Context: AGILE is a gamma-ray astrophysics mission which has been in orbit since 23 April 2007 and continues to operate reliably. The gamma-ray detector, AGILE-GRID, has observed Galactic and extragalactic sources, many of which were collected in the first AGILE Catalog. Aims: We present the calibration of the AGILE-GRID using in-flight data and Monte Carlo simulations, producing Instrument Response Functions (IRFs) for the effective area A_eff), Energy Dispersion Probability (EDP), and Point Spread Function (PSF), each as a function of incident direction in instrument coordinates and energy. Methods: We performed Monte Carlo simulations at different gamma-ray energies and incident angles, including background rejection filters and Kalman filter-based gamma-ray reconstruction. Long integrations of in-flight observations of the Vela, Crab and Geminga sources in broad and narrow energy bands were used to validate and improve the accuracy of the instrument response functions. Results: The weighted average PSFs as a function of spectra correspond well to the data for all sources and energy bands. Conclusions: Changes in the interpolation of the PSF from Monte Carlo data and in the procedure for construction of the energy-weighted effective areas have improved the correspondence between predicted and observed fluxes and spectra of celestial calibration sources, reducing false positives and obviating the need for post-hoc energy-dependent scaling factors. The new IRFs have been publicly available from the Agile Science Data Centre since November 25, 2011, while the changes in the analysis software will be distributed in an upcoming release.
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