The size of the observable universe is determined by the distance light has had the opportunity to travel since the Big Bang, given the current age of the universe. Since the universe is estimated to be about 13.8 billion years old, the observable universe has a radius of approximately 46.5 billion light-years (not to be confused with the age of the universe, as the expansion of space itself contributes to this apparent discrepancy). This means that the observable universe extends up to a distance of roughly 93 billion light-years in diameter.
However, it's important to note that this observable universe represents only the portion of the universe from which light has had enough time to reach us since the Big Bang. Beyond that, the universe might extend much farther, and its size is still a topic of scientific investigation. We cannot directly observe or interact with regions beyond our observable universe because the light from those regions has not reached us yet, and the expansion of space prevents us from accessing them.
As for what lies beyond the observable universe, it is currently unknown. There are several possibilities, including the concept of a "multiverse" where our universe is just one among many, each with different physical properties. Another possibility is that the universe is infinite and extends indefinitely. However, our current observational and theoretical knowledge is limited, and further research and exploration are needed to gain a deeper understanding of the nature and boundaries of the universe.