How massive is the universe?
It's hard to say, but it's really really big.
If you mean the universe as in everything around us, including outside of our galaxy, then its unknown. The universe is ever-expanding and growing, so we will never have an exact measurement.
Currently our 'observable universe' is 28 billion light-years in diameter . When you calculate that to kilometers, well you get a really really big number.
One Astronomical Unit, or AU for short, is 150 million km. And in a single light year there is 63241.1 AU. And we have 28 billion light-years in diameter that we can see.
So! Here is the math!
63241.1AU x 28,000,000,000ly = 1,770,750,800,000,000AU
1,770,750,800,000,000AU x 150,000,000km = 2.6561262e+23
So our current observable universe is 2.6561262e+23km.