An in-principle calculation demonstrating how little land is really needed
Renewable energy resources are more diffuse than concentrated fossil energy, requiring wind farms spread o’er many leagues, and array upon array of solar panels. But is this a fundamental barrier to employing renewables at scale, as some would have you believe? The answer is nay, and it can be quickly seen from some back-of-the-envelope calculations (and with the assistance of some pretty maps), that no more than 7,000 square miles of photovoltaic panel surface area would be needed to generate 100% of US electricity. This is less than 0.2% of the contiguous US land area, and a small fraction of urban area in the US.
This demand could be satisfied with existing rooftops and other impermeable surfaces, such as parking lots. And of course, no all-renewable portfolio would actually be 100% solar, but this exercise shows that land area is not a limiting factor in scaling solar.
To inform our calculations, let us first introduce some fundamentals concerning solar resources…
Commercially available solar panels now routinely convert 20% of the energy contained in sunlight into electricity, a truly remarkable feat of science and engineering, considering that it is theoretically impossible for silicon-based solar cells to be more than 32% efficient. This upper bound, known as the Shockley-Queisser Limit, was first calculated by the eponymous scientists (who actually gave 30% as their original limit) in the Journal of Applied Physics in 1961  (see also updates by Rühle ).
Now, if we can answer why solar panels are thus limited, we can understand the essentials of photovoltaics (PV), which have their basis in the photoelectric effect, and p-n semiconductor junctions. While many have never heard of it, the photoelectric effect is of monumental importance, and when Albert Einstein received the 1921 Nobel Prize in physics, it was “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect,” while p-n junctions lie at the foundations of modern electronics, including transistors and LEDs. Indeed, a solar cell is essentially an LED in reverse: Instead of an electric current generating light, light generates electric current!
I wrote several hundred pages of a book that amounted to exhorting people to alter their own habits of residential energy consumption (turn down the heat, you rogues!), as well as upgrade their built environment (e.g. insulate the attic) and appliances, or even, *gasp*, add solar to their roofs. All this because the numbers, at least in the abstract, showed that such banal acts of conservation (not counting solar) can reduce the carbon footprint of residential energy use by at least 30-50%, from a baseline average of about 12 metric tonnes (1 tonne = 1 metric ton) of CO$_2$-equivalent (CO$_2$e). But a demonstration of how, over the course of roughly 5 years, the net energy use in my house actually fell progressively from around 17,000 kWh of electricity per year down to less than zero (net) seems in order.