Rapid intensification (RI) of tropical cyclones (TCs) provides a great challenge in operational forecasting and contributes significantly to the development of major TCs. RI is commonly defined as an increase in the maximum sustained surface wind speed of at least a certain threshold within 24 hr. The most widely used threshold is 30 kt (15.4 m/s), which was determined statistically. Here we propose a new definition for RI by objectively clustering TCs using the intensification rate, initial intensity, and radius of the maximum wind speed (RMW). A group of 770 samples is separated at a threshold of 45 kt (23.2 m/s). The threshold is 40 kt (20.6 m/s) for the western North Atlantic, where TC size measurements are more reliable. Monte Carlo experiments demonstrate that the proposed threshold is robust even considering the uncertainty in RMW of as high as 30 km. We show that, when a TC undergoes RI, its maximum wind speed is approximately 60 ± 15 kt (30.9 ± 7.7 m/s) and the RMW is 45 ± 20 km. The new threshold outperforms the conventional threshold of 30 kt/24 hr in describing the bimodal distribution of lifetime maximum intensity and explaining the annual count of Category 5 TCs. This new definition provides a more physically based threshold and describes a more reliable representation of extreme events. Although more comparisons are needed for operational application, it is likely to be desirable for case-based process studies and could provide a more valuable metric for TC intensification classification and research.