ComEst calculates the completeness of CCD images conducted in astronomical observations saved in the FITS format. It estimates the completeness of the source finder SExtractor (ascl:1010.064) on the optical and near-infrared (NIR) imaging of point sources or galaxies as a function of flux (or magnitude) directly from the image itself. It uses PyFITS (ascl:1207.009) and GalSim (ascl:1402.009) to perform the end-to-end estimation of the completeness and can also estimate the purity of the source detection.