We present a new method for determining the sensitivity of X-ray imaging observations, which correctly accounts for the observational biases that affect the probability of detecting a source of a given X-ray flux, without the need to perform a large number of time-consuming simulations. We use this new technique to estimate the X-ray source counts in different spectral bands (0.5–2, 0.5–10, 2–10 and 5–10 keV) by combining deep pencil-beam and shallow wide-area Chandra observations. The sample has a total of 6295 unique sources over an area of 11.8 deg2 and is the largest used to date to determine the X-ray number counts. We determine, for the first time, the break flux in the 5–10 keV band, in the case of a double power-law source count distribution. We also find an upturn in the 0.5–2 keV counts at fluxes below about 6 × 10−17erg s−1cm−2. We show that this can be explained by the emergence of normal star-forming galaxies which dominate the X-ray population at faint fluxes. The fraction of the diffuse X-ray background resolved into point sources at different spectral bands is also estimated. It is argued that a single population of Compton thick active galactic nuclei (AGN) cannot be responsible for the entire unresolved X-ray background in the energy range 2–10 keV.