This paper presents the complete characterization of a kilo-electron-volt laser-based x-ray source. The main parameters of the electron motion (amplitude of oscillations and initial energy) in the laser wakefield have been investigated using three independent methods relying on spectral and spatial properties of this betatron x-ray source. First we will show studies on the spectral correlation between electrons and x-rays that is analyzed using a numerical code to calculate the expected photon spectra from the experimentally measured electron spectra. High-resolution x-ray spectrometers have been used to characterize the x-ray spectra within 0.8–3 keV and to show that the betatron oscillations lie within 1 µm. Then we observed Fresnel edge diffraction of the x-ray beam. The observed diffraction at the center energy of 4 keV agrees with the Gaussian incoherent source profile of full width half maximum <5 µm, meaning that the amplitude of the betatron oscillations is less than 2.5 µm. Finally, by measuring the far field spatial profile of the radiation, we have been able to characterize the electron's trajectories inside the plasma accelerator structure with a resolution better than 0.5 µm.