Designs of the single-, dual-, wide-band rectangular dielectric resonator antennas (DRAs) are discussed. Using new single-band formulas, the resonance frequency of the DRA can be determined easily from the given DRA dimensions and vice versa. Also, new formulas for designs of dual-mode rectangular DRAs are derived in this paper. From the derivation, the limit of the frequency ratio is also found and discussed. The formulas can be used to design a dualband DRA or a wideband DRA when the two resonance frequencies are close to each other. To validate our results, three single-, dual-, and wide-band rectangular DRAs were designed using the new formulas. In each case, the reflection coefficient, radiation pattern, and antenna gain were simulated and measured. Good agreement between the calculated, simulated, and measured results is obtained.