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tokens: Zeeman splitting is based on the works of Landi Degl’Innocenti (1976) , Schadee (1978) , Rees et al. (1989) , and Larsson et al. (2014) . For each considered Zeeman split spectral line, ZRAD requires the following precalculated quantities: the energy levels and transitions taken from the Leiden Atomic and Molecular DAtabase (LAMDA; Schöier et al. 2005 ) or JPL spectral line catalog ( Pickett et al. 1998 ), Landé factors of the energy levels used, line strengths of the allowed transitions between Zeeman sublevels, and the radius of the gas species used. For the line shape, ZRAD includes the natural, collisional, and Doppler broadening (line shape: Voigt profile) and the magneto-optic effect (line shape: Faraday-Voigt profile; Larsson et al. 2014 ). The Voigt and Faraday-Voigt profiles are obtained from the real and imaginary part of the Faddeeva function, respectively ( Wells 1999 ). In ZRAD, a fast and precise solution of the Faddeeva function is realized with the Faddeeva package ( Johnson 2012 ). 3. Zeeman splitting We consider the Zeeman splitting theory as outlined in Sect. 3 of our previous work ( Brauer et al. 2017 ). In the following, we provide a brief description of the most important physical quantities. By assuming that the Zeeman shift is negligible when compared to the line width , the circularly polarized fraction can be written as a function of the derivative of the net flux as (see Crutcher et al. 1993 ; Brauer et al. 2017 ) whereas the frequency shift owing to Zeeman splitting can be calculated with Here, is the Bohr magneton, the Landé factor, and the total angular or atomic momentum quantum number projected on the magnetic field vector . A single prime denotes the upper level; a double prime denotes the lower level of the line transition. Following Eqs. ( 1 ) and ( 2 ), the magnetic field strength in the LOS direction can be obtained by fitting the derivative of the net flux profile to the circularly polarized fraction of a Zeeman split spectral line. The derived LOS magnetic field strength converges toward a reference magnetic field strength if the assumption of Eq. ( 1 ) is valid and the LOS is optically thin ( Brauer et al. 2017 ). The reference magnetic field strength can be calculated by averaging the LOS magnetic field strength weighted with the spectral line net flux along the LOS to the observer as follows: Here, is the magnetic field strength at a certain position, is the unit vector in the LOS direction, and is the path length along the LOS. 4. Spectral lines of CN at 113 GHz Zeeman observations of CN are usually performed by observing seven of the nine hyperfine transitions at ( Falgarone et al. 2008 ; Pillai et al. 2016 ). However, we limit ourselves to the spectral lines at and since they represent two extreme cases (see Table 1 ; Crutcher et al. 1999 ; Falgarone et al. 2008 ). The line at has the largest Zeeman shift and one of the highest relative sensitivities to compared to the other lines. In contrast, the