Is there an easy way to tell the size of a scalar (preferably in bytes)?

use bytes;
my $len = length $var;
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And while I'm thinking of it, if I go grab a file over HTTP using LWP::UserAgent, is there an easy way to tell the size of what I downloaded?

Servers should (but aren't required) to send a Content-Length header. If the server didn't send it, then there isn't a way you can tell the size until you've already downloaded it. Most servers will send that header, but you should code in such a way that it gracefully handles the lack of Content-Length.