Particle Image Velocimetry (PIV) based pressure field calculation is becoming increasingly popular in experimental fluid dynamics due to its non-intrusive nature. Errors propagated from PIV results to pressure field calculations are unavoidable, and in most cases, non-negligible. However, the specific dynamics of this error propagation process have not been unveiled. This dissertation examines both why and how errors in the experimental data are propagated to the pressure field by direct analysis of the pressure Poisson equation. Error in the pressure calculations are bounded with the error level of the experimental data. The error bounds quantitatively explain why and how many factors (i.e., geometry and length scale of the flow domain, type of boundary conditions) determine the resulting error propagation. The reason that the type of flow and profile of the error matter to the error propagation is also qualitatively illustrated. Numerical and experimental validations are conducted to verify these results. The results and framework introduced in this research can be used to guide the optimization of the experimental design, and potentially estimate the error in the reconstructed pressure field before performing PIV experiments.