This paper proposes a novel analytical model to predict zero quantized DCT coefficients for fast video encoding. The dynamic range of quantized DCT coefficients are analyzed and a threshold scheme is derived in order to determine DCT and quantization computations to be skipped without video quality degradation. The proposed model is compared with other models in the literature. Experimental results demonstrate that the proposed analytical model can greatly reduce the computational complexity of video encoding without any performance degradation, and outperforms other models.