The Astronomisches Rechen-Institut ("Astronomical Calculation Institute", ARI), is a research institute in Heidelberg, Germany, dating from the 1700s. Beginning in 2005, the ARI became part of the Center for Astronomy at Heidelberg University (Zentrum für Astronomie der Universität Heidelberg, ZAH). Prior to this, the institute had belonged directly to the state of Baden-Württemberg.
The ARI has a rich history. It was founded in 1700 in Berlin-Dahlem by Gottfried Kirch. It had its origin in a patent application by Frederick I of Prussia, who introduced a monopoly on publishing star catalogs in Prussia. In 1945 the Institute was moved by the Americans nearer to the United States Army Garrison Heidelberg. On January 1, 2005 the combined Center for Astronomy institute formed by combining ARI, with the Institute of Theoretical Astrophysics (Institut für Theoretische Astrophysik, ITA) and the Landessternwarte Heidelberg-Königstuhl ("Heidelberg-Königstuhl State Observatory", LSW).
The ARI has been responsible among other things for the Gliese catalog of nearby stars, the fundamental catalogs FK5 and FK6, and the annually-published "Apparent Places of Fundamental Stars" (APFS), stellar ephemerides that provide high-precision mean and apparent positions of over three thousand stars for each day.