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Negative bias temperature instability (NBTI) has become one of the major causes for reliability degradation of nanoscale circuits. In this letter, we propose a simple analytical model to predict the delay degradation of a wide class of digital logic gate based on both worst case and activity dependent threshold voltage change under NBTI. We show that by knowing the threshold voltage degradation of a single transistor due to NBTI, one can predict the performance degradation of a circuit with a reasonable degree of accuracy. We find that digital circuits are much less sensitive (approximately 9.2% performance degradation in ten years for 70 nm technology) to NBTI degradation than previously anticipated.