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Density of Air adjustment

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Hi all,

I've crunched some numbers using the formulas here.

Originally, I was optimistic about these numbers, until I double-checked them against another calculator here.

I'm confused. Is there a reason the wiki's calculation for power uses 1/2 the density of air, instead of the full density? I'm not claiming to be an expert or anything, but because of the substantial number difference I was getting I wanted to confirm. The second calculator also has a hard-coded slope, which will definitely affect the numbers as well.

Going to go back and run my numbers again making sure I didn't make a mistake.