Clifford's Algebraic Approach in Determining the Direction of Qibla

While classical methods and hisab methods based on spherical trigonometry and vector algebra are commonly used, this article introduces a more elegant, purely geometric alternative using Clifford Algebra (within the framework of Geometric Algebra). This method uses unit vectors in three-dimensional space to represent the positions of the observer and the Kaaba, then projects these vectors onto the local horizontal plane using geometric operations such as the dot product and the outer product. The results of the Qibla direction calculations for five major cities in Indonesia—Jakarta, Surabaya, Medan, Bandung, and Makassar—when compared with the spherical trigonometry and vector algebra methods, show high consistency, with a maximum difference of less than 0°. Further validation using data from the Qibla Locator also confirms the method's accuracy. Clifford Algebra has proven to be an accurate, intuitive, and computationally efficient approach, with great potential for applications in digital navigation systems, augmented reality, and science education. Thus, this method offers a powerful modern alternative for determining the direction of the Qibla through hisab