What are the differences between \newdimen, \newskip and \newlength?

Question

What are the differences between \newdimen, \newskip, and\newlength?

When should I use each of them? Please give me a non-trivial example for each case.

Answer 1

\newlength is the LaTeX2e version of \newskip. It has extra check to avoid redefinition or illegal name. In LaTeX2e, it is defined

\def\newlength#1{\@ifdefinable#1{\newskip#1}}

For example,

\newlength\foo % OK
\newlength\foo % redefinition ERROR!

\newlength\endbar % ERROR: \endbar is illegal command name in LaTeX2e.
% It is reserved by LaTeX kernel to define bar environment together with \bar

\newskip only allocates a new skip (glue, or rubber space) register. If you use low-level TeX command \newskip instead, no error message will be shown.

You should always use \newlength rather than \newskip in LaTeX.

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\newdimen is another low-level TeX macro that allocates a new dimension register, it is different with \newskip. They have different meaning. For example,

\newdimen\rigidlength
\rigidlength=2pt % or \setlength{\rigidlength}{2pt}

\newlength\rubberlength % you cannot use \newdimen here
\setlength{\rubberlength}{2pt plus 2pt minus 1pt}

Answer 2

\newlength is LaTeX syntax and always a skip register:

\documentclass{article}
\newskip\foo
\foo=1cm plus 1mm minus 3mm
\newdimen\bar
\bar=1cm %plus 1mm minus 3mm % not possible
\newlength\baz
\setlength\baz{1cm plus 1mm minus 3mm} 
\begin{document}
\the\foo \par
\the\bar \par
\the\baz
\end{document}