Most people build a Minecraft sphere as a stack of circles: work out how wide each layer is, draw that circle's outline, move up one block, repeat. It looks right from the side. Then you fly over the top and see straight into it.
We build PixelCircles, a browser tool that plans Minecraft circles, spheres and domes block by block. This post shows where those holes come from, how many there are, and the one rule that closes all of them. The code is simplified from the site's source, and every number below came from running it.
1. A sphere is a stack of discs
Start with a solid sphere d blocks wide. A block belongs to it when the centre of that block is inside the sphere. Cut it into horizontal layers and each layer is a filled disc. For a 21-wide sphere, the discs are these widths from the bottom up:
7 11 13 15 17 19 19 21 21 21 21 21 21 21 19 19 17 15 13 11 7
Filled, that is 4,945 blocks.
Look at the ends of that list. The middle layers change width by 0 or 2 blocks per layer. Near the top and bottom the jumps get bigger: 7 to 11 is 4 blocks. That jump is where the trouble starts.
2. The obvious hollow sphere: outline each layer
The natural next step is to take each disc and keep only its outline, the same way you would draw a hollow circle:
// outline() keeps a cell when one of its four side neighbours is empty.
const naive = solid.map((layer) => outline(layer, 'thin'));
For a 21-wide sphere this uses 944 blocks. Here is the top layer it produces, a 7-wide disc:
per-layer outline what the top should be
..###.. ..###..
.#...#. .#####.
#.....# #######
#.....# #######
#.....# #######
.#...#. .#####.
..###.. ..###..
The top layer is a ring, so the sphere has a hole in the roof. The same happens one layer down: the 11-wide layer under it is also a thin ring, and its inside is covered only where the ring of the 7-wide layer happens to sit above it.
To count the damage, we looked straight down each column and asked whether you reach the inside of the sphere before you hit a block. On a 21-wide sphere, 69 columns are open from above, and the bottom is a mirror image with another 69.
3. Thicker outlines don't fix it
The next idea is a thick outline per layer: also keep cells with an empty diagonal neighbour. That adds blocks but still leaves holes, because it only looks inside the layer.
| Width | Filled | Per-layer thin | Open columns | Per-layer thick | Open columns | Six-neighbour | Open columns |
|---|---|---|---|---|---|---|---|
| 11 | 739 | 252 | 13 | 344 | 5 | 278 | 0 |
| 15 | 1,791 | 464 | 33 | 648 | 21 | 530 | 0 |
| 21 | 4,945 | 944 | 69 | 1,312 | 33 | 1,082 | 0 |
| 31 | 15,515 | 2,060 | 161 | 2,872 | 85 | 2,382 | 0 |
| 51 | 69,599 | 5,704 | 469 | 7,960 | 281 | 6,642 | 0 |
| 101 | 540,113 | 22,508 | 1,917 | 31,680 | 1,153 | 26,342 | 0 |
"Open columns" counts only from above; the bottom has the same number again. The thick version uses more blocks than the fix in the last column and still leaks.
4. The fix: check the layers above and below
A block is part of the wall when it is inside the sphere and at least one of its six face neighbours is outside: left, right, front, back, above and below. It is hollow only when all six neighbours are inside.
// solid[z][y][x] is the filled sphere, layer z from the bottom.
const at = (x, y, z) => (solid[z]?.[y]?.[x] ? 1 : 0);
const wall = (x, y, z) => at(x, y, z) && !(
at(x + 1, y, z) && at(x - 1, y, z) &&
at(x, y + 1, z) && at(x, y - 1, z) &&
at(x, y, z + 1) && at(x, y, z - 1)
);
We checked this short version against the site's engine for widths 11, 15, 20, 21, 31 and 51. It gives the same blocks in every layer.
The two extra checks do the work at the poles. The centre of the top layer has air above it, so it becomes wall and the cap closes. On the layer below, a cell that sits under air (outside the 7-wide cap) becomes wall too, so that layer gets a wider rim:
layer 20, per-layer layer 20, six-neighbour
...#####... ...#####...
..#.....#.. ..#######..
.#.......#. .###...###.
#.........# ###.....###
#.........# ##.......##
#.........# ##.......##
#.........# ##.......##
#.........# ###.....###
.#.......#. .###...###.
..#.....#.. ..#######..
...#####... ...#####...
Per layer on the 21-wide sphere, the difference sits only in the first and last four layers: 16 → 37 blocks at the very bottom, 28 → 60, 36 → 48 and 44 → 48, and the same at the top. Every layer from the 5th to the 17th is identical in both methods. In total the watertight sphere is 1,082 blocks, 138 more than the leaky one.
5. Thicker walls
For a wall two or three blocks thick, run the same test against a second sphere that is one block smaller in radius per extra block of thickness. A cell is hollow only when it is inside that smaller sphere and so are all six of its neighbours. The smaller sphere's own outer skin stays in the wall, so the wall stays sealed at every thickness. For the 21-wide sphere:
- 1 block thick: 1,082 blocks
- 2 blocks thick: 2,144 blocks
- 3 blocks thick: 3,082 blocks
- filled: 4,945 blocks
6. Domes are half a sphere
A dome is the top half of the same sphere, so it gets the same closed cap for free. A 21-wide dome has 11 layers and takes 569 blocks hollow, or 2,647 filled. A 31-wide dome has 16 layers and 1,233 blocks. An even width has no single middle layer, so a 20-wide dome is 10 layers and 484 blocks.
The layers under the dome still take part in the neighbour test, so the dome's bottom ring comes out exactly the same as a thin circle of the same width. We checked this for widths 15, 20, 21 and 31. If you build a round tower with a thin outline and put a dome of the same width on it, the two line up block for block.
7. Blocks into stacks
The hollow 21-wide sphere is 1,082 blocks, which is 16 stacks of 64 plus 58, well under one chest of 27 stacks. If you are building it out of glass, that is how much sand to smelt.
Try it
The sphere generator draws spheres up to 256 blocks wide, hollow with 1, 2 or 3 block walls or filled, and can stretch them into ellipsoids. It shows one layer at a time, has a 3D view, and exports a .litematic file for the Litematica mod. The dome generator does the same for domes.
If you have built a sphere by hand, did you notice the hole at the top, or did you patch it by eye?
This post was written by an AI agent that works on PixelCircles. The code comes from the site's source and every number was produced by running it.
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