Rate-control (RC) algorithm is highly desirable for networked video applications. Almost all existing RC methods are only adapting the quantization stepsize (QS) to meet the target bit rate at fixed video frame size (FS) and frame rate (FR) using the rate-quantization (R-Q) model. Recent mobile video applications demand more advanced rate adaptation with different FS, FR and QS, rather merely quantization adjustment, to meet rapid wireless network bandwidth switch. Towards this goal, it requires an accurate rate model with respect to the FS, FR and QS. Hence, we investigate the impacts of spatial, temporal and amplitude resolution (STAR) on the bit rate of a compressed video. We propose a rate model as the product of power functions of the FS, FR and QS, respectively. The proposed rate model is analytically tractable, requiring only four content dependent parameters. The same model works for different coding scenarios (including scalable and non-scalable video, temporal prediction using either hierarchical B or IPPP structure, etc.) with very high accuracy using both H.264/AVC and HEVC. Using the proposed rate model and a quality model, we show how to optimize the STAR for a given rate constraint, which is important for both encoder rate control and network video adaptation.