Massive windings must be used for strong magnetic field applications, which results in low magnetic field uniformity. In this paper, a simple circular Helmholtz coil system is analyzed to identify the main causes of the problems, which arise for high intensity uniform magnetic field applications. Here, dominant deformations of the circular solenoid winding cross-section shape and its dimensions effects on the generated magnetic field and its uniformity are analyzed. These analyses can be applied to the modified Helmholtz coil and multi-axial systems, as well. The system dimensions are optimized and normalized to easily scale the given results for any desired uniform magnetic field and workspace without doing further laborious calculations. The optimized dimensions increase the magnetic field uniformity in a large portion of the available workspace and realize the desired magnetic field at the center of the system. Also, the necessary conductor mass and the total electrical power are reduced. To verify the given analyses, two small-scale Helmholtz coil systems have been implemented and their generated magnetic fields and nonuniformities have been measured under a variety of conditions.