Surface normal holds significant importance in visual environmental perception, serving as a source of rich geometric information. However, the state-of-the-art (SoTA) surface normal estimators (SNEs) generally suffer from an unsatisfactory trade-off between efficiency and accuracy. To resolve this dilemma, this paper first presents a superfast depth-to-normal translator (D2NT), which can directly translate depth images into surface normal maps without calculating 3D coordinates. We then propose a discontinuity-aware gradient (DAG) filter, which adaptively generates gradient convolution kernels to improve depth gradient estimation. Finally, we propose a surface normal refinement module that can easily be integrated into any depth-to-normal SNEs, substantially improving the surface normal estimation accuracy. Our proposed algorithm demonstrates the best accuracy among all other existing real-time SNEs and achieves the SoTA trade-off between efficiency and accuracy.