<p>We present a method to compute the symmetry-resolved entanglement entropy of spherical regions in higher-dimensional conformal field theories. By employing Casini-Huerta-Myers mapping, we transform the entanglement problem into thermodynamic calculations in hyperbolic space. This method is demonstrated through computations in both free field theories and holographic field theories. For large hyperbolic space volume, our results reveal a universal expansion structure of symmetry-resolved entanglement entropy, with the equipartition property holding up to the constant order. Using asymptotic analysis techniques, we prove this expansion structure and the equipartition property in arbitrary dimensions.</p>