16.6.2 \phantom & \vphantom & \hphantom ¶

Synopsis:

\phantom{subformula}

or

\vphantom{subformula}

or

\hphantom{subformula}

The \phantom command creates a box with the same height, depth, and width as subformula, but empty. That is, this command causes LaTeX to typeset the space but not fill it with the material. Here LaTeX will put a blank line that is the correct width for the answer, but will not show that answer.

\begin{displaymath}
  \int x^2\,dx=\mbox{\underline{$\phantom{(1/3)x^3+C}$}} 
\end{displaymath}

The \vphantom variant produces an invisible box with the same vertical size as subformula, the same height and depth, but having zero width. And \hphantom makes a box with the same width as subformula but with zero height and depth.

In this example, the tower of exponents in the second summand expression is so tall that TeX places this expression further down than its default. Without adjustment, the two summand expressions would be at different levels. The \vphantom in the first expression tells TeX to leave as much vertical room as it does for the tower, so the two expressions come out at the same level.

\begin{displaymath}
    \sum_{j\in\{0,\ldots\, 10\}\vphantom{3^{3^{3^j}}}}
      \sum_{i\in\{0,\ldots\, 3^{3^{3^j}}\}} i\cdot j
\end{displaymath}

These commands are often used in conjunction with \smash. See \smash, which includes another example of \vphantom.

The three phantom commands appear often but note that LaTeX provides a suite of other commands to work with box sizes that may be more convenient, including \makebox (see \mbox & \makebox) as well as \settodepth (see \settodepth), \settoheight (see \settoheight), and \settowidth (see \settowidth). In addition, the mathtools package has many commands that offer fine-grained control over spacing.

All three commands produce an ordinary box, without any special mathematics status. So to do something like attaching a superscript you should give it such a status, for example with the \operatorname command from the package amsmath.

While most often used in mathematics, these three can appear in other contexts. However, they don’t cause LaTeX to change into horizontal mode. So if one of these starts a paragraph then you should prefix it with \leavevmode.