Well it really depends on what you want it to be. Many people say that it is infinite. And that’s not wrong..well almost. It turns out you can proof that universe is indeed infinite with little knowledge of math. In math there are certain numbers called irrational numbers which do not end. For example the value of “pi” doesn’t terminate, it just goes on and on without repeating. So if you are going to put the value of pi in an equation, you are not going to find the exact solution. This is because there will always be some digits in the value of pi which you have not calculated. You cannot compensate for this uncalculated value with some other number like rounding it off, because it will be also make the solution wrong.Irrational numbers are weird and non ending.
But think about this. If you were to write the value of pi without stopping like 3.14285714……………. in a long piece of paper, what would happen? You see the problem? You cannot stop because you cannot get to the infinity.
Now think about this in other way. While you are writing the value, you are using paper and ink. These are matter. And we have limited supply of them. And no I am not talking about paper and ink because you can convert any matter into other matter with using little bit energy which itself will transform to another form of energy. So you can turn every tree, every grain of sand, every living being into paper. If you want to turn earth itself to paper you can do it, really. But this supply of matter and energy is limited. You have to work with what you have got. You cannot create some extra matter, and so for that part no extra paper. If you are going to write continuously, at some point you have to put a fullstop as all the matter have exhausted. So what after that? There is still endless digits to calculate
So here the question arises. What is the universe then? Does it end where all the matter ends? Or we have to account for what we did not calculate? This in case of space will be nothing because there is no matter to calculate. So infinity like our universe have a part called nothing!
This doesn’t end here. When big bang happened nearly 13.8 billion years ago all matter should have scattered in all direction in same rate. This should make the shape of the universe a circle. The area of a circle is . You can go on and calculate the radius but no one can calculate the exact area of universe.