How do you compute the coordinates of antipodes?

Factual Questions
1

There has been talk about antipodes recently on the Straight Dope, which makes me wonder how to compute the geographic coordinates of the antipodal point to a given point. There must be a way to compute it, but I’m not sure how.

Reactivating my geometry (it seems to be more of a geometry than a geography question) from school, I figure that you get the latitude of the antipodal point by replacing degrees north of the equator with the same number of degrees south, and vice versa.

It seems to be more complicated with longitude. My WAG would be to change degrees east of Greenwich (or any other meridian chosen as starting point) to degrees west of Greenwhich, and vice versa; but in addition, you have to subtract the number of degrees from 180.

To give an example: If you have a place located at 41° 54’ N, 87° 39’ W (that’s Chicago), the antipodes would be at 41° 54’ S, 92° 21’ ( = 180° - 87° 39’) E.

Am I correct with that, or what is the correct algorithm for computing the antipodes?

2

Yes, you are correct.

ETA: There’s an antipodal map here.

3

Stupid boring southern Hemisphere. Looks Like I would pretty much have to drive to Medicine Hat to dig a hole all the way through the earth.

4

That’s short, but it sums up pretty much all I wanted to know. Thanks!