Datacenters are built to house massive internet services at an affordable price. Both Op-ex (long-time operational expenditure) and Cap-ex (one-time construction costs) are directly impacted by datacenter power consumption. Thus, DVFS (dynamic voltage and frequency scaling) is widely adopted to improve per node energy efficiency. However, it is well known but has not yet been fully explored that such schemes affect an application's power consumption and performance simultaneously. This paper focuses on the impact of DVFS on performance of an application and proposes an analytical model to quantitatively characterize the relationship between an application's performance and a processor's frequency, which can be leveraged to predict the performance of an application at any frequency. Specifically, according to different memory subsystem resources accessed, instructions of an application are divided into two parts:on-chip instructions and off-chip instructions, which can be modeled independently. On-Chip instructions refer to instructions which only access on-chip resources, and their execution time is frequency-relevant and can be modeled using a linear function. Off-chip instructions stand for instructions accessing the main memory, and their execution time is dominated by memory access latency and is frequency- irrelevant. By the division and modeling of the two parts, a quantitative model can be obtained between the execution time of an application and frequency of a processor. Evaluations using two different platforms and all benchmarks of SPEC 2006 show that the derived models are very precise, with average prediction error less than 1.34%.