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TeX Frequently Asked Questions
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Put the word in a box, and measure the width of the box. For example,

\newdimen\stringwidth
\setbox0=\hbox{hi}
\stringwidth=\wd0

Note that if the quantity in the \hbox is a phrase, the actual measurement only approximates the width that the phrase will occupy in running text, since the inter-word glue can be adjusted in paragraph mode.

The same sort of thing is expressed in LaTeX by:

\newlength{\gnat}
\settowidth{\gnat}{\textbf{small}}

This sets the value of the length command \gnat to the width of “small” in bold-face text.