Parametric Surface Graph: Spiral Ramp
A ramp that rises as it rotates.
z = atan(y / (x + 0.001)) + 0.2*sqrt(x^2 + y^2)Quick facts
- Formula: z = atan(y / (x + 0.001)) + 0.2*sqrt(x^2 + y^2)
- Category: parametric
- Tags: parametric, surface, vector calculus
What this graph represents
Angle creates the spiral height change while radius adds outward slope.
Where it appears in calculus
Good for explaining polar angle in 3D.
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: Why does height wrap around the center?
Answer: Height uses the angular position, so rotating changes z.
Related graphs
Explore more parametric examples and compare shapes, slices, and contour behavior.
Torus
z = sin(sqrt(x^2 + y^2))A donut-shaped parametric surface used in geometry and visualization.
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.
Explore more tools
Use these free browser tools to extend your graphing workflow.