The resolution of ultrafast studies performed at extreme ultraviolet and X-ray free-electron lasers is still limited by shot-to-shot variations of the temporal pulse characteristics. Here we show a versatile single-shot temporal diagnostic tool that allows the determination of the extreme ultraviolet pulse duration and the relative arrival time with respect to an external pump-probe laser pulse. This method is based on time-resolved optical probing of the transient reflectivity change due to linear absorption of the extreme ultraviolet pulse within a solid material. In this work, we present measurements performed at the FLASH free-electron laser. We determine the pulse duration at two distinct wavelengths, yielding (184±14) fs at 41.5 nm and (21±19) fs at 5.5 nm. Furthermore, we demonstrate the feasibility to operate the tool as an online diagnostic by using a 20-nm-thin Si3N4 membrane as target. Our results are supported by detailed numerical and analytical investigations.