Methods to implement stochastic simulations on the graphics processing unit (GPU) have been developed. These algorithms are used in a simulation of microassembly and nanoassembly with optical tweezers, but are also directly compatible with simulations of a wide variety of assembly techniques using either electrophoretic, magnetic, or other trapping techniques. Significant speedup is possible for stochastic particle simulations when using the GPU, included in most personal computers (PCs), rather than the central processing unit (CPU) that handles most calculations. However, a careful analysis of the accuracy and precision when using the GPU in stochastic simulations is lacking and is addressed here. A stochastic simulation for spherical particles has been developed and mapped onto stages of the GPU hardware that provide the best performance. The results from the CPU and GPU implementation are then compared with each other and with well-established theory. The error in the mean ensemble energy and the diffusion constant is measured for both the CPU and the GPU implementations. The time taken to complete several simulation experiments on each platform has also been measured and the speedup attained by the GPU is then calculated.