By extending our previously established model, here we present a new model called "PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 3.0," which can instantaneously estimate terrestrial cosmic ray fluxes of neutrons, protons, ions with charge up to 28 (Ni), muons, electrons, positrons, and photons nearly anytime and anywhere in the Earth's atmosphere. The model comprises numerous analytical functions with parameters whose numerical values were fitted to reproduce the results of the extensive air shower (EAS) simulation performed by Particle and Heavy Ion Transport code System (PHITS). The accuracy of the EAS simulation was well verified using various experimental data, while that of PARMA3.0 was confirmed by the high R2 values of the fit. The models to be used for estimating radiation doses due to cosmic ray exposure, cosmic ray induced ionization rates, and count rates of neutron monitors were validated by investigating their capability to reproduce those quantities measured under various conditions. PARMA3.0 is available freely and is easy to use, as implemented in an open-access software program EXcel-based Program for Calculating Atmospheric Cosmic ray Spectrum (EXPACS). Because of these features, the new version of PARMA/EXPACS can be an important tool in various research fields such as geosciences, cosmic ray physics, and radiation research.