Laplacian in LaTeX: nabla^2, Delta and laplacian

Short answer: core LaTeX has no Laplacian command. Write the operator as \nabla^2 (or \Delta, or \nabla\cdot\nabla) in math mode, or load the CTAN physics package and use \laplacian. This guide is for researchers and analysts typesetting equations in papers, theses and reports who need the Laplacian to compile correctly and read unambiguously.

What it is used for in research

The Laplacian is the second-order differential operator that appears in diffusion and heat equations, wave equations, Poisson and Schrodinger equations, and in image and graph analysis. In a manuscript you typically need it in three forms: the bare operator, the operator applied to a function (for example the Laplacian of a field), and the operator inside a larger equation with bracketed arguments. Notation differs between fields, which is why the symbol choice matters as much as the command.

latex laplacian symbol: which one to write

Two notations are in everyday use: nabla squared and capital delta. Overleaf’s symbol list places \nabla under miscellaneous symbols and \Delta under Greek letters, and lists \triangle and \partial as separate miscellaneous symbols (Overleaf, List of Greek letters and math symbols, read 2026-11-08). Because \Delta is also used for finite differences, changes and triangles, \nabla^2 is the less ambiguous choice when your paper also uses \Delta for something else. Whichever you pick, define it once near the first use and keep it consistent.

Install or access (official source only)

The core route needs nothing beyond a working LaTeX installation. For equations with numbering or environments such as equation*, load amsmath in the preamble with \usepackage{amsmath} (Overleaf, Mathematical expressions, read 2026-11-08).

The \laplacian command comes from the physics package, documented in its CTAN manual at mirrors.ctan.org/macros/latex/contrib/physics/physics.pdf. The manual says to insert \usepackage{physics} in the preamble, after \documentclass and before \begin{document} (section 1.3, read 2026-11-08).

Step-by-step task: typeset a Laplacian

Method A: core LaTeX, no extra package

1. Put the expression in math mode: inline with $...$ or \(...\), or display with \[...\] or \begin{equation}...\end{equation} (Overleaf, Mathematical expressions).
2. Write the operator as \nabla^2. Applied to a function: \nabla^2 \psi.
3. For the delta convention write \Delta \psi. For the expanded definition write \nabla \cdot \nabla \psi.
4. Compile and check that the symbol matches the notation defined in your text.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
  \nabla^2 \psi = \frac{\partial^2 \psi}{\partial x^2} + \frac{\partial^2 \psi}{\partial y^2}
\end{equation}
\end{document}

Method B: the physics package and laplacian

1. Add \usepackage{physics} to the preamble, after \documentclass and before \begin{document}.
2. Use \laplacian on its own to print the operator.
3. Use \laplacian{\Psi} to apply it to an argument in the default mode.

\documentclass{article}
\usepackage{amsmath}
\usepackage{physics}
\begin{document}
\[ \laplacian{\Psi} \]
\end{document}

Output and how to read it

Per the physics manual, bare \laplacian prints the nabla-squared operator, so the result of Method B is the same operator as \nabla^2 from Method A, not a delta. If your journal or field expects the delta form, use \Delta explicitly. Compare outputs side by side in a scratch document before committing to a macro across a long thesis.

You write	Package needed	Operator printed
\nabla^2	none	nabla squared
\Delta	none	capital Greek delta (also read as finite difference or change)
\nabla \cdot \nabla	none	divergence of the gradient, written out
\laplacian	physics	nabla squared (per the package manual)

Troubleshooting

Undefined control sequence on laplacian

This error means the command is not defined in your document. \laplacian is not in core LaTeX (it does not appear in Overleaf’s symbol lists); load the physics package as in Method B, or use \nabla^2.

Confusing Delta, triangle and partial

\Delta is a Greek capital, \triangle is a triangle symbol and \partial is the partial-derivative sign; they are different commands in Overleaf’s lists. Use \partial inside the derivatives and \Delta or \nabla^2 for the operator.

Free alternatives (table)

Route	Extra package	Trade-off documented in the sources
Core command \nabla^2 or \Delta	None	Works in any LaTeX document; you size delimiters yourself
physics package \laplacian	physics (CTAN)	Short macro and auto-sized delimiters

FAQ

How do you write the Laplacian symbol in LaTeX?

Use \nabla^2 or \Delta in math mode. With the physics package loaded, \laplacian also works.

Is laplacian part of standard LaTeX?

No. It is defined by the physics package, which you load with \usepackage{physics}.

Is the Laplacian the same as the Laplace transform?

No. The Laplacian is a differential operator; the Laplace transform is an integral transform. For the latter see Laplace transform in LaTeX. The unrelated Laplace distribution is a probability model.

Related guides

For other vector notation see vectors in LaTeX; to number your equations see labelling equations in LaTeX; for the absolute-value delimiters see absolute value in LaTeX; to compile without installing anything see online LaTeX editors.

Sources (official docs)

• Overleaf, List of Greek letters and math symbols, read 2026-11-08.
• Overleaf, Mathematical expressions, read 2026-11-08.
• CTAN, The physics package manual, section 1.3, read 2026-11-08.