To expand a bit on the first part of the first reply, you can define your "push_button" sub like this:

sub push_button {
    my $celsius = $ent -> get();
    my $farienhiet = ($celsius*9/5)+32;
    my $msg = sprintf( "%s Celsius = %3.1f Fahrenheit\n", $celsius, $f
+arienhiet )
    $txt -> insert('end', $msg);
}
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That way, it shows both the input and output values, and doesn't erase any previous information. (But since the information is in an editable Text widget, the user can easily delete lines.)