The Sun will not turn into a black hole at the end of its life. It will follow a different evolutionary path. The fate of a star like the Sun depends on its mass.
The Sun is considered a low to medium-mass star. In approximately 5 billion years, it will exhaust its nuclear fuel and start undergoing significant changes. It will enter a phase called the red giant phase, where it will expand in size and become much larger than its current size. During this phase, the Sun will engulf the inner planets, including Earth.
After the red giant phase, the Sun will shed its outer layers, forming a planetary nebula, and what remains of its core will be a dense, hot object called a white dwarf. A white dwarf is not a black hole but a highly dense stellar remnant composed mainly of electron-degenerate matter.
The size of the white dwarf that the Sun will become is estimated to be roughly the size of Earth. However, it will be much more massive than Earth because it will contain the remnants of the Sun's mass compressed into a small volume.
To form a black hole, a star needs to be significantly more massive, roughly several times the mass of the Sun. Only when such a massive star exhausts its nuclear fuel and undergoes a supernova explosion can it potentially collapse into a black hole, leaving behind a region of spacetime with an intense gravitational pull.
In summary, the Sun will not become a black hole but will evolve into a white dwarf after it exhausts its nuclear fuel, and it is estimated to be roughly the size of Earth.