The math does add up. You would need 2.85ml of the reconstituted Rocephin to make 1gm. The dissolving powder increases the total amount of the volume in the vial that you would draw from. As long as you get around that 2.85ml when you withdraw the med from the vial you're fine. I put 2.1ml in and withdraw the entire amount from the vial and that gives me around 3ml in my syringe. No matter what volume of Rocephin is in the injection, it will irritate the tissue and hurt. I would seem to think that a smaller volume would be less painful. Just my thoughts.