In this study, ferromagnetic shape memory alloys (FSMAs) have shown great potential as active components in next generation smart devices due to their exceptionally large magnetic-field-induced strains and fast response times. During application of magnetic fields in FSMAs, as is common in several magnetoelastic smart materials, there occurs simultaneous rotation of magnetic moments and reorientation of twin variants, resolving which, although critical for design of new materials and devices, has been difficult to achieve quantitatively with current characterization methods. At the same time, theoretical modeling of these phenomena also faced limitations due to uncertainties in values of physical properties such as magnetocrystalline anisotropy energy (MCA), especially for off-stoichiometric FSMA compositions. Here, in situ polarized neutron diffraction is used to measure directly the extents of both magnetic moments rotation and crystallographic twin-reorientation in an FSMA single crystal during the application of magnetic fields. Additionally, high-resolution neutron scattering measurements and first-principles calculations based on fully relativistic density functional theory are used to determine accurately the MCA for the compositionally disordered alloy of Ni2Mn1.14Ga0.86. The results from these state-of-the-art experiments and calculations are self-consistently described within a phenomenological framework, which provides quantitative insights into the energetics of magnetostructural coupling in FSMAs. Based onmore » the current model, the energy for magnetoelastic twin boundaries propagation for the studied alloy is estimated to be ~150kJ/m3.« less