Crank length
 

Inseam cm x 1.25 + 65 = really?

No. Not really.

There is a range of crank sizes that will work for someone. I prefer just making a straight percentage calculation in a range from x 0.19 which is short to 0.216 which is quite long. If you want to ride in an aero position then shorter is better. You would have to be a freak to be able to get a good aero position with x 0.216 cranks yet apparently it works for some.

The longer the cranks, the lower the saddle. But, also the more risk of encroaching on the belly.

In general I'm happy with a bit longer cranks, but despite more leverage, the longer rotation circle means there is no free energy.

I use inseam in inches X 5.5. Seems to work well except for very tall riders where standard BB heights won't allow proper crank lengths.

Formula above has me on 166.8mm. I have been reading* about longer cranks increasing sheer forces on the knee, and advantages of opening up the hip angle w/shorter cranks.
I think there may also be some benefits w/above as it relates to aging.
Am putting 170's on my rides. Not a big diff from 172.5 on the rd bike but substantive coming from 175 on the mtn. bike.

* https://bikedynamics.co.uk/FitGuidecranks.htm

What's on your bike right now? Do they bother you? Crank length calculations are bunk. You power output and cadence and riding conditions will determine what length of crank you might like.

Really? So someone 5'2" should be riding 177.5's?
I've had knee issues long ago due to overuse and not stretching and more recently job related imobility stuff but going into retirement and now having the time to ride every day I figure anything I can do to minimize wear and tear on body is a no brainer.

Well, Pantani at 5'8" did ride 180mm in the mountains, but we might allow that he's a special case. I have a 6'7" riding buddy who rides 175mm, so it is to some extent all over the place. But most folks find that 5.5 formula I posted is good. By that formula, my wife rides 151mm and likes that. I ride 170 and 175 and don't notice the difference. The formula says 165 for me.

No.

No matter what the height or inseam a person has, they should ride the crank length that gives them what they want.

I'd be on 174.5 mm cranks in your formula. Several years ago I tried to run 170 mm cranks but had an annoyance behind the back side of my knee. Tried real hard to like them for 4 full months but finally swapped back to the 165 mm cranks I seem to do best on. Every time I get on a bike with longer cranks I feel like I'm thrashing about and get tired quickly if nothing else.

I've got a 87.6 cm inseam.

At best, formulas for crank length might tell you the most length you should consider. But not what you should get or start at.

5' 2" with a 90 cm inseam? Wow.

I personally like a little longer cranks. And believe that I'm happier with my legs going through a full and open movement rather than spinning in tiny circles.

The more riding I do, the better the knees feel. And, I've had times when I had been off the bike for a bit, and on the feet too much. And, a 10+ mile ride was vital for recuperation.

But, everything within reason. So your hypothetical 5'2 rider should probably be looking at much shorter cranks than someone 5'10, or > 6'.

Nonetheless, there may not be a formula that would take any rider and give their exact specs.

Perhaps there would also be some training the body to one's own bike.

So, say a bike fitter does a bunch of test on two younger 5'10" newbies, and decided 165 gave peak power for both of them. But, instead, they're sent home with one set of 157 cranks, and the other with 180 cranks. Send them out to ride 5000 miles. Then retest for power output. Will the tests all show the different riders still need the 165 cranks, or will they have habituated to what was on their bike? My guess is the riders would tend towards what they were training with.