So what does it mean to destroy the world really? Fortunately if you mean all of humanity that means we've got a lot of land to cover, all the oceans and all the land just to be sure. That's a whopping 510,072,000 square kilometers. That's a lot, trust me. So let's assume that if you're out at ocean during the apocalypse, it's too late for you, and if you're on an ice cap you've removed yourself from the gene pool anyway, crazy researchers :) Then there is only 148,940,000 square kilometers of land left, according to Wikipedia.
Ok, now onto the destruction. Although we all know the awesome power of the atomic bomb, they don't actually do all that much destruction in comparison to the world. Yeah, there's a radioactive dust cloud etc, but let's ignore that since it is really survivable. The largest ever exploded nuclear weapon was the Soviet Union's Tsar Bomb at 50 Megatons. At this size it is powerful enough to cause third degree burns at 100km, and light damage at 700km from the epicentre. Now not every bomb is a Tsar bomb, and actually most have significantly less yield. A number of sources including Encarta and wikipedia state a typical nuclear weapon causes moderate damage up to 24kms away.
Quantity has definitely decreased in recent years. Today there are less than 5,000 active warheads. If we expand it to the available inactive warheads as well there are a total of 20,000. So now we've got our quantity and maximum yield.
SO if we take the 148,940,000 square kilometers of land area divided by 20,000 bombs with a coverage of 24kms we get about 50% coverage. So it's not 10 times over, but it's not too shabby either, but that's only the land area. If we go to the full earth it's only 15%. Now of course we could target cities and so forth, but it's nice know that it's a pretty safe bet some people would survive in the nuclear apocalypse.
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