Spherical Cap Calculator

Enter sphere radius and cap height to solve the cap geometry with the valid 0 < h ≤ 2R domain shown explicitly.

Sphere radius R

Cap height h

Volume = —V = πh²(R − h/3), with 0 < h ≤ 2R.

—Base radius

—Curved area

—Base area

—Total area

Use one consistent length unit. Volume is returned in cubic units and areas in square units. A cap height larger than 2R is geometrically invalid and is rejected.

Spherical-cap geometry cross-check

Calculate base radius, curved area, base area and volume from sphere radius and cap height, or solve cap height from radius plus target volume.

Solve forSphere radius RCap height hTarget volume

—Base radius

—Curved area

—Volume

—Solved height

Ready.

Use consistent measurements and valid geometric assumptions

Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.