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We have a length property:
set theText to "blah"
theText's length --> 4
For intensive calculations, you may use the command count, which is faster:
count theText --> 4
Some times, you may wish calculate the length of a very long text (eg, 479MB), and you won't hold such amount of text in a variable, but in an external text file. You can choose your favorite and reliable *nix tool, or just:
set longFile to alias "path:to:longFile.txt"
get eof of longFile --> long number