surface example

3D Elliptic Gaussian Surface Graph

A stretched bell surface with different widths by axis.

z = exp(-(x^2 / 8 + y^2 / 2))

Quick facts

  • Formula: z = exp(-(x^2 / 8 + y^2 / 2))
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The y term shrinks faster than the x term, making the mound narrow in y.

Where it appears in calculus

Good for explaining ellipses in level curves.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

Embed this graph

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

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Teacher prompt

Question: Which direction is narrower?

Answer: The y direction is narrower because its exponent term grows faster.

Related graphs

Explore more surface examples and compare shapes, 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.

Gaussian Surface

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

A smooth bell-shaped surface centered at the origin.

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.

Sine Wave Surface

z = sin(x) + sin(y)

Two perpendicular sine waves combined into one surface.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Generator

Print graph-based classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners