There was this guy that made a pumped hydro water tank on his roof and by his calculations a cubic meter of water was equivalent to a AA battery.

That sounds crazy. Let’s do some math. From what I can find, a double A battery contains about 10-14 kilojoules of energy. Let’s use 14 to be charitable.

A cubic meter of water weighs about 1000kg. We know the formula for potential gravitational energy U = mgh. So if we used all the energy from the battery, we could lift the water:

14000 = 1000 * 9.81 * h
h = 14000 / (1000 * 9.81) ≈ 1.43 meters (4 feet 8 inches)

That assumes 100% efficiency of course. Still, lifting a ton of water even two feet ain’t nothing to sneeze at. Batteries have a lot of energy.