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The sun is: 6300 W/cm^2

> inside of a nuclear reactor

Inside means volume? That's not the same unit, so I'm not really sure how to calculate that.

Interestingly, on a per-volume bases, the sun's output is quite low. The sun is just very very large.

And you find the sun is only: 1.383×10^-6 horsepowers per gallon :) Or if you insist: 0.2725 W/m^3, which as you can see is really really low.