In alternating field demagnetizers, it is required that as large a uniform magnetic field as possible be produced at the sample space by using a given power supply. To calculate the strength of the magnetic field inside alternating field coils to any desired accuracy, a computer oriented algorithm is developed. Next, the shape of alternating field coils that produce large peak fields is investigated. Although there is a shape of coils that gives absolute maximum magnetic field, it is found that multilayer solenoids are usually satisfactory for maximum field as well as field uniformity requirements. The process of designing an alternating field coil is formulated and some convenient figures and tables are presented.