A quantitative spectral analysis of 24 A supergiants in the Sculptor Group spiral galaxy NGC 300 at a distance of 1.9 Mpc is presented. A new method is introduced to analyze low-resolution (~5 A) spectra, which yields metallicities accurate to 0.2 dex including the uncertainties arising from the errors in Teff (5%) and log g (0.2 dex). For the first time the stellar metallicity gradient based on elements such as titanium and iron in a galaxy beyond the Local Group is investigated. Solar metallicity is measured in the center and 0.3 solar in the outskirts and a logarithmic gradient of –0.08 dex kpc−1. An average reddening of E(B − V) ~ 0.12 mag is obtained, however, with a large variation from 0.07 to 0.24 mag. We also determine stellar radii, luminosities, and masses and discuss the evolutionary status. Finally, the observed relationship between absolute bolometric magnitudes Mbol and flux-weighted gravities gF = g/T4eff is investigated. At high temperatures the strength of the Balmer lines depends solely on the flux-weighted gravity, which allows a precise direct determination of log gF with an accuracy of 0.05-0.1 dex. We find a tight relationship between Mbol and log gF in agreement with stellar evolution theory. Combining these new results with previous work on Local Group galaxies, we obtain a new flux-weighted gravity-luminosity relationship (FGLR), which is very well defined and appears to be an excellent alternative tool to determine distances to galaxies.