The Astrometric Data-Reduction Software (ADRS) processes fringe, delay, environmental, and calibration data for PRIMA narrow-angle astrometry. It is automated software designed to provide fully-calibrated differential delays and separation angles. The ADRS is divided into on-line and off-line processing. The former deals with calibration and data compression, while the latter applies corrections and calculates science quantities. PRIMA is the first VLTI instrument that may require removal of long-term environmental trends. The trend identification and fitting routines are not part of the distributed on-line and off-line processing software. Instead, files containing fit parameters will be updated regularly. Coding is presently underway. The PRIMA error budget summarizes the principal sources of error in PRIMA astrometric observations.