How the circle is computed — the Bresenham midpoint algorithm
Every blueprint starts from one question: for each row of the grid, which blocks sit closest to a true mathematical circle? This generator answers it with the Bresenham midpoint circle algorithm, the integer-only method graphics programmers have used since the 1960s to draw circles on pixel screens. A Minecraft block grid is a pixel grid, so the fit is exact.
It works in four steps. 1. Place the center and radius: for diameter d the radius is (d−1)÷2 blocks. 2. Start at the top of the circle and walk clockwise through a single octant — one eighth of the circle. 3. At each step an integer decision variable picks the next block: whichever block center lies closest to the ideal circle. No floating point, no guessing. 4. Mirror that octant eight ways. Because only one octant is ever computed and the rest is mirrored, the blueprint is perfectly symmetrical by construction — and because the math is pure integers, diameter 9 produces the identical blueprint every single time.
Odd vs. even diameters. Odd diameters center on a single block. Even diameters center on a 2×2 block junction instead. To keep using the same integer algorithm for even sizes, the generator rasterizes at half-block resolution (twice the detail), then folds the coordinates about the center junction. A plotted point landing exactly on the junction belongs to both middle blocks, which is what keeps even circles exactly symmetrical instead of lopsided.
Worked example 1: hollow circle, diameter 9
Say you are building a 9-wide wizard tower. Radius R = (9−1)÷2 = 4. The midpoint algorithm walks the first octant and picks four blocks: (4,0), (4,1), (3,2), (3,3) — measured in blocks right and down from the top of the circle. Mirrored eight ways, that becomes the 24-block outline:
...XXX...
.XX...XX.
.X.....X.
X.......X
X.......X
X.......X
.X.....X.
.XX...XX.
...XXX...
Filling every row between the leftmost and rightmost outline block gives the filled disc: 61 blocks. A two-wide wall (thick) needs 40. In stacks of 64: the hollow ring is 24 blocks (not even half a stack); the filled floor is 61 blocks (just under one full stack).
Worked example 2: even diameter 10, plus a 7-diameter sphere
Diameter 10 is even, so there is no single center block — the middle is the 2×2 junction of rows 5–6 and columns 5–6. Mark those four blocks first; everything mirrors around them. The outline needs 36 blocks, the filled disc 88 (one stack of 64 plus 24):
..XXXXXX..
.XX....XX.
XX......XX
X........X
X........X
X........X
X........X
XX......XX
.XX....XX.
..XXXXXX..
For a dome, use the Sphere tab. A solid 7-diameter sphere is built as 7 stacked layers with diameters 4, 6, 7, 7, 7, 6, 4 — the middle layer is the full 7-wide circle. Solid: 207 blocks. Hollow shell (outlines only): 104. A dome is the top 4 layers: 122 blocks solid, 60 for the shell.
Block counts for popular diameters
Quick reference for odd diameters. Hollow = one-block outline (walls, rings). Thick = two-block wall. Filled = solid disc (floors, sphere layers).
| Diameter | Hollow | Thick | Filled |
|---|
| 5 | 12 | 16 | 21 |
| 7 | 16 | 28 | 37 |
| 9 | 24 | 40 | 61 |
| 11 | 28 | 52 | 97 |
| 13 | 32 | 60 | 129 |
| 15 | 40 | 72 | 177 |
| 17 | 44 | 84 | 221 |
| 19 | 52 | 96 | 277 |
| 21 | 56 | 108 | 349 |
| 23 | 64 | 120 | 413 |
| 25 | 68 | 132 | 489 |
| 27 | 72 | 140 | 569 |
| 29 | 80 | 152 | 657 |
| 31 | 84 | 164 | 749 |
| 33 | 92 | 176 | 845 |
| 35 | 96 | 188 | 957 |
| 37 | 100 | 196 | 1,073 |
| 39 | 108 | 208 | 1,193 |
| 41 | 112 | 220 | 1,313 |
| 43 | 120 | 232 | 1,441 |
| 45 | 124 | 244 | 1,581 |
| 47 | 132 | 256 | 1,733 |
| 49 | 136 | 268 | 1,877 |
| 51 | 140 | 276 | 2,025 |
| 53 | 148 | 288 | 2,209 |
| 55 | 152 | 300 | 2,369 |
| 57 | 160 | 312 | 2,553 |
| 59 | 164 | 324 | 2,725 |
| 61 | 168 | 332 | 2,909 |
| 63 | 176 | 344 | 3,117 |
| 65 | 180 | 356 | 3,305 |
| 67 | 188 | 368 | 3,513 |
| 69 | 192 | 380 | 3,721 |
| 71 | 196 | 388 | 3,941 |
| 73 | 204 | 400 | 4,181 |
| 75 | 208 | 412 | 4,405 |
| 77 | 216 | 424 | 4,645 |
| 79 | 220 | 436 | 4,889 |
| 81 | 228 | 448 | 5,145 |
| 83 | 232 | 460 | 5,401 |
| 85 | 236 | 468 | 5,653 |
| 87 | 244 | 480 | 5,941 |
| 89 | 248 | 492 | 6,213 |
| 91 | 256 | 504 | 6,493 |
| 93 | 260 | 516 | 6,769 |
| 95 | 264 | 524 | 7,065 |
| 97 | 272 | 536 | 7,377 |
| 99 | 276 | 548 | 7,685 |
| 101 | 284 | 560 | 8,005 |
Building tips
- Mark the center first. One block for odd diameters, a 2×2 square for even. Build outward from it and mistakes stay visible while they are cheap to fix.
- Hollow for walls, filled for floors. A hollow ring is the cheapest way to raise circular tower walls; switch to filled for floors, ceilings, and platforms where you do not want to see through.
- Smooth the corners with stairs. Generate a hollow circle one or two diameters larger than needed, then place stairs along the diagonal steps of the outline with their backs facing outward. The stairs visually round off exactly the corners the block grid leaves behind.
- Build domes bottom-up. Work through the sphere layer table from layer 1 upward and leave the top layers for last — you will be standing on finished work instead of scaffolding.
- The Nether roof loves circles. Bedrock up there is flat and mob-proof, so filled-circle foundations are quick to lay. Bring scaffolding: even a 31-diameter dome is 16 layers of placing blocks above your head.
- Let /fill do the boring part. For filled circles, stand where you want the center and paste the generated commands one row at a time (Java Edition). A 9-diameter floor goes up in 9 commands.
Frequently asked questions
What is a Minecraft circle generator?
A Minecraft circle generator turns a diameter into a block-by-block blueprint: a grid that shows exactly which blocks to place so the result looks like a smooth circle in-game. You enter a diameter, pick hollow, thick, or filled, and get a printable plan with row numbers, a block count, and optional /fill commands. Everything on this page runs in your browser; nothing is uploaded.
Should I use an odd or even diameter?
Odd diameters (5, 7, 9...) have a single center block, which makes it easy to mark the middle of towers, domes, and circular rooms. Even diameters (6, 8, 10...) have a 2x2-block center instead, which suits builds that need a symmetrical middle opening, like a 2-wide doorway or a central pillar cluster. The generator handles both: odd circles are centered on one block, even circles on a 2x2 junction, and both stay perfectly symmetrical.
What is the difference between hollow, thick, and filled?
Hollow draws a one-block-wide outline: the cheapest option and the right choice for walls, rings, and tower shells. Thick adds a second inner ring, giving a sturdier two-block wall in a single pass. Filled covers the whole disc, which is what you want for floors, ceilings, platforms, and the individual layers of a sphere.
How does the generator compute the circle? What is the Bresenham algorithm?
The generator uses the Bresenham midpoint circle algorithm, the classic computer-graphics method for drawing circles on a pixel grid. It starts at the top of the circle and steps around one octant, using a small integer decision variable to choose, at each step, the block closest to the true mathematical circle. The octant is then mirrored into all eight, which guarantees perfect symmetry. Because it is pure integer math, the result is deterministic: the same diameter always gives the same blueprint.
How accurate are the circles?
Every outline block sits within about one block of the true mathematical circle, which is the best any block grid can do. The algorithm picks the nearest block at every step rather than eyeballing it, so curves come out as smooth as Minecraft's grid allows, with no lopsided bumps. If a circle looks slightly angular at very small diameters (below 7), that is the grid itself, not an error: a 5-wide circle only has 5 blocks of resolution to work with.
Can I generate ovals too?
Yes. Switch to the Oval tab and enter a width and height. Ovals use the midpoint ellipse algorithm, the two-axis cousin of the circle algorithm, so they get the same symmetry and nearest-block guarantees. Ovals are handy for elliptical courtyards, boat hulls, stadium fields, and dragon-egg-style nests.
Can I generate spheres and domes?
Yes. The Sphere tab stacks filled-circle layers: for a diameter-d sphere it computes each layer's width from the sphere equation and lists every layer with its own diameter and block count, so you can build bottom-up, one blueprint per layer. A dome is simply the top half of that stack; the tool totals dome layers separately. A solid 7-diameter sphere needs 207 blocks, while its hollow shell needs 104.
How do I transfer the blueprint into my Minecraft world?
Build one row at a time using the row numbers on the blueprint, counting blocks from the left edge. For filled circles, the fastest route is the /fill commands the tool generates: stand where you want the center, then paste one command per row (Java Edition). Each command fills one full row relative to your position, so a 9-diameter filled circle goes up in 9 commands. For hollow outlines, build the outline runs row by row; they never cover the interior.
Does this work in both Java and Bedrock Edition?
The blueprints work identically in both editions because block placement is the same grid. The /fill commands are written in Java Edition syntax; Bedrock's /fill works the same way for simple block fills, but command details can differ, so Bedrock players may prefer building from the visual blueprint.
Can I use stairs or slabs to make smoother circles?
Yes, and it is a common pro trick. Generate a hollow circle one or two diameters larger than you need, then place stairs along the diagonal steps of the outline with the stair backs facing outward. The stairs visually round off the corners the block grid leaves behind. Slabs work the same way for flatter curves on floors and roofs.
How many blocks do I need for a 20-diameter hollow circle?
64 blocks for the outline. As a rule of thumb, a hollow circle needs roughly pi times the diameter (about 63 for diameter 20), while a filled circle needs roughly pi times the radius squared (about 332 blocks at diameter 20). The tool's material estimate converts any count into stacks of 64 and can add a waste percentage for misplaced blocks.
What is the maximum diameter?
The tool accepts diameters from 1 to 129. Above that the blueprint grid becomes hard to read and slow to render, and very few builds need it: a 129-diameter circle is already wider than most render distances comfortably show. For mega-builds, generate the circle in quarters and mirror them, or build it with /fill commands row by row.
Any tips for big circular builds, like Nether ceiling bases or domes?
Mark the center first (one block for odd diameters, a 2x2 for even) and work outward in rings so mistakes stay visible early. For domes, build the sphere layer table from the bottom up and leave the top layers for last. On the Nether roof, where bedrock is flat and mob-proof, filled circles make excellent foundations; bring scaffolding, because even a 31-diameter dome is 16 layers of placing blocks above your head.
Is this generator free? Do I need to install anything?
Yes, it is completely free and installs nothing. The generator, the PNG/SVG export, and the /fill command builder all run locally in your browser with plain JavaScript, so your blueprints never leave your device and the page works offline once loaded.