How many grams of explosive are equivalent to the energy in a battery?

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.

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 Li-Fe 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 Li-Fe one.