  I calculate the diffuse flux of electron antineutrinos from all supernovae
using the information on the neutrino spectrum from SN987A and the information
on the rate of supernovae from direct supernova observations. The interval of
flux allowed at 99 % confidence level is 0.05 - 0.35 cm^-2 s ^-1 above the
SuperKamiokande (SK) energy cut of 19.3 MeV. This result is at least a factor
of 4 smaller than the current SK upper limit of 1.2 cm^-2 s ^-1, thus
motivating the experimental efforts to lower the detection energy threshold or
to upgrade to higher volumes. A Megaton water Cherenkov detector with 90 %
efficiency would record 2 - 44 inverse beta decay events a year depending on
the energy cut.
