use Socket qw( inet_aton );

if (inet_aton('83.1.1.1') lt inet_aton('82.1.1.1')) {
   print("is less than\n");
} else {
   print("isn't less than\n");
}
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All the string comparison operators (lt, gt, le, ge, eq, ne and cmp) work here.

This "trick" is also useful for sorting.

my @sorted_ips = map substr($_, 4),
                 sort
                 map inet_aton($_).$_,
                 @ips;
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You might also find the modules Net::IP or NetAddr::IP of interest.

By the way, the problem is your code is that you pad the elements of @calc, yet you use $*_start and $*_end (not the padded elements) to form $calc1 and $calc2.

Update: Added the sorting code and the list of relevant modules.
Update: Changed substr($_, 5) to substr($_, 4).
Update: Added the explanation as to why the OP's code didn't work.