smallest paddock for humane rotational grazing

hi just trying to get an idea of what yall thing would be the smallest humane size paddock for rotational grazing my 5 Dexter cows I am not talking about carying capacity but how much room they need to stretch out go for a run ect it you were doing moves 20 times a day and had really great grass a paddock the size of there body would probably work in terms of feed but this would be too cramped to be humane

Based on my own experimentation with sheep I'm going to say 3-4 times their body length in both dimensions [length and width] can be fine depending on the personality of the breed and the individual. For many ruminants [beyond the first few months of age when they actually play] running is less a desire and more just an emergency panic button. Plenty of food and a bit of room to stretch out and shuffle around seemed to make my sheep happy.

For five dexter cattle I definitely wouldn't make the pen less than 20x20 [400 square feet], but I feel somewhere between that and 900 sq. ft. [minimum 20 feet in any dimension] might suffice if forage was plentiful unless you've got a rambunctious one or there's conflict in the herd and somebody needs to be able to get away.

NOTE: this is pure conjecture based on the behavior of sheep, I have no direct experience with cattle yet [but I'm looking to get into them, and Dexter are the breed I'm most interested in at this point.]

I think the proper way to look at the question of "humane" is ensuring that a paddock is large enough to provide the cows enough forage for the time they're in it.  Most likely, the point at which a given paddock is too small to be considered humane in regards to space is going to require such frequent moves (as in, many multiple times per day) as to be untenable anyway.  To put it in concrete terms, if you move the cows no more than four times per day (and on a good, highly diverse farm, you certainly have better things to do than move them even that often), the paddock size for each move ought to give them plenty of space to move about.

Paddock shape comes into play, too.  A long, rectangular paddock gives them a bit more room to stretch their legs than a square one of the same square footage.

Other factors might include whether or not you want to give the girls space to run (and adult cows do like to run on occasion, and not necessarily as a fear response), whether they have access to sufficient shade, etc.