How high can a player go?

Solution 1:

There is no limit to a player's height. The Y coordinate is tracked with the same size of variable as the X and Z, so you can go as infinitely* high as you can travel infinitely* far. There is no extra limitation placed on player height, so the only limitation is how to get there.

With cheats on, you can use /tp to experiment with how high you can go, and you can see your position by toggling on the debug screen with F3.

_{* Not actually infinite, but it takes many days of real time to walk that far.}

Solution 2:

The answer to your question can easily be found on the Minecraft wiki.

The maximum height (coordinates) a player can reach is displayed as "6.7108E7" (6.7E7 is 6.7 times 10^7th, or 67 million, approximately 2^26th)

Solution 3:

You can reach 1 quadrillion blocks. After that you will get kicked with the message "Illegal Stance".