Ultrasound imaging is widely used due to its safety, affordability, and real-time capabilities, but its 2D interpretation is highly operator-dependent, leading to variability and increased cognitive demand. 2D-to-3D reconstruction mitigates these challenges by providing standardized volumetric views, yet existing methods are often computationally expensive, memory-intensive, or incompatible with ultrasound physics. We introduce UltraGauss: the first ultrasound-specific Gaussian Splatting framework, extending view synthesis techniques to ultrasound wave propagation. Unlike conventional perspective-based splatting, UltraGauss models probe-plane intersections in 3D, aligning with acoustic image formation. We derive an efficient rasterization boundary formulation for GPU parallelization and introduce a numerically stable covariance parametrization, improving computational efficiency and reconstruction accuracy. On real clinical ultrasound data, UltraGauss achieves state-of-the-art reconstructions in 5 minutes, and reaching 0.99 SSIM within 20 minutes on a single GPU. A survey of expert clinicians confirms UltraGauss' reconstructions are the most realistic among competing methods. Our CUDA implementation will be released upon publication.