Scaling absolute values

Question

How I make in Latex the modulus, or absolute value, match the size of the expression within? I want to know what are the sizes available.

Example:

$$\mid\frac{\partial I}{\partial M}\mid
  = \frac{T^2 dg}{4\pi^2}$$

Answer 1

I suggest you load the mathtools package and define a macro called \abs as follows:

\usepackage{mathtools} % for '\DeclarePairedDelimiter' macro
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

Then, in the body of the document, you'd write

\[
\abs*{\frac{\partial I}{\partial M}} = \frac{T^2 dg}{4\pi^2}
\]

The * ("star" or "asterisk") symbol after \abs indicates to LaTeX that the delimiter symbols (here: plain vertical bars) should be scaled vertically to the height and depth of the macro's argument.

Here's a screenshot to compare the look of the auto-sized fences (which happens to corresponds to \bigg) and of the look that results from choosing \Big manually. Speaking for myself, I have slight preference for look produced by the manually-chosen size.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}

auto-sized (\texttt{\textbackslash bigg}):
\[
\abs*{\frac{\partial I}{\partial M}} = \frac{T^2 dg}{4\pi^2}
\]

\bigskip
using \texttt{\textbackslash Big} directly:
\[
\abs[\Big]{\frac{\partial I}{\partial M}} = \frac{T^2 dg}{4\pi^2}
\]

\end{document}

Answer 2

Use

\[\left|\frac{\partial I}{\partial M}\right|
  = \frac{T^2 dg}{4\pi^2}\]

instead. Note that \mid is a relation symbol, and not appropriate here. It produces different spacing, for one.

The \left…\right construction can be used with all kinds of parentheses, brackets, and the like.

(Incidentally, replaced $$ by proper math delimiters.)