What is a 3D graphing calculator?
A 3D surface plotter shows the height z assigned to each horizontal position (x, y). A flat plane, bowl and saddle all have different height patterns. For equations with just x and y, use the 2D Graphing Calculator.
How to plot a 3D function
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Enter an expression such as x² + y² using caret notation x^2 + y^2. You can also type z = x^2 + y^2. Choose the half-width for both horizontal axes and the vertical limit for z, then select Plot Surface. Drag to rotate, or use the rotation, zoom and reset-view buttons. Use coordinate graph paper (paid link) to sketch coordinate slices before plotting.
Surface sampling and projection
The plotter evaluates z on a rectangular grid. It also checks each tile’s center and leaves a gap where a tested value is undefined, outside the vertical limit, or the sampled heights change sharply. The chart uses an orthographic projection with separate horizontal and vertical scales. Read vector components with the Vector Calculator.
How to read the 3D graph
The x and y labels mark the positive horizontal directions, and z marks positive height. Tile colors move from blue at lower z values toward gold at higher values. The vertex range describes the mesh actually drawn. The separate origin check evaluates the function at x = y = 0 even if the result lies outside the graph window. Use multivariable calculus references (paid link) to explore more examples of level curves and surfaces.
Worked example: plot a paraboloid
Choose Load example to plot z = x^2 + y^2 with x and y from −3 to 3 and a vertical limit of 18. The origin is at height 0, and each of the four window corners is at height 18. Compare z = x^2 − y^2 to see a saddle. Use mechanical pencils (paid link) for sketching those differences by hand.
Supported syntax and plot limits
Use +, −, *, /, ^, parentheses, pi, e, and named functions such as sin(x), sqrt(x) or ln(x). Trigonometric arguments are in radians. The window uses one half-width from 0.01 to 100 and one vertical limit from 0.01 to 10,000. Enter one explicit surface per plot. Implicit equations, parametric curves, exact extrema and surface-area integration are outside the tool’s scope. Use graphing calculators (paid link) for handwritten exercises away from the browser.
3D Graphing Calculator FAQs
This tool takes an explicit height. Plot sqrt(1-x^2-y^2) and -sqrt(1-x^2-y^2) separately to explore the two hemispheres.
Tiles can be omitted because sampled values are undefined, beyond the vertical limit or change steeply across a tile. Adjust the window or increase resolution to inspect the region.
Yes. Drag inside the plot, or use the labeled rotation buttons. Use Zoom in and Zoom out to change the camera view.
Sources and methodology
These resources explain the concepts and browser behavior behind this independent tool.