3D Graphing Calculator
Plot a surface z = f(x, y) in interactive 3D — rotate and zoom, free online.
Drag the surface to rotate. e.g. x^2-y^2, sin(x)*cos(y), sqrt(x^2+y^2)
About this calculator
A 3D graphing calculator plots a surface defined by z = f(x, y) as a rotatable wireframe. Enter an expression in x and y, such as sin(x) * cos(y) or x^2 - y^2, and drag to orbit the surface in three dimensions. Useful for visualising multivariable functions, saddle points and peaks.
The calculator sweeps x and y across a grid, evaluates your expression at each grid point to get a height z, and connects those heights into a mesh that stands up off the flat xy-plane. Dragging orbits the camera around the surface so you can look at it from any angle, and the zoom control moves you nearer or further away. This turns an abstract two-variable formula into a shape you can actually see — hills, valleys, ridges and the pass-shaped saddle points where a surface rises in one direction while falling in another.
For a worked example, z = x^2 - y^2 draws the classic saddle (Pringle) surface: along the x-axis it curves upward like a valley, while along the y-axis it curves downward, meeting at a saddle point at the origin. By contrast z = sin(x) * cos(y) produces a regular egg-carton of alternating bumps and dips. It is used in multivariable calculus to picture partial behaviour, locate maxima, minima and saddle points, and understand the geometry of a function of two variables.
Frequently asked questions
How do I enter a 3D function?
Type an expression in both x and y, for example x^2 - y^2 or sin(x)*cos(y). The calculator evaluates it across a grid and draws the resulting surface.
Can I rotate the surface?
Yes. Drag the surface to orbit it, and use the zoom control to move closer or further away.
What does z = f(x, y) mean?
It means the height z of the surface at each point is worked out from that point’s x and y coordinates. Every (x, y) on the flat plane gets a height, and those heights together form the surface.
How do I plot a saddle surface?
Enter x^2 - y^2. It rises along one axis and falls along the other, meeting at a saddle point at the origin — the standard example of a surface that is neither a peak nor a valley there.
What kinds of surfaces can I visualise?
Anything you can write as an expression in x and y: paraboloids (x^2 + y^2), saddles (x^2 - y^2), ripples (sin(x)*cos(y)) and combinations of trig, powers, roots and logs.
How is this different from the 2D graphing calculator?
The 2D tool plots y = f(x) as a curve on a flat grid. This 3D tool plots z = f(x, y) as a surface in space, so it shows how a value depends on two inputs at once rather than one.
Results are estimates for general guidance only, not financial, medical or tax advice.