park tool site has two methods that will work for me.

1.) going big ring to big ring and and adding an inch

2.) using a mathematical equation to figure out the overall length

I cannot use the old chain as I have swapped out the cassette and crank for a different size.

So which of these methods (or post others) is the standard by which chains are sized properly?

The second is to predict how much chain you'll need, but you always confirm by direct measurement when fitting.

Note that the big/big plus 1" measurement is the minimum length. Campagnolo uses a different method, small/small with all slack out and the RD cage under minimum tension, which yields the longest chain possible. OTOH, Shimano uses a third method based on cage angle which yields a mid length chain. Note that if the gear combination uses the full take-up capacity of the RD, the minimum, maximum, and mid-length will all be the same.

If I have the option of a longer than minimum length chain (excess RD take up capacity) I prefer fitting a longer chain, so that down the road, I may remove a damaged link without replacing the chain.

^^^ This. As FB noted the second method just gives you a good approximation but the first method assures the chain will shift into big-big without damage.

Campy's small-small with no slack works fine if you stay within the rear derailleur's "wrap" limits. If you exceed them, as I often do, you can make the chain too short to allow the absolutely necessary ability to shift into big-big.

I'm a big/big fan but not so much that I argue with folks who use one of the other methods.

+1

I'm a big/big + 1 full link fan, but recently used the small/small derailleur slack method to set the length for a derailleur swap. The new one had a shorter cage and different dimensions. I wound up going 1 link shorter than the big/big method would've dictated. It permitted the new derailleur to work best.

I definitely must avoid cross chain extremes with this setup, though.

Now I am going to argue.

The beauty of the big/big method is it produces the shortest chain that will safely cover the big/big combination. That's important. If your chain is shorter than that, and you ever accidentally shift into the big/big, you can do serious damage to your bike in less time than it took me to type this sentence.

+1

The big/big +1" produces the MINIMUM chain length. If you're running a derailleur with excess wrap capacity, you can always go longer (as I do), but you can never go shorter. Over the years I've known too many knowledgeable riders who run derailleurs over capacity, and opted to pinch at the short end. Famous last words for drivetrains and rear hubs are "I never cross chain anyway".

If you run a derailleur over capacity pinch at the long end. The worst that can happen is you shift to small/small and the chain hangs down like a pregnant possum's belly. But nothing will break.

This statement should be posted as a "stricky" on top of this forum with a bold, capitalized READ THIS before it. It is by far the best statement of why big-big is the absolute minimum chain length anyone should ever use.