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For atomic bombs especially, strength is often measured in tons, kilotons, megatons, gigatons.

A ton is a measure of weight (perhaps also force?), and the bomb definitely doesn't weigh in the megatons. I don't imagine $mass \times acceleration$ has much to do with the strength of a bomb, and any way I can come up with for this to be a measure of energy per distance seems shaky at best.

I've also heard a certain number of tons of TNT, which might make sense but I don't know if this is the same thing or just a common comparison, like saying a ship is as long as two football fields.

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    $\begingroup$ It is the mass of TNT needed to release the same amount of energy $\endgroup$ Commented Mar 6, 2017 at 19:40
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    $\begingroup$ was it so difficult to check wikipedia?en.wikipedia.org/wiki/TNT_equivalent $\endgroup$
    – user126422
    Commented Mar 6, 2017 at 19:41
  • $\begingroup$ "tons" ---> "tons of TNT equivalent" which is a convenient size for measuring medium-sized explosions, and something people were familiar with during World War II Then metric prefixes are added for properly big ones (100, 2050, and 500 pound bombs were commonplace bomber loadouts). $\endgroup$ Commented Mar 6, 2017 at 19:42
  • $\begingroup$ "A ton is a measure of weight" Note that weight is a force, measured in Newtons. Tons is a measure of mass. The everyday-use of the word "kg" as weight is not accurate. $\endgroup$
    – Steeven
    Commented Mar 6, 2017 at 19:45
  • $\begingroup$ @Steeven You'll find that in everyday language and in the law that applies to commercial transactions the distinction between force and mass is elided. To the point that for commercial purposes "kilogram" means what an engineer would call a "kilogram-force" (i.e. the weight of on kilogram-mass in a 1g field). $\endgroup$ Commented Mar 6, 2017 at 19:49

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As several of the commenters mentioned, what you are referring to is the TNT equivalent of that explosion. "One ton of TNT" is a unit of energy equal to 4.184 GJ. As its name suggests, that amount of energy is what is released by detonating a metric ton of TNT (1000kg).

One of the issues nuclear weapons face is that they are so extraordinarily powerful that normal human experience doesn't properly convey the damage they cause. Little Boy, the bomb dropped on Hiroshima, had a yield of 63GJ. That number just doesn't mean much to people. Orders of Magnitude (Energy) is one of my favorite sites for trying to capture the sheer magnitude of energies, and it suggests that the energy of Little Boy is equal to about the energy stored in six fully loaded Airbus A380s, but that still doesn't quite capture the explosive yield in an intuitive way.

Many bombs are measured by their mass or weight. We talk of 500 pound bombs or 2000 pound bombs. When we do, we typically talk about the mass or weight of the entire device (The MK84 was a 2000 pound bomb, but only 954 pounds of that was Tritonal explosives), but it seems like a reasonable way to get the sheer magnitude across to people who are used to dealing with such bombs. When we phrase the 63GJ of energy as "15kT of TNT," or perhaps more magnificently as "15,000,000 kg of TNT equivalent," those who are used to dropping 500kg and 1000kg bombs take notice and give it proper respect.

Of course, like any communication approach, the term has been shortened. Instead of saying "15 kilotons of TNT equivalent," we've gotten used to measuring our nuclear weapons units like that and shorten it to "15 kilotons."

The TNT equivalent turns out to be a rather effective tool. For instance, we can capture the raw power of modern thermonuclear weapons in a human accessible form. Little Boy was a 15kT(0.015MT) bomb, and Fat Man was a 20kT(0.020MT) bomb. The whole sum of ordinance dropped in WWII is estimated to be around 3000kT (3.0MT), which gives you a sense of just how much we dropped during the war. Know modern thermonuclear weapons are in the 25,000-100,000kT (20-100MT) range!

It also extrapolates frighteningly for non-man-made circumstances. While the largest tested nuclear weapon, Tsar Bomba, topped out at 100MT, and total worldwide nuclear testing has set off perhaps 540MT of nuclear energy, they pale to that of natural forces. The Chicxulub impact, believed to be the cause of the extinction of the dinosaurs 60 million years ago was estimated at 10,000,000MT of force.

Just goes to show how small we really are in the greater scheme of things.

A "fair units" chart showing all of these numbers in the same
units: megatons of TNT equivalent (MT).
        MT        Event
----------------  ------------
        0.000206  MK-84 (nicknamed "Hammer" by F-117 pilots)
        0.015     Little Boy
        0.020     Fat Man
        3.        All WWII ordinance
       25.        US thermonuclear weapon from Cold War Era
      100.        Tsar Bomba (theoretical maximum)
      540.        Sum of all nuclear tests ever undertaken
100000000.        Chicxulub impact
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