The mass of the supermassive black hole at the center of our galaxy, known as Sagittarius A* (Sgr A*), is approximately 4.3 million times the mass of the Sun. This value was determined through various observations and measurements, including studies of the orbits of stars near the black hole and the analysis of gas motions within the central region of our galaxy.

It's important to note that the precise mass of Sgr A* is still a subject of ongoing research and refinement. Different methods and techniques used for measuring its mass may provide slightly different estimates. However, the value of 4.3 million solar masses is widely accepted as the best current estimate for the mass of the supermassive black hole at the center of our Milky Way galaxy.