surface example
3D Ripple Surface Graph
Circular waves radiate outward from the center.
z = sin(sqrt(x^2 + y^2))Teacher prompt
Why are the waves circular?
The height depends on distance from the origin, not on x or y separately.
min z 0.00max z 0.0056 samples
What this graph represents
Because the input is radial distance, all points at the same distance from the origin share the same height.
Where it appears in calculus
This helps connect polar distance to 3D surface shape.
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageRelated graphs
Open another surface page and compare shape, slices, and contour behavior.
Saddle Surface
z = x^2 - y^2A 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^2A bowl-shaped surface that opens upward.
Inverted Paraboloid
z = 12 - x^2 - y^2A dome-shaped surface with a highest point at the center.