Magnetometers are key instruments on board spacecraft that probe the plasma environments of planets and other solar system bodies. The linear conversion of raw magnetometer outputs to fully calibrated magnetic field measurements requires the accurate knowledge of 12 calibration parameters: six angles, three gain factors, and three offset values. The in-flight determination of 8 of those 12 parameters is enormously supported if the spacecraft is spin-stabilized, as an incorrect choice of those parameters will lead to systematic spin harmonic disturbances in the calibrated data. We show that published equations and algorithms for the determination of the eight spin-related parameters are far from optimal, as they do not take into account the physical behavior of science-grade magnetometers and the influence of a varying spacecraft attitude on the in-flight calibration process. Here, we address these issues. Based on decade-long developments and experience in calibration activities at the Braunschweig University of Technology, we introduce advanced calibration equations, parameters, and algorithms. With their help, it is possible to decouple different effects on the calibration parameters, originating from the spacecraft or the magnetometer itself. A key point of the algorithms is the bulk determination of parameters and associated uncertainties. The lowest uncertainties are expected under parameter-specific conditions. By application to THEMIS-C (Time History of Events and Macroscale Interactions during Substorms) magnetometer measurements, we show where these conditions are fulfilled along a highly elliptical orbit around Earth.