The Smallest U.S. Nuclear Weapon

The smallest U.S. nuclear weapon ever developed, the W-54, had a minimum yield of “only” 10 tons of TNT equivalent (0.01 kilotons) and could be carried by a single soldier in an (awkwardly large) backpack. Such a weapon was deliberately made as a “bridge” between conventional and nuclear explosives yields. 

By comparison, the Oklahoma City Bombing in 1995 is commonly cited as having been around 2.5 tons of TNT equivalent (0.0025 kilotons). The largest conventional weapons globally (the U.S. MOAB and the Russian FOAB, both fuel-air bombs) have yields in the range of 10-40 tons of TNT equivalent (0.01–0.04 kilotons). 

To put things in perspective, consider one of the most iconic battlefield nuclear weapons, the M65 atomic cannon (you have possibly seen footage or photographs of its testing in 1953). The M65 could fire 280 mm atomic shells to 20 miles or so. The warhead used in the test footage, the W9 warhead, had an explosive yield of 15 kilotons —15,000 tons of TNT equivalent. That is enough explosive power to destroy a medium-sized city, take a chunk out of a major city's downtown area, or damage about 4 square miles anywhere else. As a tactical weapon in the 1950s, the goal would have been to take out Soviet tanks or troop formations, such as those imagined to be streaming through the Fulda Gap in the event of a Soviet invasion of Western Europe. 

But 15 kilotons is the same explosive power as the atomic bomb dropped on Hiroshima in 1945 with such devastating effect.  

From here (the numbers related to the Oklahoma City Bombing were corrected from the inaccurate text in the original without editorial indication in the text above).

The Hiroshima A-Bomb weighed 9,700 pounds (including 64 kg of Uranium-235) producing a 13-18 kiloton yield, and the Nagasaki A-Bomb weighed 10,300 pounds (including 6.2 kg of Plutonium-239) producing a 19-23 kiloton yield.

The estimated strength of the explosion at the Port of Beirut [in the year 2020] is 0.3-0.5 kt.

The final weapon was 10.862 inches (275.9 mm) in diameter, 15.716 inches (399.2 mm) in length and 50.9 pounds (23.1 kg) in weight, and was packaged in a fiberglass housing coated in a conductive lacquer to provide an electrical shield.

From Wikipedia. 

Of the 50.9 pounds of weight, depending upon the version, 26 pounds were high explosives,  3.5 pounds were plutonium, and 5.3 pounds were uranium. The high explosives were the detonator for the nuclear materials.

Wikipedia suggests that the yield was closer to 20 tons than to 10 tons of TNT stated above, which is at the high end of the yield of the most potent heavy bomber carried "bunker buster" bombs, which are the most powerful conventional explosive weapons in military use. 

Minor modifications of essentially the same bomb could have a yield as high as 1,000 tons of TNT, which would be 50 times more powerful.

This 50.9 pound nuclear bomb is about the same size as an infantry carried Javelin anti-tank missile or a Viper Strike small guided bomb for a jet fighter or a main battle tank shell. It is about twice the size of a 3 inch naval gun shell. It is about half the size of a Hellfire missile often carried by U.S. helicopter gunships and drones, or a 155mm howitzer shell, or a British Brimstone anti-tank missile.

But, this small nuclear bomb is roughly 800 times more potent than a conventional weapon of the same size, or alternatively, 800 times lighter than a conventional chemical explosive weapon with the same explosive punch. 

The range of historical nuclear weapon yields is summarized here. The most powerful nuclear weapon ever detonated was the the Soviet Tsar Bomba with a yield of 50,000,000 tons of TNT. The most powerful nuclear weapon every deployed by the U.S. military (among the so called "H-bombs") had a yield of 25,000,000 tons of TNT (the Mrk-41 B41 nuclear bomb which weighted 4800 kg), and until 1997 there were nuclear bombs with yields of up to 9,000,000 tons of TNT in the U.S. nuclear arsenal (the B53 nuclear bomb used on a Titan II missile). The most powerful nuclear weapon currently in U.S. service (the B83 nuclear bomb) has a yield of 1,200,000 tons of TNT. 

More typical nuclear warheads in U.S. service have yields of 100,000 tons (the M76 used on Trident II missiles in clusters of 8-12 warheads - with the lower number imposed by treaty), 300,000 tons (the M87 used on Peacekeeper missiles in clusters of 10 warheads), and 475,000 tons (the M88 used on Trident II missiles in clusters of 8-12 warheads - with the lower number imposed by treaty).

So, a single modern U.S. nuclear missile's combined warheads have 40 to more than 160 times the yield of the most powerful nuclear bomb used in World War II by the U.S., even without going beyond treaty limits.

Crudely speaking, the yield from eight to twelve warheads in a single nuclear missile is enough to destroy an entire major metropolitan area, as compared to a WWII A-bomb's ability to "destroy a medium-sized city, take a chunk out of a major city's downtown area, or damage about 4 square miles anywhere else."

It isn't clear how much smaller than 51 pounds a viable nuclear weapon could be made if a serious engineering effort were devoted to doing so. 

If yield could be scaled linearly (which is more optimistic than any really realistic assumption), you could obtain the yield of a Hellfire missile or 155mm howitzer shell, with sufficient punch to destroy a main battle tank, with a "nuclear grenade" of just 2-4 ounces, which would be bigger than a .50 caliber machine gun bullet but smaller than a 30mm cannon/grenade launcher round, and about the same as a 20mm-25mm cannon/grenade launcher round.