Organic semiconductors are attractive for optical sensing applications due to the effortless processing on large active area of several cm(2), which is difficult to achieve with solid-state devices. However, compared to silicon photodiodes, sensitivity and dynamic behavior remain a major challenge with organic sensors. Here, we show that charge trapping phenomena deteriorate the bandwidth of organic photodiodes (OPDs) to a few Hz at low-light levels. We demonstrate that, despite the large OPD capacitances of ~10 nF cm(-2), a frequency response in the kHz regime can be achieved at light levels as low as 20 nW cm(-2) by appropriate interface engineering, which corresponds to a 1000-fold increase compared to state-of-the-art OPDs. Such device characteristics indicate that large active area OPDs are suitable for industrial sensing and even match medical requirements for single X-ray pulse detection in the millisecond range.