Sample size and power calculations are an important part of designing new sequence-based association studies. The recently developed SEQPower and SPS programs adopted computationally intensive Monte Carlo simulations to empirically estimate power for a series of variant set association (VSA) test methods including the sequence kernel association test (SKAT). It is desirable to develop methods that can quickly and accurately compute power without intensive Monte Carlo simulations. We will show that the computed power for SKAT based on the existing analytical approach could be inflated especially for small significance levels, which are often of primary interest for large-scale whole genome and exome sequencing projects. We propose a new χ2-approximation-based approach to accurately and efficiently compute sample size and power. In addition, we propose and implement a more accurate “exact” method to compute power, which is more efficient than the Monte Carlo approach though generally involves more computations than the χ2 approximation method. The exact approach could produce very accurate results and be used to verify alternative approximation approaches. We implement the proposed methods in publicly available R programs that can be readily adapted when planning sequencing projects.