are outside this explicit z = f(x, y) mode.
Why does my surface show spikes or holes?
Samples hit points where the expression is undefined or extremely steep, such as division by zero or sqrt of a negative value. Narrow the x and y bounds, rewrite the formula, or avoid the singular curve. Densifying the grid reveals more detail but can also expose more bad samples.
How is this different from a 2D graphing calculator?
A 2D grapher plots y = f(x) in the plane. This tool plots a height field z = f(x, y) in three dimensions. You need two independent inputs to define each surface point. Cross-sections of the 3D plot recover familiar 2D curves.
Can I plot more than one surface?
Yes. Add expressions to the list and assign colours. Overlapping surfaces help compare models, such as x^2+y^2 versus 0.5*(x^2+y^2). Toggle visibility when one mesh hides another.
Does the calculator solve equations for x and y?
No. It evaluates and displays surfaces. Finding roots, intersections with planes, or algebraic solves is a separate symbolic or numeric step. Use the plot to locate features by eye, then solve analytically or with another solver.
Why is auto-spin disabled on my device?
When the browser reports a reduced-motion preference, auto-spin turns off so the camera stays put. You can still orbit manually. That respects motion sensitivity without removing the 3D view.