The goal of any particle accelerator is to optimize the transport of a charged particle beam along a set path by confining the beam to a small region close to the design trajectory and directing it accurately along the beamline. To do so in the simplest fashion, accelerators use a system of magnets that exert approximately linear electromagnetic forces on the charged beam. These electromagnets bend the beam along the desired path, in the case of bending magnets, and constrain the beam to the desired area through alternating focusing and defocusing effects, in the case of quadrupole magnets. We can model the transport of such a beam through transfer matrices representing the actions of the various beamline elements. However, space charge effects, produced from self electric fields within the beam, defocus the beam and must be accounted for in the calculation of beam emittance. We present below the preliminary results of a MATLAB code built to model the transport of a charged particle beam through an accelerator and measure the emittance under the influence of space charge effects. We demonstrate the method of correctly calculating the emittance of a beam under space charge effects using a least square fit to determine the initial properties of the beam given the beam size measured at a specific point after transport. Show Partial Abstract