# Can 140 square miles of solar panels power the US?

In the book The Upcycle (copyright 2013) by William McDonough and Michael Braungart, the authors make the following claim:

... consider exactly how much desert area covered in solar collectors would be required to power the entire United States: 140 square miles.

Is it possible to reproduce these numbers?

As a starting point, the net summer capacity in the US in 2014 was 1,068,422.2 MW, according to the EIA.

Converting square miles to square meters, this means each square meter would need to produce 2,946.6 W/m^2.

Considering the amount of sunlight hitting the earth at the top of the atmosphere is 1,367 W/m^2 (source), we have a problem.

As this is obviously a hypothetical exercise, we're not concerned with the logistics of building such an array, transmitting the power, or what to do at night. At the very least, the system should either match the total annual electricity consumption of the US (3,724,867,821 MWh in 2013), or the peak demand (listed above).

### Summary

No, that's way too little. I think "140 miles square" has got mangled into "140 square miles".

### Running the numbers

Following on from one of Elon Musk's presentations, which showed an area of about 10,000 km2 as the area of PV panels needed to power the USA, the question came up on the Skeptics Stack Exchange.

Taking the numbers from this fact-checking of Elon Musk's blue square - how much solar to power the US: US electricity consumption is about 425 GW. And 10,000 km2 of the best currently-commercially-available PV panels would give about 500 GW of mean electricity. Now, that's putting aside time-matching supply and demand, transmission losses, and so on: it's just looking at multi-year average supply and multi-year average demand.

Now, allowing for a ratio of about 2.5:1 for the actual amount of land spanned by such an installation would mean about 25,000 km2 of land spanned. (because one doesn't blanket-cover a desert area without gaps, as that wouldn't be the most economical physical arrangement)

The difference between this 25,000 km2 and the claim is pretty huge: 140 square miles is 362 km2.

### How did this error happen?

I've seen errors of this scale before. In all the other cases — and so, I'm guessing, in this case — an editor or non-technical author has taken a technical source, and swapped the order of two words: the distance unit and the "square", and in doing so has completely mangled the meaning. So "metres square" becomes "square metres"; or "km square" becomes "square km"; or "miles square" becomes "square miles". It's an easy editing mistake to make: "square miles" is much more common than "miles square", and to a non-technical editor or author, they might sound like different ways of saying the same thing (even though they are completely different in reality). And so the editor/author does their job and replaces an unusual variant with its much more common supposed synonym, unwittingly transforming the meaning.

If the claim had been that an area of 140 miles square of PV could power the USA, then that would be entirely reasonable: that would be about 50,000 km2, which is a conservative over-estimate of the area needed. So I think "140 miles square" has got mangled into "140 square miles". (the former is 140 times the area of the latter)

### What does it mean to say "it would power the US"?

These claims of "X resource needed to power Y" are usually about mean (average) supply and mean demand, and that's typically a one-year or multi-year average. This is equivalent to saying that total production over the period would be at least as much as total consumption over the same period. The estimates aren't done to present a completely specified working system; but to give an idea of the scale of resource needed.

Occasionally, the context makes it clear if it is about a much more sophisticated bit of modelling, typically a dispatch model, that is matching supply and demand in each timeslice (e.g. every half-hour for a year). Even then, it's not about peak capacity equalling peak demand, but about half-hourly supply meeting or exceeding half-hourly demand. (Peak capacity is rarely an interesting or relevant number for modern generation systems; whereas for dirty old systems, it was indeed a standard metric.)

• On the typo, I think you're exactly right - right after the sentence I quoted, they describe taking an eight hour journey to drive around the field. However, I've got a bit of an issue with the 425GW number - dividing consumption by the hours in a year doesn't really give you the correct number for capacity.
– LShaver
Oct 6 '16 at 14:17
• Yes, the math is correct, but not the method - I would argue you'd need to be able to match the peak demand (the 1,068 GW number I quoted), not the average demand. To make a fair comparison, the system should either match the peak demand, or the total consumption - not the averages. Perhaps this deserves its own question.
– LShaver
Oct 6 '16 at 14:23
• @LShaver I've updated my answer to clarify things raised in comments. So thanks for those comments: they've helped me see where I needed to provide more explanation. Oct 7 '16 at 5:10