There was a scientific study done late in the Cold War during the 1980's that postulated that if somebody could construct a thermonuclear device so powerful that its explosive yield would reach or even exceed 50,000 megatons that its detonation on dry land would cause enough of a catastrophic blast effect and global fallout that it would kill every single human being on the face of the planet except those who were in survival bunkers and shelters deep underground and who didn't emerge for at least two to three years after the explosion.
The key point of that being, naturally, that somebody
would survive a nuclear war. At the height of the Cold War the cumulative explosive power of all the world's nuclear arsenals was somewhere around 16,000 megatons, less than a third of the power of the theoretical "Mankind Killer" and with the exception of the most dire anti-nuclear activists of the time it was assumed that there would still be a substantial human population on the planet even after the wake of a Cold War nuclear conflagration (albeit one thrown back to the time of the steam engine if not the Dark Ages).
The chances of every single human being perishing short of a major asteroid, meteorite or comet nucleus collision on the scale of or even worse than the Yucatan impact of 65 million years ago are pretty slim. Not impossible, but they're not great.