Spin dynamics in the itinerant antiferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>SrCr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>As</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

SrCr$_2$As$_2$ is an itinerant antiferromagnet in the same structural family as the SrFe$_2$As$_2$ high-temperature superconductors. We report our calculations of exchange-coupling parameters $J_{ij}$ for SrCr$_2$As$_2$ using a static linear-response method based on first-principles electronic-structure calculations. We find that the dominant nearest-neighbor exchange coupling $J_{\rm{1}}>0$ is antiferromagnetic whereas the next-nearest-neighbor interaction $J_{\rm{2}}<0$ is ferromagnetic with $J_{\rm{2}}$/$J_{\rm{1}}$~=~$-0.68$, reinforcing the checkerboard in-plane magnetic structure. Thus, unlike other transition-metal arsenides based on Mn, Fe, or Co, we find no competing magnetic interactions in SrCr$_2$As$_2$, which aligns with experimental findings. Moreover, the orbital resolution of exchange interactions shows that $J_1$ and $J_2$ are dominated by direct exchange mediated by the Cr $d$ orbitals. To validate the calculations we conduct inelastic neutron-scattering measurements on powder samples that show steeply dispersive magnetic excitations arising from the magnetic $\Gamma$ points and persisting up to energies of at least 175 meV. The spin-wave spectra are then modeled using the Heisenberg Hamiltonian with the theoretically-calculated exchange couplings. The calculated neutron-scattering spectra are in good agreement with the experimental data.