I'm trying to calculate the amount of power from the sun hitting the earth, but I am getting a number which is off by a factor of ~4.

I calculate the "area" of the earth, as seen from the sun, and then divide that by the surface area of a sphere of radius 1 AU, to get the portion of the sun's rays we absorb, and then I multiply that by the solar luminosity. 

Mathematica gives me this:


![\text{UnitConvert}\left\[\frac{\pi  \text{Quantity}\[\text{AstronomicalData}\[\text{Earth},\text{Diameter}\],\text{m}\]^2}{4 \pi  \text{Quantity}\[1,\text{astronomocal units}\]^2} \text{L}_{\odot },\text{W}\right\]][1]

But when I [put it into Wolfram|alpha][2], I get this result:

![4 x mean solar power intercepted by earth][3]

Am I doing something wrong? where could that big an error be introduced? Is "mean power intercepted by earth" different than what I'm calculating?


  [1]: https://i.sstatic.net/516fe.png
  [2]: http://www.wolframalpha.com/input/?i=697%20PW
  [3]: https://i.sstatic.net/ve0BK.png