surface example

3D Spiral Height Surface Graph

A wrapped height field based on angle.

z = atan(y / (x + 0.001))

Quick facts

  • Formula: z = atan(y / (x + 0.001))
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The arctangent changes with direction around the origin.

Where it appears in calculus

Use it carefully to discuss angle and branch behavior.

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: What does the height mainly depend on?

Answer: It depends mainly on the angle of the point from the origin.

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

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Worksheet Generator

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How to Graph z=f(x,y)

Step-by-step guide for beginners