On a check swing, how far around must the bat go for it to be considered a swing???

Official baseball rules state that it is a swing "if the batter offers at the pitch." That leaves a lot up to interpretation. Over the years umpires have adopted their own meaning to this rule and it varies from umpire to umpire. One term commonly used is did the batter "break" his wrists, or in other words did the batters hands move (bend) from a fixed position? Others consider the front of the plate. If the bat crosses the "plain" of the plate it is a swing. End result, it is up to the judgement of the umpire, not a concrete rule.

It must cross home plate to be considered a swing

Half way or so... Just leave it up to the third base umpire.

It must pass home plate to be officially called a "strike." Even if only the tip passes it is still a strike.

it cant cross the plate

it has to pass the first base line if ur a righty, third base line if ur a lefty.

A check swing is half way across the plate any farther than its a strike

it cant go pass the foul line, thats why the third base or first base umpire has to call it

Last time I explain this -- there are guidelines but no steadfast "break-the-wrists,barrel-past-the-plate" stuff. Real simple -- Umpire's judgment as to whether or not it is a swing.

This is up to the judgement of the umpire. The plate umpire can make the call, or it can be appealed to the 1st base or 3rd base umpire, depending on the side of the plate in which the hitter is standing. That's because the call must be made by the umpire who is in the best position to see how far the batter allowed the bat head to go. Some umpires will judge by whether or not the bat head crossed the front of the plate.

However, because it's up to the judgement of the umpire, some will go by whether or not the batter "broke" his wrists during the swing. (This is one of the reasons that hitters must have strong wrists.)

Either way, the call can't be argued, or rather, can't be argued without person doing the arguing being ejected from the game..

There is nothing in the rule book that addresses this. In general, if the barrel of the bat goes beyond the batter, it's a swing.

No credible umpire buys into the "did the batter break his wrists" philosophy. If the batter broke his wrists, I'm stopping the game so the poor guy can get some medical help.