Positronium is a bound state of an electron with a positron. In particle physics a complete understanding of positronium energy levels is the basis for finding the energy levels of more complex systems. It is important to determine if theoretical results match the experimental. We attempted to approximate the energies of positronium using non relativistic quantum electrodynamics, at a higher precision than earlier work. The calculations were made with numerical integrations either done by VEGAS or Mathematica. Further work needs to be done so that the calculation is complete. This project was made possible by funding from F&M's Hackman Summer Scholars Program.