How many grams of explosive are equivalent to the energy in a battery?
Solution 1
One alkaline AA cell has about $11\,\rm kJ$ of energy. For a laptop battery, it is $360\,\rm kJ$. Chevrolet Equinox fuel cell has $58\,\rm MJ$ of energy.
One kilogram of TNT carries about $4.184\,\rm MJ$ of energy. Divide the numbers from the previous paragraph by this constant to see that the AA cell, laptop battery, and electric car battery have $2.6\,\rm g$, $86\,\rm g$, or $14\,\rm kg$ of TNT. Note that TNT usually releases all the energy abruptly.
Gunpowder has $3\,\rm MJ/kg$ or so. It means you have to add about $35\%$ to get the right estimate for the mass of equivalent gunpowder.
If you could release the energy from the batteries very quickly, the explosion could be equally devastating as the corresponding gunpowder and TNT except that batteries can't release energy this quickly.
Solution 2
A battery's energy capacity is normally quoted in Amp hour, (or $\rm mAh$) the number of amps it could (in theory) supply for an hour. If you multiply this by the voltage you get energy.
Specifically, if you multiply by $3600$ seconds in an hour you get Joules.
A NiMH rechargable AA cell is about $2200\,\rm mAh$ and is $1.2\,\rm V$:
$$2200\,\mathrm{mA} \cdot 3600\,\mathrm{s} \cdot 1.2\,\mathrm{V} = 9.5\,\mathrm{kJ}$$
A LiFe 3.7v cell is about 3x more energy.
According to wikipedia a classic hand grenade contains 50g of TNT. Since TNT contains about 4KJ/g this is an energy content of 200KJ. So a grenade contains 20x as much energy as a regular AA cell or 7x as much as LiFe one.
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Gnubie
Updated on December 28, 2020Comments

Gnubie almost 3 years
In the movie Terminator 3: Rise of the Machines, Arnie's fuel cells were twice shown to be extremely devastating when their stored energy was released.
In real life, how many grams of, say, gunpowder or TNT are equivalent to the energy stored in
 An AA alkaline battery
 A laptop battery
 An electric car battery
Would the batteries be as devastating as the explosives if the energy could be released all at once (within milliseconds, say)? Presumably the power of chemical explosives come from the volume of gas they release...

Alan Rominger about 11 yearsOne AA battery doesn't have 11 kJ. They differ in real life, but for retail alkaline AA batteries, we're talking about 2.2 to 4.8 kJ.

LuboÅ¡ Motl about 11 yearsDear alan, click at my 11kJ  I provided a source for my claim, unlike you.

John Rennie about 11 yearsen.wikipedia.org/wiki/AA_battery#Chemistry_and_capacity. Capacities are rather variable but LuboÅ¡'s value of 11kJ for an AA alkaline battery seems about right.

Alan Rominger about 11 yearsSorry, the 11 kJ would be in the range of Alkaline or LiFeS2 batteries as per Wikipedia en.wikipedia.org/wiki/AA_battery. The link given for the 11 kJ, however, gives me 2223 kJ for all of the mouse models by multiplying (J/day)*(months*31).

mmc about 11 years@AlanSE At the footer of the first page it says: "*Avg energy in 1 AA Alkaline cell approx. 11KJ".

Cees Timmerman almost 9 yearsNice, but you left out the explosives.