"Definitive" in the sense that it effortlessly converts into all related units, not in the amount of units handled. :)

Of course it would be nice to add some limited parsing and intrinsic "understanding" of units and I can see how I'd go about implementing the basic idea (split into numerator and denominator, convert, divide), but how complex a unit specification should it be able to handle? I don't want to add so much weight that it turns into a small expression evaluator. I'm thinking one unit in the numerator, one in the denominator, and one power given for each sounds like a viably complex, sufficiently flexible spec.

Makeshifts last the longest.

This doesn't have to be complicated. Split on * and before /, then check for /\^\d+$/:

    my @units= split m#(?<=.)(?:(?=/)|\*)#, $units, -1;
    my %power;
    for my $unit (  @units  ) {
        my $power= 1;
        if(  $unit =~ s#\^(\d+)$##  ) {
            $power= $1;
        }
        if(  $unit =~ s#^/##  ) {
            $power= -$power;
        }
        $power{$unit} += $power;
    }
    # ...
[download]

then you have to find units that you can convert to with matching powers. So, if you start with kg/cm/sec [ which becomes (kg=>1,cm=>-1,sec=>-1) ] and are asked to return lb/ft/hr (lb=>1,ft=>-1,hr=>-1), then you have to convert from kg to lb, then convert cm to either ft or hr (there will be no cm-to-hr path so you'll do cm-to-ft), then convert the left-overs, sec-to-hr. And you're done.

(Updated and tested.)

        - tye