Minecraft Sphere Generator

How the layers are worked out

The sphere is a cube of D × D × D blocks. A block belongs to the sphere when its centre is no further from the middle of the cube than half the diameter; a block exactly on that distance is included. In integer terms: (2i + 1 − D)² + (2k + 1 − D)² + (2j + 1 − D)² ≤ D², where i and j run across and k runs up.

Cut the sphere into horizontal slices and each slice is a disc, the same rule as the circle generator but with a smaller radius as you move away from the middle. Layer 1 is the bottom. Drag the layer slider to see each slice and its row readout.

Hollow or solid

Solid counts every block inside. Hollow keeps only the blocks that touch empty space on at least one of their six faces, which leaves a shell one block thick.

A small check you can do by hand: diameter 3 solid has layers of 5, 9 and 5 blocks, 19 in total. Hollow removes the single block in the middle, leaving 5, 8 and 5, which is 18.

Reading the result

Build from the bottom layer up, using the row readout for each layer. The per-layer list gives the block count for each slice, which is useful for checking your work as you go. For half a sphere, use the dome generator. To turn the total into stacks of other sizes, or into chests, use the stack calculator.

Most placeable blocks stack to 64, and some items differ (Minecraft Wiki). A voxel grid only approximates a sphere, so the shape is the nearest set of whole blocks under this rule.

Questions

What is the largest size?

Diameter 101. Larger spheres are a lot of blocks, and the layer view stays readable up to that size.

Is layer 1 the top or the bottom?

The bottom. Layers count upward.

Not an official Minecraft product, and not affiliated with Mojang or Microsoft. See also the circle chart.