Does anyone know what percentage of the world can use solar power?

Of the world? Or of land masses with people on it?

100% of the world is capable of using solar power to some extent, as there is no place on earth that is totally devoid of solar radiation.

But to make it economically attractive, you need to consider seasonal variations in sunlight, weather patterns, distance to load centers, and local alternative energy sources.

For example, nobody is going to build a solar power generating facility in Ketchikan, Alaska where there is cloud cover for over half the year, there are short daylight hours due to its northern latitude, and there is ample opportunity for green run of river hydro. On the other hand, Yuma, Arizona is a good candidate for solar energy because its sunny there more than 300 days per year, there is not much seasonal variation in daylight hours, and the sun is high enough on the horizon year round.

Keep in mind that solar energy will never replace established emission-free firm energy sources like hydro and nuclear because you can't store the energy efficiently for use at night time – when you need the electricity the most!