Aceh is home to numerous historic mosques, many of which remain active places of worship and have been designated as cultural heritage sites. Their qibla (qiblah) orientations, however, may differ from modern astronomical calculations, while attempts at correction often encounter concerns regarding historical ijtihād, religious legitimacy, and heritage preservation. This study evaluates the qibla orientation of 13 cultural heritage mosques in Aceh using Google Earth-based geospatial analysis interpreted through the perspectives of fiqh, science, and tradition. The results show that 53% of the mosques exhibit substantial deviations of more than 5°, while 47% fall within the high- or moderate-precision categories. Based on these findings, the study develops a Multi-Model Framework for Qibla Direction Tolerance integrating five models: the Astronomical 3-Point Model, Symbolic Kaaba Radius Model, Actual Haram Boundary Model, Sociological Tolerance, and Fiqh Tolerance. The framework distinguishes geometric precision from normative legitimacy and enables qibla orientation to be evaluated contextually without neglecting astronomical accuracy, fiqh considerations, historical value, and community acceptance.
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