We derive new empirical calibrations for strong-line diagnostics of gas-phase metallicity in local star-forming galaxies by uniformly applying the Te method over the full metallicity range probed by the Sloan Digital Sky Survey (SDSS). To measure electron temperatures at high metallicity, where the auroral lines needed are not detected in single galaxies, we stacked spectra of more than 110 000 galaxies from the SDSS in bins of log[O ii]/Hβ and log[O iii]/Hβ. This stacking scheme does not assume any dependence of metallicity on mass or star formation rate, but only that galaxies with the same line ratios have the same oxygen abundance. We provide calibrations which span more than 1 dex in metallicity and are entirely defined on a consistent absolute Te metallicity scale for galaxies. We apply our calibrations to the SDSS sample and find that they provide consistent metallicity estimates to within 0.05 dex.