.png&w=64&q=75){kind=small}
Two notations are standard: \Delta in pure mathematics and \nabla^2 in physics and engineering. Both mean the divergence of the gradient. Note the capital: \delta is the lowercase letter, not the operator. The Laplace *transform* is a different thing and is written \mathcal{L}.
All ways to write it
| Command | Use | Package | Copy |
|---|---|---|---|
\Delta | capital delta, the traditional Laplacian | none | |
\nabla^2 | del squared | none | |
\nabla \cdot \nabla | explicit divergence of gradient | none | |
\laplacian | upright ∆ with spacing | physicsnot in KaTeX | |
\Box | d'Alembertian □, the spacetime Laplacian | amssymb |
Commands marked with a package need that \usepackage line in a LaTeX document. “Not in KaTeX” means the command will not render in KaTeX- or MathJax-based tools such as Markdown previews, Jupyter and Confluence math apps; use one of the other forms there.
Example
\Delta u = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0Laplace's equation in two dimensions.
Questions
Laplacian or Laplace transform — which symbol?
The Laplacian operator is \Delta or \nabla^2. The Laplace transform is \mathcal{L}\{f(t)\}. People searching 'latex laplace symbol' usually want \Delta.
Related symbols
- Nabla (gradient) ∇
\nabla - Delta Δ
\delta - Partial derivative ∂
\partial - Laplace transform ℒ
\mathcal{L}\{f(t)\}
Using laplacian in Confluence
Confluence Cloud has no built-in LaTeX. With LaTeX Math for Confluence you add a math macro to any page, type \Delta and it renders inline or as a block, with a live preview while you edit. The app uses KaTeX, so pick one of the commands above that is not marked “not in KaTeX”.