To date, optical studies of single molecules at room temperature have relied on the use of materials with high fluorescence quantum yield combined with efficient spectral rejection of background light. To extend single-molecule studies to a much larger pallet of substances that absorb but do not fluoresce, scientists have explored the photothermal effect, interferometry, direct attenuation and stimulated emission. Indeed, very recently, three groups have succeeded in achieving single-molecule sensitivity in absorption. Here, we apply modulation-free transmission measurements known from absorption spectrometers to image single molecules under ambient conditions both in the emissive and strongly quenched states. We arrive at quantitative values for the absorption cross-section of single molecules at different wavelengths and thereby set the ground for single-molecule absorption spectroscopy. Our work has important implications for research ranging from absorption and infrared spectroscopy to sensing of unlabelled proteins at the single-molecule level.