Answer: a lot.
According to the Energy Information Agency, the planet uses 500 quadrillion btus of energy every year, and that number is expected to rise to 678 quadrillion in twenty years. Starting with those figures, and then a lot of back-of-an-envelope math, Land Art Generator Initiative has mapped the surface area required to provide the entire planet’s energy from the sun in 2030. They also did one for off-shore wind generation.
The end calculation was 191,817 square miles (496,805 square km) of land for solar panels, spread around the world. For wind it comes to 11,748,294 5 MW capacity turbines covering 5874147 square miles off-shore.
More Silly Math
The problem with these sorts of rough estimates is just how rough they are. As numerous comments point out, Land Art’s figures do not take into account power loss through transmission, or other inefficiencies. One way to check their math is to look at actual projects on the ground and see how they measure up to the figures being bandied about.
First Solar just inked a deal to build a 2 gigawatt plant in Inner Mongolia covering 25 square miles, or 36 million square meters. Land Art’s estimate requires 200 watts generation per square meter, but First Solar is only getting about 56 watts per meter, fully installed. Granted, First Solar’s panels are lower efficiency, around 10%. But even if you double that to 20%, you still get barely half the capacity, 112 watts per meter, that Land Art uses for its estimates (200 watts/.2 kilowatts per sq. meter).
So according to my back-of-the-back-of-the-envelope math, based on current fully-installed standards, you’d have to double the land needed from Land Art’s estimate.
And as for cost, if built in the States, the Mongolia plant would cost about $5.5 billion, or $2.75 a watt. Based on Land Art’s estimate of 99 trillion watts of capacity needed, that’s $273 trillion worth of panels. And First Solar’s panels are actually cheaper than most. Residential installations are around $7 a watt.
That’s a lot of money. Maybe we’d be better off getting our power from space.