The recent observations of muon charge ratio up to about 10 TeV and of atmospheric neutrinos up to energies of about 400 TeV has triggered a renewed interest into the high-energy interaction models and cosmic ray primary composition. A reviewed calculation of lepton spectra produced in cosmic ray induced extensive air showers is carried out with a primary cosmic ray spectrum that fits the latest direct measurements below the knee. In order to achieve this, we used a full Monte Carlo method to derive the inclusive differential spectra (yields) of muons, muon neutrinos and electron neutrinos at the surface for energies between 80 GeV and hundreds of PeV. Using these results the differential flux and the flavor ratios of leptons were calculated. Furthermore, we could quantify systematic uncertainties of atmospheric muon- and neutrino fluxes, associated to the models of the primary cosmic ray spectrum and the interaction models.