https://en.wikipedia.org/wiki/Energy_density_Extended_Refere... lists "battery, Lithium ion" as 0.46–0.72 MJ/kg.

: user@host:~; units
2529 units, 72 prefixes, 56 nonlinear units

You have: 40 kg * 0.6 MJ/kg
You want: MJ
* 24
/ 0.041666667

(The 13.5 kWh in 114 kg tyingq cites for a Powerwall 2 in https://news.ycombinator.com/item?id=26682770 works out to 0.43 MJ/kg, which includes some power electronics as well as the batteries themselves. The US$12500 price ghaff cites in https://news.ycombinator.com/item?id=26682837 works out to under 4 kJ/US$, or US$925/kWh, which is a terribly high price even for lithium-ion.)

24 MJ would be 1 MJ/hour for 24 hours, or 3 MJ/hour for 8 hours, about 300 or 800 watts, respectively. Some houses use much more than that; others use much less. If you're looking at your electric bill, 500 watts would be about 370 kWh per month:

You have: 500 watts * 1 month
You want: kWh
* 365.2422
/ 0.0027379093

40 kg of lithium-ion batteries are indeed roughly the size of a backpack (≈20 liters), though I wouldn't call it a small backpack. Around here, the retail price for the batteries would probably be closer to US$2400 retail than the less than US$2000 they cite, but that's not an error in their calculations; it's just that they're using a lower price of US$140/kWh.

The article claims that in the early 01990s this quantity of batteries would have cost US$75k. I'm pretty sure this is wrong. This quantity of lithium-ion batteries might have cost US$75k, but even today lead-acid batteries cost half what lithium-ion batteries do.

I don't think the price of lead-acid batteries has changed that much over the last 25 or even 50 years, though admittedly I don't have any 30-year-old battery catalogs to check pricing in. Lithium-ion batteries in the 01990s would have weighed only a little more than lithium-ion batteries today, so it looks like they're using the pricing of lithium-ion batteries and the weight of lead-acid batteries.

If you're powering your house from batteries, you should probably do it with lead-acid batteries, not lithium-ion batteries. The big disadvantage of lead-acid batteries is that they weigh roughly three times what lithium-ion batteries do (per joule), so lead-acid electric cars had roughly a third the range of lithium-ion electric cars. But the weight is not enough to matter for a house.

There is enough lithium in Earth's crust to power the world economy through the night. There is, I think, not enough lead. So although lead is currently cheaper, lithium is more scalable. Other less developed candidate options include sodium batteries and aluminum fuel cells.

Nickel-iron batteries might be even cheaper, though I'm not sure, and they're definitely more scalable. Nobody sells them anymore, though lots of telecom centers still run on them.

It's unfortunate that the article cites a power capacity, "1.2 gigawatts-worth of storage", but not an energy capacity, for the US's utility-scale storage rampup last year. 1.2 gigawatts for five minutes would be 100 MWh, in the quaint units used in the energy markets; 1.2 gigawatts for 12 hours would be 14'400 MWh. There is a very significant difference between these; one requires 144 times as much battery behind it than the other. By contrast, the difference between 100 MWh over 5 minutes (1.2 gigawatts) and 100 MWh over 12 hours (0.008 gigawatts) is mostly a matter of what shape the batteries are and how much active cooling is needed. One wonders if this is not simply an error because the author did not know the difference between gigawatts and gigawatt-hours.