Here are some facts and figures from an article in the Bulletin of the Atomic Scientists.

• The nuclear weapons dropped on Hiroshima and Nagasaki were 15 and 20 kilotons.
• The largest nuclear weapon tested by the United States was Castle Bravo, at 15 MT, in 1954. It was bigger than the scientists calculated it was going to be, and produced more fallout.
• The largest weapon tested by the Soviet Union was Tsar Bomba at 50 MT in 1961. They actually designed the bomb to be 100 MT and intentionally exploded it only halfway.

You can make bigger nuclear bombs by using smaller ones (relatively speaking) to set them off. There seems to be almost no theoretical limit to how high you could go.

At a secret meeting of the General Advisory Committee of the Atomic Energy Commission, Teller broached, as he put it, “the possibility of much bigger bangs.” At his Livermore laboratory, he reported, they were working on two new weapon designs, dubbed Gnomon and Sundial. Gnomon would be 1,000 megatons and would be used like a “primary” to set off Sundial, which would be 10,000 megatons. Most of Teller’s testimony remains classified to this day, but other scientists at the meeting recorded, after Teller had left, that they were “shocked” by his proposal. “It would contaminate the Earth,” one suggested…

It is hard to convey the damage of a gigaton bomb, because at such yields many traditional scaling laws do not work (the bomb blows a hole in the atmosphere, essentially). However, a study from 1963 suggested that, if detonated 28 miles (45 kilometers) above the surface of the Earth, a 10,000-megaton weapon could set fires over an area 500 miles (800 kilometers) in diameter.

Bulletin of the Atomic Scientists

Bombs this big have no strategic or practical use, they tell us. I don’t find this comforting. It just takes one madman to not get that and try something reckless one time, and our civilization is gone.