parametric example
Parametric Surface Graph: Spherical Cap
A cap from a sphere parameterized by angles.
z = sqrt(max(0, 16 - x^2 - y^2))Teacher prompt
Why does the cap have a circular edge?
The visible domain stops where the sphere meets z=0.
min z 0.00max z 0.0060 samples
What this graph represents
The live graph uses the upper hemisphere equation.
Where it appears in calculus
Good for comparing implicit and parametric views of a sphere.
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.
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.