Magnet coils may be excited into internal voltage oscillations by transient voltages. Such oscillations may electrically stress the magnet's dielectric components to many times its normal stress. This may precipitate a dielectric failure, and the attendant prolonged loss of service and costly repair work. Therefore, it is important to know the natural frequencies of oscillations of a magnet during the design stage, and to determine whether the expected switching transient voltges can excite the magnet into high-voltage internal oscillations. The series capacitance of a winding significantly affects its natural frequencies. However, the series capacitance is difficult to calculate, because it may comprise complex capacitance network, consisting of intra- and inter-coil turn-to-turn capacitances of the coil sections. A method of calculating the series capacitance of a winding is proposed. This method is rigorous but simple to execute. The time-varying transient voltages along the winding are also calculated.