Inertial navigation on a chip has been an unfulfilled dream limited by the noise and stability of micromechanical Coriolis gyroscopes. While silicon has been the mainstream material for microelectromechanical system (MEMS) devices, the performance of silicon MEMS gyroscope has come near the physical limit of its material properties. To overcome these limitations, we explore the potential of silicon carbide (SiC), specifically 4H-SiC, as a promising substrate for substantially enhancing MEMS gyroscope performance, owing to its small phonon Akhiezer dissipation and in-plane isotropic hexagonal crystal lattice. Here we report on low-noise electrostatic acoustic resonant gyroscopes with mechanical Q factors in excess of a few million fabricated on bonded 4H silicon carbide-on-insulator wafers. The reported gyroscopes use megahertz bulk acoustic wave (BAW) mode for wide open-loop bandwidth. The gyroscopes are actuated and tuned electrostatically using micron gaps defined by wafer-level deep reactive ion etching (DRIE). Experimental results indicated that these batch-fabricated SiC gyroscopes have very minimum inherent imperfections across wafers, and upon tuning, beyond-tactical grade gyroscope performance is achieved under various testing conditions. Moreover, we highlight the higher quality factor of the silicon carbide BAW resonators at higher temperatures, in contrast to conventional silicon devices. This characteristic enables temperature stabilization through ovenization while achieving better gyroscope performance. The 4H-SiC BAW gyroscopes demonstrated here are the first of their kind and pave the way for the use of 4H-SiC as a superior acoustic material for next-generation MEMS positioning, navigation, and timing (PNT) devices.