You can create element and append characters to it until you detect wrapping, e.g. by observing changes in offsetHeight
(you can optimze it using bisection algorithm).
This is of course very dependent on browser, system, installed fonts and user's settings so you would have to calculate it for each fragment of text each time page is displayed, resized or when user changes font size (even full-page zoom introduces some off-by-one errors which could cause number of characters change).
Therefore it may be an overkill in most situations and when implemented poorly cause more trouble than it solves.
There are other solutions, e.g. if you want to ensure that only one line is visible you can use white-space:nowrap
and overflow:hidden
and in some browsers text-overflow:ellipsis
to make text cut nicely. Or if you don't want words cut, use 1-line high container with overflow:hidden
.