Magnetocrystalline anisotropy is a fundamental property of magnetic materials that determines the dynamics of magnetic precession, the frequency of spin waves, the thermal stability of magnetic domains, and the efficiency of spintronic devices. We combine torque magnetometry and density functional theory calculations to determine the magnetocrystalline anisotropy of the metallic antiferromagnet Fe2As. Fe2As has a tetragonal crystal structure with the Neel vector lying in the (001) plane. We report that the fourfold magnetocrystalline anisotropy in the (001) plane of Fe2As is extremely small, K-22 = -150 J/m(3) at T = 4 K, much smaller than the perpendicular magnetic anisotropy of ferromagnetic structure widely used in spintronic devices. K-22 is strongly temperature dependent and close to zero at T > 150 K. The anisotropy K-1 in the (010) plane is too large to be measured by torque magnetometry and we determine K-1 = -830 kJ/m(3) using first-principles density functional theory. Our simulations show that the contribution to the anisotropy from classical magnetic dipole-dipole interactions is comparable to the contribution from spin-orbit coupling. The calculated fourfold anisotropy in the (001) plane K-22 ranges from -290 to 280 J/m(3), the same order of magnitude as the measured value. We used K-1 from theory to predict the frequency and polarization of the lowest frequency antiferromagnetic resonance mode and find that the mode is linearly polarized in the (001) plane with f = 670 GHz.