A calibration technique is demonstrated which allows the determination of absolute atom concentrations in flames: two-photon laser-excited fluorescence signals from known atom concentrations generated in a discharge flow reactor are related to the fluorescence signals in a flame under identical excitation and detection conditions. With this method, absolute H atom profiles in several low-pressure hydrogen-oxygen flames have been obtained. For the same flame conditions, local temperature and absolute OH concentration profiles have been determined using laser-induced fluorescence (LIF). The experimental results are compared to the predictions of a one-dimensional flame model. The application of the new calibration technique to the atom detection in hydrocarbon flames is discussed.