Of the 38x10^13 TW of sunlight power flowing out in all directions from our Sun, only half a billionth of it meets the Earth - that number comes the area ratio involved: pi times Earth's radius squared, divided by 4 pi the Earth-Sun distance squared; with Earth's radius of 6370 km and the Earth-Sun distance about 150 million km the number is 4.5x10^-10. Total solar power intercepting Earth is the simple multiple: about 170,000 TW, or 13,000 times total present world energy use.
This incoming energy drives Earth's weather and provides energy directly or indirectly for almost all living things. Of the total, about 50,000 TW is reflected from Earth's clouds or surface. About 80,000 TW is absorbed and heats the surface and atmosphere directly. The remaining 40,000 TW of incoming solar energy evaporates water; we capture just a tiny part of that water cycle in our hydroelectric dams.
Barring solar collectors high in the atmosphere (or in space (1)) only the 120,000 TW that reaches the surface is really accessible. That amounts to a net power input of close to 1 kW/m^2 - but only for a surface directly under the sun, perpendicular to the Earth-sun angle. Averaged over the entire surface and the day-night cycle the solar power input to a square meter on Earth's surface is just 250 W on average.
One problem for solar and other renewable forms is their diffuse nature. With typical modules only about 15% efficient, 250 W coming in means an average of less than 40 W output per square meter. To produce 13 TW entirely from solar power would require capturing the energy input to 325,000 square km of Earth's average surface.
We can do a little better than that by choosing ideal locations. Also keep in mind the output is electricity, which is almost entirely available for useful work. Most primary energy use is converted to useful work at a much lower rate, about 35% for example for coal-fired electric plants, so to supply present human needs from solar PV power could perhaps be done with just 5 TW of electric power, or 125,000 km^2.
This may still seem like a huge number, but to put it into perspective the US now has an "impervious surface area" (paved roads, parking lots, buildings, etc.) of slightly over 100,000 km^2 (2). Paving that same area with solar panels could power the whole world. It's well within our physical capabilities - the economic issues are of course another question, which we hope to address in another brief article here.
(1) Arthur Smith, "Earth vs. Space for Solar Energy, Round Two", Physics and Society, April 2004
(2) C.D. Elvidge et al, "U.S. Constructed Area Approaches the Size of Ohio", EOS Trans. AGU 85, 233 (2004)