surface example

3D Gaussian Surface Graph

A smooth bell-shaped surface centered at the origin.

z = exp(-(x^2 + y^2))

Teacher prompt

Where is the maximum value?

The maximum is at the origin, where x and y are both 0 and z equals 1.

min z 0.00max z 0.0056 samples

What this graph represents

The value is largest at the center and falls quickly as the distance from the origin grows.

Where it appears in calculus

This is useful for teaching radial symmetry and multivariable limits.

Embed this graph

Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.

Open embed page

Related graphs

Open another surface page and compare shape, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.

Monkey Saddle

z = x^3 - 3*x*y^2

A three-way saddle with three valleys and three ridges.