Parametric Surface Graph: Torus
A donut-shaped parametric surface used in geometry and visualization.
z = sin(sqrt(x^2 + y^2))Quick facts
- Formula: z = sin(sqrt(x^2 + y^2))
- Category: parametric
- Tags: parametric, surface, vector calculus
What this graph represents
The live widget shows a radial wave placeholder while the page explains the torus parameters.
Where it appears in calculus
Use this to introduce two-parameter surfaces.
How to use this graph
- Rotate the surface by dragging with your mouse or finger
- Use the Embed button to copy an
<iframe>for your LMS or lesson page - Click PNG to export a classroom-ready image
- 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.
Open embed pageTeacher prompt
Question: What do the two parameters control?
Answer: One parameter moves around the main ring, and the other moves around the tube.
Related graphs
Explore more parametric examples and compare shapes, slices, and contour behavior.
Mobius Strip
z = atan(y / (x + 0.001))A one-sided strip with a half twist.
Helicoid
z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)A screw-like minimal surface.
Wave Sheet
z = sin(x) * cos(y)A parametric sheet whose height is a wave product.
Ripple Disk
z = sin(sqrt(x^2 + y^2))A circular ripple described naturally with radius and angle.
Spherical Cap
z = sqrt(max(0, 16 - x^2 - y^2))A cap from a sphere parameterized by angles.
Spiral Ramp
z = atan(y / (x + 0.001)) + 0.2*sqrt(x^2 + y^2)A ramp that rises as it rotates.
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Use these free browser tools to extend your graphing workflow.