Pressure is a scalar quantity because

Pressure is defined as the force per unit area [2]. However, in a rigorous physical sense, pressure is a scalar quantity because it is specifically the ratio of the magnitude of the force component acting normal (perpendicular) to a surface to the area of that surface [4]. While force and area can be treated as vectors, pressure itself has no inherent direction; it acts equally in all directions at a given point within a fluid [3]. The direction of the resulting force is always determined by the orientation of the surface area it acts upon, not by the pressure itself. Therefore, pressure is defined by the normal component of the force divided by the area, making it a scalar proportionality constant between the vector force and the vector area.

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 6: Pressure, Winds, Storms, and Cyclones > 6.1 Pressure > p. 82
2. [2] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 6: Pressure, Winds, Storms, and Cyclones > Snapshots > p. 94
3. [4] https://www.khanacademy.org/science/ap-college-physics-1/xf557a762645cccc5:fluids/xf557a762645cccc5:untitled-354/v/fluid-pressure
4. [3] https://sathee.iitk.ac.in/article/physics/physics-pressure/