Abstract At energies below 100 keV, measurements of the X-ray linear attenuation coefficient μ , require either a mono-energetic source or a detector with good energy resolution. The majority of X-ray sources contain a spread of energies whilst detectors have finite energy resolution. Beam hardening, arising from the preferential attenuation of lower energy X-rays, introduces systematic errors to μ measurements. These errors are examined for measurements with characteristic X-rays, and for poly-energetic sources in conjunction with energy dispersive detection. Industrial and medical applications are considered, at energies 5–110 keV for biological materials, aluminium, iron and copper.