The Laplacian combines second derivatives along each selected axis. In Cartesian variables it looks like $abla^2 f = f_{xx} + f_{yy} + f_{zz}$ for a three-variable scalar field.

Each second derivative measures curvature in one direction. Positive curvature contributes bowl-like behavior, negative curvature contributes saddle-like behavior, and zero means no second-order bending in that direction.

The calculator keeps those curvature channels separate so you can see how the final operator is built, not just the final symbolic answer.