A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth. The sun has a energy output of around 4e26 W, of which most would be available to do useful work.
The original proposal simply assumed there would be enough solar collectors around the star to absorb the starlight, not that they would form a continuous shell. Rather, the shell would consist of independently orbiting structures, around a million kilometres thick and containing more than 1e5 objects. But various science fiction authors seem to have misinterpreted the concept to mean a solid shell enclosing the star, usually having an inhabitable surface on the inside, and this idea was so compelling that it has been the main use of the term in science fiction. The earliest appearance of this version seems to be Robert Silverberg's novel _Across a Billion Years_.
A third kind of shell would be very thin and non-rotating, held up by the radiation pressure of the sun. It would consist of statites. Essentially it is a "dyson bubble", where reflecting sails reflect light onto collectors for use in external habitats. Its mass would be very smalll, on the order of a small moon or large asteroid.
- Anders Sandberg from
the Dyson Spheres FAQ
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