Minecraft operates on a grid of three coordinates: X, Y, and Z, with the Y-coordinate taking account of the position of something vertically, also known as altitude.
In Minecraft terms, altitude is measured based on the bottom face of a particular block layer. Currently, the lowest possible block layer is Y=0, though this will be changing with the introduction of the Deep Dark biome in the Caves & Cliffs Part 2 update for Minecraft: Java and Bedrock Editions, which will change the lowest layer to Y=-64. In these same versions, the top-facing height limit is currently Y=256.
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Height in Minecraft: More info on altitude and the Y-coordinate
In reality, Minecraft's sky and height continue to generate well past its limit, but these areas are inaccessible to players in the vanilla build of the game. The game generates sky space roughly until it hits a block level of 2^1024 (180 uncentillion), which is the largest height Minecraft's code can distinguish from infinity. There are also theoretical spaces underground as far as -30,000,000.
Physical features of each layer of the Overworld dimension in Minecraft are generated by altitude. Each of these features are given a specific range that they are permitted to generate within. For example, stone blocks are only able to generate between Y layers 1 and 132 if being distributed normally. This accounts in limited capacity for blocks in the Nether and the End dimensions in Minecraft as well, though the limits of block generation differ, as many players are aware that there is a wide open space above the "roof" of the Nether for example, where Netherrack blocks cease to generate but air still does.
The height limit has changed over time and has grown along with Minecraft, being limited to a maximum positive Y-height of 64 blocks in the classic version of Minecraft: Java Edition. Early versions of Pocket Edition were also limited to 127 blocks before being doubled during the Alpha stage of development. Bedrock Edition, however, released in Beta with a standard 255 block height limit, but is extendable to as high as 319 blocks due to the experimental gameplay toggle which is available on the platform.
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