LaTeX Commands and Macros: \newcommand, \renewcommand and \def

\documentclass{article}
\usepackage{amsmath,amssymb}

\newcommand{\R}{\mathbb{R}}                         % no arguments
\newcommand{\norm}[1]{\lVert #1 \rVert}            % one argument
\newcommand{\vecnorm}[2][2]{\lVert #2 \rVert_{#1}}  % optional first argument
\DeclareMathOperator{\tr}{tr}                       % operator name
\renewcommand{\vec}[1]{\mathbf{#1}}                % change an existing command

\begin{document}
Let $\vec{x} \in \R^n$ with $\norm{\vec{x}} \le 1$.
Then $\vecnorm{\vec{x}} \le \vecnorm[1]{\vec{x}}$ and $\tr(A) = \sum_i a_{ii}$.
\end{document}

Everything you type in LaTeX that starts with a backslash is a command, and a macro is simply a command you define yourself. Defining macros is how you keep notation consistent (change \R once and every occurrence follows), shorten long constructions and give meaning to markup. This guide covers how to define commands with \newcommand, with and without arguments, how to change existing ones with \renewcommand, when \def and \NewDocumentCommand are the right tool, and lists the 40 LaTeX commands (the “LaTeX codes” people search for) you will use most.

How to Define a Command in LaTeX with \newcommand

The full syntax is \newcommand{\name}[number of arguments][default]{definition}. Only the name and the definition are required. Put the definitions in the preamble, after the packages they use, so that they apply to the whole document:

\documentclass{article}
\usepackage{amssymb}

\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\eps}{\varepsilon}
\newcommand{\octree}{\textsc{Octree}}

\begin{document}
For every $\eps > 0$ there is $n \in \N$ with $x_n \in \R$.
This guide was compiled with \octree{} in seconds.
\end{document}

A command without arguments swallows the space after it, so \octree is prints “Octreeis”. Write \octree{} is, or load the xspace package and end the definition with \xspace, which adds a space unless punctuation follows. In math mode the space does not matter, because math ignores spaces anyway.

\newcommand with Arguments

Give the number of arguments in brackets and refer to them as #1, #2 and so on. Each argument is passed in its own pair of braces:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\keyword}[1]{\textbf{\emph{#1}}}

\begin{document}
A \keyword{norm} satisfies $\norm{x + y} \le \norm{x} + \norm{y}$ and
$\abs{\inner{x}{y}} \le \norm{x}\,\norm{y}$.
\[ \pd{f}{x} + \pd{f}{y} = 0 \]
\end{document}

An argument can be used several times or not at all, and the definition can call other macros. If an argument is a single token you can leave out the braces (\norm x works), but always bracing them avoids surprises.

Optional Arguments in \newcommand

A second pair of brackets after the argument count gives the first argument a default value and makes it optional. The optional argument is written in square brackets when the command is used:

\documentclass{article}
\usepackage{amsmath}

% [2][2]: two arguments, the first is optional with default 2
\newcommand{\vecnorm}[2][2]{\lVert #2 \rVert_{#1}}
% [1][Note]: one argument, optional, default "Note"
\newcommand{\remark}[1][Note]{\textbf{#1:}\ }

\begin{document}
$\vecnorm{x}$, $\vecnorm[1]{x}$, $\vecnorm[\infty]{x}$

\remark Optional arguments are in brackets.

\remark[Warning] Only the first argument can be optional.
\end{document}

\newcommand allows exactly one optional argument and it is always #1. For an optional argument in another position, several optional arguments or a starred variant, use \NewDocumentCommand (below).

\renewcommand and \providecommand

\renewcommand has the same syntax but only works on a command that already exists. Use it to change the names LaTeX prints, adjust class settings or redefine a symbol:

\documentclass{article}
\usepackage{amsmath,amssymb}

\renewcommand{\abstractname}{Summary}      % heading of the abstract
\renewcommand{\contentsname}{Overview}      % heading of the table of contents
\renewcommand{\vec}[1]{\boldsymbol{#1}}     % bold vectors instead of arrows
\renewcommand{\arraystretch}{1.3}           % taller table rows

\providecommand{\R}{\mathbb{R}}             % only if no package defined it

\begin{document}
\tableofcontents
\begin{abstract}
The vector $\vec{v}$ is bold.
\end{abstract}
\section{Introduction}
Text.
\end{document}

\providecommand defines the command only when it does not exist yet and quietly does nothing otherwise. It is handy in a file that is \input into several documents, or for a macro that a package or class might also define.

Math Operators with \DeclareMathOperator

For a function name such as tr, rank or argmax, do not define \newcommand{\tr}{\text{tr}}. \DeclareMathOperator from amsmath sets the name upright and adds the same spacing as \sin or \log. The starred form puts limits under the name in display math:

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator*{\argmax}{arg\,max}

\begin{document}
$\tr A + \rank B$
\[ \hat\theta = \argmax_{\theta \in \Theta} L(\theta) \]
\end{document}

\DeclareMathOperator only works in the preamble. For a one-off use \operatorname{rank} in the body. More on operator names in math functions.

\def vs \newcommand

\def is the TeX primitive underneath \newcommand. It defines a macro with no safety checks: \def\end{...} silently replaces the command that closes every environment, and the document breaks with errors far from the cause. \newcommand refuses the same name with “Command \end already defined”.

\documentclass{article}

% Delimited arguments: something \newcommand cannot do
\def\point(#1,#2){\ensuremath{(#1;\,#2)}}
% \let copies the current meaning of a command
\let\oldemph\emph
\renewcommand{\emph}[1]{\textbf{\oldemph{#1}}}

\begin{document}
The \emph{point} \point(3,4) lies on the circle.
\end{document}

Use \def for delimited arguments and in package code, and \let to save a command before redefining it. In a document, prefer \newcommand and \renewcommand.

\NewDocumentCommand (xparse)

\NewDocumentCommand describes every argument with a letter, so it can handle what \newcommand cannot: several optional arguments, an optional argument after a mandatory one, and starred variants. It came with the xparse package and has been part of the LaTeX kernel since 2020, so no package is needed on a current TeX distribution.

\documentclass{article}
\usepackage{amsmath}

% s = optional star, m = mandatory, O{2} = optional with default 2
\NewDocumentCommand{\pnorm}{s m O{2}}{%
  \IfBooleanTF{#1}
    {\left\lVert #2 \right\rVert_{#3}}
    {\lVert #2 \rVert_{#3}}%
}
\RenewDocumentCommand{\vec}{m}{\mathbf{#1}}

\begin{document}
$\pnorm{\vec{x}}$, $\pnorm{\vec{x}}[\infty]$, $\pnorm*{\frac{\vec{x}}{2}}[1]$
\end{document}

Defining Environments with \newenvironment

Environments work the same way, with code for the beginning and code for the end. Arguments can only be used in the beginning code:

\documentclass{article}

\newenvironment{note}[1][Note]
  {\par\medskip\noindent\textbf{#1.}\ \itshape}
  {\par\medskip}

\begin{document}
\begin{note}
Environments group their content.
\end{note}
\begin{note}[Tip]
Use \verb|\renewenvironment| to change an existing one.
\end{note}
\end{document}

For numbered theorem-like environments use \newtheorem instead; see theorems and proofs.

The 40 Most Used LaTeX Commands (LaTeX Codes)

These are the commands that appear in almost every LaTeX document. The package column says what to load; an empty cell means the command is built in.

\documentclass{article}
\usepackage{amsmath,amssymb,graphicx,hyperref}

\title{A Short Example}
\author{Ada Lovelace}
\date{\today}

\begin{document}
\maketitle
\tableofcontents

\section{Introduction}\label{sec:intro}
This is \textbf{bold}, \textit{italic}, \emph{emphasised}, \underline{underlined}
and \texttt{monospaced} text.\footnote{A footnote.} See \href{https://useoctree.com}{Octree}.

\subsection{Math}
\begin{itemize}
  \item $\frac{a}{b} + \sqrt{x} + \sum_{i=1}^{n} i^2 + \int_0^1 f(x)\,dx$
  \item $\alpha \in \mathbb{R}$ and $\left( \frac{1}{2} \right) \cdot 2 = 1 \text{ exactly}$
\end{itemize}
Section~\ref{sec:intro} is the one you are reading.
\end{document}

For symbols beyond these, see Greek letters and math symbols and special characters; for the basics of how a document is put together, start with Learn LaTeX.

Common Errors and Fixes

Missing braces are the most common cause of strange output with macros that take arguments. Without braces only the next single token is the argument:

\documentclass{article}
\newcommand{\keyword}[1]{\textbf{#1}}
\begin{document}
\keyword important     % only the "i" is bold
\keyword{important}    % the whole word is bold
\end{document}

Frequently Asked Questions

How do I define a new command in LaTeX?

Put \newcommand{\name}{definition} in the preamble, for example \newcommand{\R}{\mathbb{R}}, and then write \R wherever you want the definition. For arguments, give their number in brackets and use #1, #2 in the definition: \newcommand{\norm}[1]{\lVert #1 \rVert} turns \norm{x} into ‖x‖.

What is the difference between \newcommand and \renewcommand?

\newcommand defines a command that does not exist yet and stops with “Command \x already defined” if it does. \renewcommand changes a command that already exists and stops with “Command \x undefined” if it does not. \providecommand defines the command only when it is missing and otherwise does nothing.

How do I give a LaTeX command an optional argument?

Add the default value as a second bracket: \newcommand{\vecnorm}[2][2]{\lVert #2 \rVert_{#1}}. The first argument (#1) is now optional and defaults to 2, so \vecnorm{x} gives the 2-norm and \vecnorm[\infty]{x} the infinity norm. \newcommand allows only one optional argument, and it must come first; use \NewDocumentCommand for anything more.

Should I use \def or \newcommand in LaTeX?

Use \newcommand in documents. \def is the underlying TeX primitive: it silently overwrites any existing command, including essential ones such as \end or \section, and has no syntax for optional arguments. \newcommand checks the name first and reports an error instead. \def is still useful in package code and for delimited arguments.

What are LaTeX codes?

People often call LaTeX commands “LaTeX codes”. Each starts with a backslash, such as \section, \textbf or \frac, and takes its arguments in braces. The most used ones set up the document (\documentclass, \usepackage), structure it (\section, \label, \ref), format text (\textbf, \emph) and write math (\frac, \sqrt, \sum).

Why do I get “Illegal parameter number in definition”?

The definition uses a #n that the command does not have: #2 in a command declared with [1], or #1 in a command declared with no argument count at all. Make the number in brackets match the highest #n in the definition. Inside the definition of a new environment, the arguments can only be used in the begin code, not in the end code.

Next Steps

• Math Functions – \operatorname and built-in operator names
• Theorems and Proofs – \newtheorem for numbered environments
• Greek Letters and Math Symbols – The symbols to build macros from
• Blackboard Bold – \mathbb for \R, \N and \Z shortcuts
• Underbrace and Overbrace – Annotating parts of an equation
• Learn LaTeX: Tutorial for Beginners – The basics, from the first document up

Free LaTeX Tools

• LaTeX Preview – Test your macros with a live PDF preview
• AI LaTeX Generator – Generate LaTeX from text descriptions
• LaTeX Symbols Reference – Look up the command for any symbol