The amount of nuclear warhead currently available with the world is good enough to make us reach back to Stone age.
Also none of the country has developed any technology to evacuate it's population during a nuclear war, the mass extinction is possible considering the aftereffect of war like food insecurity, shelter, epidemic etc.
A full nuclear war can destroy the whole world, mainly if the nuclear war involves Russia and the USA. This is the reason why all nuclear weapons should be destroyed as soon as possible.
It is essential to single out that the world is moving, once again, to a dangerous situation in which the possible use of tactical nuclear weapons could be used in a local or regional conflict with unknown consequences for the whole humankind.
The existing nuclear arsenal in the world is more than enough to destroy our whole planet in a matter of minutes. But usually, military protocols to respond to a nuclear first strike were made not only to respond militarily but to give enough time to the commanders-in-chief to negotiate a ceasefire.
So military nuclear responses are made not just to go “all-out” with everything they got but in “waves” of military response. And many of the nations of the world probably would not even be targets from these attacks because only eight countries have this kind of weapon (nine if you count Israel that still didn't officially recognized their own arsenal of nuclear weapons) .
A nuclear war would, in the best of all scenarios, change the way people of the non-belligerent nations live on this planet.
And for sure, would make human life much near to unfeasible in the belligerent nations and that’s why it is so hard to imagine any nation risking their own existence in this kind of war.
If you want to understand the technical details about the dangers of a nuclear war, I strongly recommend the reading of “One World or None: A Report to the Public on the Full Meaning of the Atomic Bomb” (Edited by Dexter Masters and Katherine Way).
This book was released just months after the drops of the bombs at Hiroshima and Nagasaki. When the most prominent scientists involved with its development (like Einstein, Szilard, Oppenheimer, etc.) decided to release a manifesto, warning about the dangers of those bombs, this resulted in a fascinating read. It has even one chapter by Albert Einstein discussing International Law.
I would like to add a few comments on your response to the question made by Satisha.
1- At this moment, there are nine nuclear weapons states China, France, the UK, India, Pakistan, Israel, DPRK, the USA, and Russia. Around 95-97% of all nuclear warheads are in the possession of the USA and Russia.
2- The bombing of Hiroshima and Nagasaki cannot be considered as a full nuclear war but a limited military attack using nuclear bombs because Japan has no nuclear weapons to use against the USA.
3- The type of nuclear bombs used against both Japanese cities is very small compared with the current nuclear weapons in the hands of 9 states, particularly those in the hands of Russia and the USA. The damage that the use of the existing types of nuclear weapons in a full nuclear war will affect many countries in different regions and will contaminate significant extension of land and water reservoirs and make them unproductive and useless during many years.
4- In a full nuclear war, the countries involved will use all of its nuclear weapons in the first or second attack and not in waves.
5- In a full nuclear war, there is no time for a ceasefire. When one of the countries involved in a full nuclear war launched the first attack against others, these countries will use all of their nuclear weapons available against the attacker and will not wait for a second wave. When a nuclear war begins, there is nothing to negotiate.
I didn’t mention nine because Israel didn’t officially recognize its arsenal. And I forgot to mention the nuclear sharing that Belgium, Germany, Italy, Netherlands, and Turkey have which is more them a hundred of U.S. nuclear heads in military bases, making them targets too. Which would probably make the majority of the northern hemisphere of the planet unfeasible to human life in an “all-out” war scenario.
Dr. Pedraza, I sincerely appreciate and respect your thoughts and expertise. But I still don’t believe that necessarily any nuclear attack would automatically escalate to an “all-out” nuclear war. Yes, nuclear weapons today are much more destructive them those in 1946. Yes, there is a massive chance of escalation; actually, the logic of the military protocols today is to make an escalation. But after a first strike, there are still decisions to be made and common sense to plea.
When I mentioned the time to negotiate I was talking about a matter of 15 minutes which would be the time to cancel the order for bombers and submarines to evaporate half of the world into radioactive dust. That’s why I mentioned the term “waves”, first we have the ICBMs (intercontinental ballistic missiles) that would be launched ASAP after or even before any nuclear strike, and then the second “wave” would be the bombers that would immediately leave their airbases with their determined targets, and the last "wave" would be the nuclear attack submarines carrying nuclear warheads.
The nuclear attack submarines were designed due to a scenario of disability of ICBMs, airbases and for counter-attack through any situation during a nuclear war after a first strike. So ICBMs, bombers and submarines; three different stages or "waves" of nuclear attacks in a matter of minutes.
So when I said negotiation and "waves" maybe I had passed the wrong idea of time and what I was talking about. At any possible nuclear strike, the notion of time decreases to minutes in a military response before the war is over and not hours nor days. I was talking about crucial decisions in a matter of minutes.