Various density functional theory (DFT) and ab initio MP2 and CCSD methods were employed in calculations of arsenic isotropic and anisotropic hyperfine parameters in three small radicals, AsH2, AsO2, and H2AsO. Convergent basis sets for these calculations were specially derived starting from Dunning's correlation-consistent sets. DFT methods proved to be particularly appropriate choice, because the results obtained with the suitable functionals are in accordance with the available experimental values. Additionally, mechanisms of hyperfine couplings were investigated by examining individual orbital contributions to spin density. The spin polarization mechanism in AsH2 was studied by evaluating one- and two-electron integrals in spin-restricted and unrestricted case. Apart from nonrelativistic, scalar-relativistic Douglas-Kroll-Hess DFT calculations were performed to examine relativistic impacts on spin density distribution.