We propose a novel method to characterize the temporal duration and shape of femtosecond x-ray pulses in a free-electron laser (FEL) by measuring the time resolved electron-beam energy loss and energy spread induced by the FEL process, with a transverse radio-frequency deflector located after the undulator. Its merits are simplicity, high resolution, wide diagnostic range, and non-invasive to user operation. When the system is applied to the Linac Coherent Light Source, the first hard x-ray free-electron laser in the world, it can provide single-shot measurements on the electron beam and x-ray pulses with a resolution on the order of 1-2 femtoseconds rms. Show Partial Abstract