Laplacian operator (∇², ∇·∇, Δ) in LaTeX

Usually, it is denoted by ∇·∇, ∇², or Δ symbols. In this tutorial, I will show you, how to get these symbols in LaTeX.

The following table will help you. Take a look.

Command	Output
$\nabla^{2}$
$\nabla\cdot\nabla$
$\Delta$

\documentclass{article}
\begin{document}

  $$ \Delta f = \nabla^{2}f = \nabla \cdot \nabla f $$
  $$ \nabla^{2} = \vec{\nabla}\cdot\vec{\nabla} $$
  $$ \nabla^{2}\mathbf{A} = \nabla (\nabla \cdot \mathbf {A} )-\nabla \times (\nabla \times \mathbf{A} ) $$

\end{document}+

Output:

The physics package also provides the \laplacian command to get the ∇² symbol in LaTeX. So you can also try this.

\documentclass{article}
\usepackage{physics}
\begin{document}

  $$ \verb|\laplacian| \rightarrow \laplacian  $$
  $$ \Delta f = \laplacian f =\nabla \cdot \nabla f $$

\end{document}

Output:

Different styles of Delta and Nabla symbol

In order to get slightly different styles of Delta and Nabla symbols you can use the \bigtriangleup and \bigtriangledown commands.

Also with the \Updelta command provided by the upgreek package, you can get a different style of Delta symbol.

\documentclass{article}
\usepackage{upgreek} % for \Updelta
\begin{document}

  $$ \verb|\bigtriangleup|\rightarrow \bigtriangleup  $$
  $$ \verb|\bigtriangledown|\rightarrow \bigtriangledown $$
  $$ \verb|\Updelta|\rightarrow \Updelta  $$
  $$ \bigtriangleup f = \bigtriangledown^{2}f = \bigtriangledown \cdot \bigtriangledown f $$

\end{document}

Output: