A precision measurement of atmospheric electron fluxes has been perfor
med on a Japanese commercial airliner (Enomoto et al.). The bulk of th
ese electrons are produced in pairs from the gamma rays emitted when p
i0's decay, which in turn have been produced in cosmic-ray-air-nucleus
collisions. These electron fluxes can be used to test elements of our
atmospheric neutrino flux calculation, i.e., the assumed primary spec
trum and the Monte Carlo shower code. Here we have modified the Monte
Carlo program which had previously been used to calculate the fluxes o
f atmospheric neutrinos by combining it with the program GEANT to comp
ute the electromagnetic part of the shower. This hybrid program now ke
eps track of the electrons produced in cosmic-ray showers as a functio
n of energy and atmospheric depth. We compare our calculated integral
fluxes above the experimental threshold energies 1, 2, and 4 GeV for a
variety of atmospheric depths and cutoff rigidities. Our results are
in good agreement (approximately a few %) with the data, but we found
we needed to boost the normalization of the primary flux by 12% over t
he value we had previously used to calculate the atmospheric neutrino
flux.