The electron cooler operating at the Antiproton Decelerator (AD) at CERN is at the end of its life cycle. The electron cooler, operated for over 40 years, has been used to decelerate anti-proton beams having an energy of about 5.3 MeV. A new electron cooler is being designed and expected to be commissioned during the Long Shutdown 3 (LS3) in 2026. The initial magnet system design consists of an array of pancake solenoid coils as well as an expansion solenoid. The mechanical alignment of the pancake coils must comply with challenging requirements, where the coils need to have 0.1 mrad angle positioning accuracy and Bz/Br < 5 × 10 −4 in terms of field quality. In this paper, a new measurement method for the determination of a solenoid coil angle is presented, which allows for faster identification of the pancake-coil angles. The method was experimentally validated on an existing transducer, and the results were used for the design of a new measurement system capable of meeting the requirements.