  The Space Telescope Imaging Spectrograph has measured the absolute flux for
Vega from 0.17-1.01 microns on the HST White Dwarf flux scale. These data are
saturated by up to a factor of 80 overexposure but retain linearity to a
precision of 0.2%, because the charge bleeds along the columns and is recovered
during readout of the CCD. The S/N per pixel exceeds 1000, and the resolution R
is about 500. A V magnitude of 0.026 +/- 0.008 is established for Vega; and the
absolute flux level is 3.46 x 10^{-9} erg cm^{-2} s^{-1} at 5556 A. In the
regions of Balmer and Paschen lines, the STIS equivalent widths differ from the
pioneering work of Hayes in 1985 but do agree with predictions of a Kurucz
model atmosphere, so that the STIS flux distribution is preferred to that of
Hayes. Over the full wavelength range, the model atmosphere calculation shows
excellent agreement with the STIS flux distribution and is used to extrapolate
predicted fluxes into the IR region. However, the IR fluxes are 2% low with
respect to the standard Vega model of Cohen. IUE data provide the extension of
the measured STIS flux distribution from 0.17 down to 0.12 microns. The STIS
relative flux calibration is based on model atmosphere calculations of pure
hydrogen WDs, while the Hayes flux calibration is based on the physics of
laboratory lamps and black body ovens. The agreement to 1% of these two
independent methods for determining the relative stellar flux distributions
suggests that both methods may be correct from 0.5-0.8 microns and adds
confidence to claims that the fluxes relative to 5500 A are determined to
better than 4% by the pure hydrogen WD models from 0.12 to 3 microns.
