3D Graphing Calculator

What Is 3D Graphing?

A normal graph has two axes: x and y. A 3D graph adds a third axis, z. That lets you draw a surface instead of a curve. The height of the surface at each point shows the value of the function.

Take the function z = x² + y². On a flat graph you cannot draw it. In 3D, it becomes a bowl shape. The bottom of the bowl sits at zero, and the sides rise as x or y grows. You can see the whole shape at once — and that is the point of 3D graphing.

3D graphs appear in calculus, physics, and engineering. They show surfaces, volumes, and how two variables change a result together. A hill on a map, the shape of a lens, or the curve of a bridge — all of these are 3D surfaces.

How to Graph in 3D

Graphing a 3D function takes four steps:

1. Type your function. Use two variables, x and y. For example, type z = sin(x) + cos(y), or z = x² − y² for a saddle shape.
2. Press GRAPH. The surface appears on the screen. If it looks flat, change the window or the zoom.
3. Drag to rotate. Click and drag with your mouse, or drag with one finger on a phone. Turn the surface to see the back, the top, and the sides.
4. Zoom and trace. Scroll or pinch to zoom in on a point. Read the x, y, and z values at that point.

Start with a simple shape. Try z = x² + y² first and turn it around. Then try z = x² − y² and see how the saddle bends up one way and down the other. Once you can read those two, you can read any surface.

3D Shapes to Try First

• Paraboloid — z = x² + y². A bowl. Good for learning to rotate and zoom.
• Saddle — z = x² − y². Rises in one direction and falls in the other.
• Plane — z = 2x + 3y. A flat tilted sheet. Good for checking the axes.
• Wave — z = sin(x) + cos(y). Rolling hills that repeat in both directions.
• Cone — z = the square root of (x² + y²). A point at the bottom that opens upward.
• Gaussian bump — z = e to the power of −(x² + y²). A single hill that fades to flat.

Each shape teaches one idea. The bowl shows a minimum. The saddle shows a point that is a minimum one way and a maximum the other way. The wave shows how a function repeats. Try them in order and the ideas build on each other.

3D Graphing vs 2D Graphing

Most school work is 2D. Use the function graphing calculator for that. Switch to 3D when a problem has two inputs — for example, when a value depends on both time and distance, or on both x and y.

For single-variable problems with a TI-84 style layout, use the TI-84 calculator online. For curves with r and theta, use the polar graphing calculator.

Specialized Graphing Tools

Need a different view? These tools work the same way and are all free.

Frequently Asked Questions