CeCd3As3 is a rare-earth triangular-lattice antiferromagnet with large inter-layer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field-evolution of the spin-excitation gaps throughout the antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on the microscopic pseudo-spin model, which, in return, yields a close quantitative description of the gap behavior. This analysis provides crucial insights into the nature of the magnetic state of CeCd3As3, with a certainty regarding its stripe order and low-energy model parameters that sets a compelling paradigm for exploring and understanding the rapidly growing family of the rare-earth-based triangular-lattice systems.