The rapidly increasing number of stellar spectra obtained by existing and future large-scale spectroscopic surveys feeds a demand for fast and efficient tools for the spectroscopic determination of fundamental stellar parameters . Such tools should not only comprise customized solutions for one particular survey or instrument , but , in order to enable cross-survey comparability , they should also be capable of dealing with spectra from a variety of spectrographs , resolutions , and wavelength coverages . To meet these ambitious specifications , we developed ATHOS ( A Tool for HOmogenizing Stellar parameters ) , a fundamentally new analysis tool that adopts easy-to-use , computationally inexpensive analytical relations tying flux ratios ( FRs ) of designated wavelength regions in optical spectra to the stellar parameters effective temperature ( T _ { \mathrm { eff } } ) , iron abundance ( [ Fe/H ] ) , and surface gravity ( \log { g } ) . Our T _ { \mathrm { eff } } estimator is based on FRs from nine pairs of wavelength ranges around the Balmer lines H \beta and H \alpha , while for [ Fe/H ] and \log { g } we provide 31 and 11 FRs , respectively , which are spread between \sim 4800 Å and \sim 6500 Å ; a region covered by most optical surveys . The analytical relations employing these FRs were trained on N = 124 real spectra of a stellar benchmark sample that covers a large parameter space of T _ { \mathrm { eff } } \approx 4000 to 6500 K ( spectral types F to K ) , [ Fe/H ] \approx - 4.5 to 0.3 dex , and \log { g } \approx 1 to 5 dex , which at the same time reflects ATHOS ’ range of applicability . We find accuracies of 97 K for T _ { \mathrm { eff } } , 0.16 dex for [ Fe/H ] , and 0.26 dex for \log { g } , which are merely bounded by finite uncertainties in the training sample parameters . ATHOS ’ internal precisions can be better by up to 70 % . We tested ATHOS on six independent large surveys spanning a wide range of resolutions ( R = \lambda / \Delta \lambda \approx 2000 to 52000 ) , amongst which are the Gaia-ESO and the SDSS/SEGUE surveys . The exceptionally low execution time ( < 30 ms per spectrum per CPU core ) together with a comparison to the literature parameters showed that ATHOS can successfully achieve its main objectives , in other words fast stellar parametrization with cross-survey validity , high accuracy , and high precision . These are key to homogenize the output from future surveys , such as 4MOST or WEAVE .