this will not calc how much space is allocated to user, however it finds total size of files owned by user and totals them up.
Code:
awk 'BEGIN{
path="/"
user="root"
total=0
cmd="find "path" -type f -user "user" -printf \"%s\\n\""
while (( cmd |getline line) >0){ total+=line }
close(cmd)
print "total size by user: "user" is: "total" bytes"
}'
