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We show that the rate for upward showers from an isotropic cosmic neutrinoflux at neutrino telescopes like IceCube is independent of the neutrino-nucleoncross section. For bins that span a relatively narrow range in energy, neitherscaling the cross section, nor changing its power-law energy behavior affectsthe upward shower rate, which depends only on the flux. The neutrino flux canbe completely known since its spectral shape can be determined by comparing therates in neighboring bins. We also show that the downward shower rate varieslinearly with cross section with a proportionality constant determined by theenergy-dependence of the cross section, independent of the power-law behaviorof the flux. The normalization and energy dependence of the cross section canbe known by comparing the downward rates in neighboring bins.

Upward shower rates at neutrino telescopes directly determine the neutrino flux