We investigate the spectral directional and hemispherical emissivity of hyperbolic metamaterials with arbitrary orientation of the optic axis. The 4 x 4 matrix method is combined with coordinate rotational transforms to circumvent projection operations. The two hyperbolic bands of hexagonal boron nitride (hBN) are examined in detail to elucidate the influence of the orientation of the optic axis on the emissivities for both transverse magnetic (TM) and transverse electric (TE) waves. The results show that the orientation of the optic axis can greatly affect the hemispherical emissivity in the two hyperbolic bands of hBN. The directional emissivity varies periodically with the azimuthal angle when TM and TE waves are coupled, resulting in conversion of polarization in the medium. For both TM and TE waves, the matching of impedance and admittance at the surface of the material is better for smaller tilting angle in the type I hyperbolic band, but the opposite is true in type II hyperbolic band where the matching becomes better for larger tilting angles. As the tilting angle increases, the hemispherical emissivity decreases in the type I hyperbolic band but increases in the type II hyperbolic band. Our conclusions can be extended to other hyperbolic materials. Therefore, this work may provide valuable guidance on characterization, measurement and tailoring of the directional and hemispherical emissivity for hBN and other hyperbolic materials with arbitrary orientation and application of such materials for manipulation of radiative heat transfer. (C) 2019 Elsevier Ltd. All rights reserved.