Recently, 3GPP packet-switched streaming (PSS) specified adaptive HTTP streaming (AHS). The client requests series of media segments and adapt the bitrates of segment to varying network resources. The current state-of-the-art rate adaptation of AHS estimates the end-to-end network capacity using the previous segment reception such as segment fetching time. However, the accuracy and the speed of such rate adaptation highly depend on the segments duration. This paper presents a novel segment duration determination method to provide accurate and fast rate adaptation of AHS. The segment duration is estimated as the minimum duration to produce the smoothed HTTP/TCP rate which represents the current network capacity. Rate adaptation method using the determined segment duration is presented. To prevent buffer draining-up, the segment duration is further restrained as fine-grained duration. Simulation results show that the proposed segment duration enables the rate adaptation algorithm to increase achievable media bitrates and reduce the play-back interruption compared with the state-of-the-art rate adaptation method of AHS.