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Calculator Answers

Block Circle Generator for Minecraft

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A block circle is a grid approximation of a circle, not a circle. Because a square grid cannot hold a curve, a generator has to decide which cells count as being inside the shape, and the choice of rule is what makes one generator's pattern differ from another's. This one keeps a cell when the centre of that cell falls inside the requested circle or exactly on its edge, which produces a pattern that is exactly symmetric left to right and top to bottom at every size. The outline is the same shape with its interior removed. The tool is independent and is not affiliated with Mojang Studios or Microsoft.

Pick a diameter in blocks, choose an outline or a filled circle, and read the pattern straight off the grid. The block count comes from the grid you are looking at, and the rule that decides which cells become blocks is written out below rather than left to guesswork.

See also: Circle Calculator – Area & Circumference, Cross Stitch Calculator, and Arc Length Calculator.

Quick Answer

Enter a diameter in whole blocks and the grid is drawn from one rule: a cell becomes a block when its centre falls inside a circle of that size. A 10-block circle is 28 blocks as an outline and 80 filled.

Not an official Minecraft product. Not approved by or associated with Mojang or Microsoft. See the Minecraft Usage Guidelines.

Size given as

blocks

Whole blocks, 1 to 128. · e.g. 10

Style

Copies the pattern as # for a block and . for a gap, one character per block, so the rows line up in any monospaced editor.

10 blocks across, 10 blocks tall.

Block circle

Blocks in the outline

28

10 x 10 grid, 10 blocks in diameter

Grid size10 x 10
Blocks used28
Filled in, it would take80 blocks
CentringEven, no centre block

A grid approximation, not a true circle. Every cell whose centre falls inside the circle is a block, which is what gives the pattern its exact left-to-right and top-to-bottom symmetry.

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Examples

Diameter 5, outline

12 blocks in a 5 x 5 grid

Diameter 10, outline

28 blocks in a 10 x 10 grid

Diameter 10, filled

80 blocks in a 10 x 10 grid

Diameter 25, outline

68 blocks in a 25 x 25 grid

How it works

Formula · block when (x + 0.5 - d/2)² + (y + 0.5 - d/2)² ≤ (d/2)²

There is one rule, and it is applied the same way at every size. No lookup tables, no hand-tuned exceptions for particular diameters.

A cell is a block when

(x + 0.5 − d/2)² + (y + 0.5 − d/2)² ≤ (d/2)²

d is the diameter in blocks, and x and y number the cells from zero.

  • the grid is d wide and d tall
  • the circle sits at the middle of it, at (d/2, d/2)
  • each cell is judged by its own centre, at (x + 0.5, y + 0.5)
  • centre inside the circle, or exactly on it, means a block

Symmetry is not applied afterwards, it falls out of the arithmetic. Column x sits (x + 0.5 − d/2) from the middle and the column mirroring it sits exactly the same distance the other way, so squaring the two gives the same number. The rows work identically. Every pattern this page draws is therefore symmetric left to right and top to bottom, at every size.

The rule, in one line

There is no lookup table behind this page and no special case per size. One inequality decides every block.

(x + 0.5 − d/2)² + (y + 0.5 − d/2)² ≤ (d/2)²

For a diameter of d the grid is d by d, the circle's centre sits at the middle of it, and every cell is given the coordinates of its own centre: cell (x, y) sits at (x + 0.5, y + 0.5). A cell is placed when that centre lies inside the circle or exactly on its edge.

The half is the whole trick. Without it you would be testing the corner of each cell rather than its middle, and the result would lean toward one side of the grid instead of sitting square on it.

Working one out by hand

Take a diameter of 7. The grid is 7 by 7, the radius is 3.5, and the centre sits at (3.5, 3.5).

  1. Take the top-left cell, (0, 0). Its centre is at (0.5, 0.5), so the offsets are 0.5 − 3.5 = −3 in both directions.
  2. Square and add. (−3)² + (−3)² = 18.
  3. Compare against the radius squared. 3.5² = 12.25, and 18 is larger, so that corner cell stays empty.
  4. Now take (1, 0), one step right. Offsets −2.5 and −3, giving 6.25 + 9 = 15.25. Still above 12.25, so still empty.
  5. And (2, 0). Offsets −1.5 and −3, giving 2.25 + 9 = 11.25. Under 12.25, so that one is a block.

Repeat for all 49 cells and 37 of them come out on. The other three corners are the same arithmetic mirrored, which is why the pattern is symmetric without anyone having to make it so.

Why the symmetry is exact rather than close

Column x has offset x + 0.5 − d/2, and the column mirroring it, d − 1 − x, has offset d/2 − x − 0.5. Those are exact negatives of each other, and squaring makes them equal.

That matters more than it sounds. For whole-number d and x both offsets are sums of integers and halves, and every such value is exactly representable in binary floating point. So the two sides of the circle are not nearly equal, they are bit-for-bit identical, at every size the page will draw. A pattern that is symmetric at diameter 9 and lopsided at 91 would be a floating-point artefact, and this rule cannot produce one.

Edge cases

  • Diameter 1. One block. The single cell's centre is the circle's centre, and the distance is zero.
  • Diameter 2. Four blocks, a square. Every cell centre is exactly √0.5 from the middle and the radius is 1, so all four qualify. It is the smallest size where the result looks nothing like a circle.
  • A fraction. Refused. Blocks are whole, so half a block is not something the grid can place, and the page says that rather than rounding silently.
  • Above 128. Refused. The ceiling is where the picture stops being useful, not where the maths stops working: at 128 across the grid is 16,384 cells, which stays responsive on a phone, and the rule itself would go on happily at any size.
  • Outline of a tiny circle. At small sizes the outline and the fill are the same shape, because no cell has all four neighbours filled. They first differ at diameter 5, where the fill is 21 blocks and the outline is 12.

Your figures stay in this page

The diameter you type and the pattern it produces are computed by this page in your browser. Nothing is sent to a server, nothing is stored after you close the tab, and there is no account. The copy button uses your own clipboard.

Outline or filled

The filled circle is every cell the rule accepts. The outline is that shape with its interior taken out: a block survives unless all four of its edge-sharing neighbours are blocks too. A block on the edge of the grid is missing a neighbour, so it always stays.

Building the outline out of the filled shape rather than measuring it separately means the two can never disagree. The outline is always a subset of the filled circle, always sits in the same square, and always inherits the same symmetry. It also gives you the useful pair of numbers: a 25-block circle is 68 blocks as an outline and 489 filled, so the inside is 421 blocks of whatever you are filling it with.

Odd and even sizes centre differently

With an odd diameter the middle of the circle lands in the middle of a block, so there is one centre block, one centre row and one centre column. Handy: you can stand on the middle and count outwards in four directions.

With an even diameter the middle lands on the seam between two blocks. There is no centre block, and the centre row and column are two wide. A 10-block circle and an 11-block circle are therefore not the same shape with one extra ring; they are laid out differently from the start. Decide which you want before you place anything, because converting between them later means rebuilding.

How close is it to a real circle?

Close, and closer as the circle gets bigger. The area of a true circle 25 blocks across is about 490.9 square blocks and the filled pattern uses 489 blocks, under half a percent out. At 10 across the true area is 78.5 and the pattern uses 80. The small sizes are where a grid has least room to work with, which is also where the shapes look least round.

For the continuous version of the same maths, the circle calculator gives area and circumference from a radius or diameter.

About the name

This is an independent tool for planning block circles in Minecraft. It is not made by, endorsed by or affiliated with Mojang Studios or Microsoft, and Minecraft is their trademark. The geometry here is ordinary grid geometry and works just as well for cross stitch, pixel art, tiling or anything else laid out on squares.

Source

This page draws its naming and disclaimer from Minecraft's published usage guidelines, which informed the naming and disclaimer used on this page, not a claim that Mojang or Microsoft signed off on this page or its wording. Verified 15 August 2026.

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Frequently asked questions

One rule, applied to every cell. For a diameter of d the grid is d by d and the circle's centre sits at its middle. A cell is placed when the centre of that cell lies inside the circle or exactly on its edge: (x + 0.5 − d/2)² + (y + 0.5 − d/2)² ≤ (d/2)². There is no lookup table and no special case per size.

No. Bresenham's algorithm walks an outline using integer arithmetic and error terms, and it is built for drawing a thin curve fast. This is a distance test applied to every cell in the grid, which is slower and produces a filled shape directly. Both approximate a circle on a grid; they are not the same method and the patterns can differ.

No, and it cannot be. A circle is the set of points at a fixed distance from a centre, and a grid offers only whole squares. What this page produces is a grid approximation: the set of grid cells whose centres fall inside the circle. Every generator has to choose such a rule, and different rules give different patterns for the same diameter.

Because at that size every cell centre is inside the circle. The radius is 1.5 and the corner cell centres are about 1.41 blocks from the middle, which is nearer than 1.5, so all nine qualify. The same happens at diameters 1 and 2. Below about 4 blocks a grid simply has too few cells to suggest a curve.

Because the test is on the centre of each block, not its corner. A cell that occupies the square from x to x+1 has its middle at x+0.5. Drop the half and you test the corners instead, and the whole pattern shifts half a block off the grid it is meant to sit on.

An odd diameter puts a cell centre exactly on the circle's centre, so there is a single middle block and a middle row that runs the full width. An even diameter puts the centre on the corner where four cells meet, so there is no middle block and two central rows instead of one. A 9-wide circle looks rounder than a 10-wide one for that reason alone.

Odd diameters generally read better, because the single centre block gives the eye something to resolve around. Very small even sizes are the worst: a diameter of 2 is a 2 by 2 square, and a diameter of 4 has flat sides two blocks long. From about 11 upward the shape is convincing at either parity.

Measurably close, and it improves with size. A diameter of 7 gives 37 blocks against a true area of 38.48, about 3.8% low. At 10 it is 80 against 78.54, 1.9% high. At 128 the error is under 1%. Small circles are the ones that look wrong, and that is arithmetic rather than a flaw in the drawing.

Because a circle is a set of points at a fixed distance from a centre, and a grid can only offer whole squares. Any rule for choosing which squares is an approximation, and different rules give different patterns for the same diameter. This page fixes one rule and states it so the answer is reproducible rather than a matter of taste.

The outline is the filled shape with its interior removed. A cell counts as interior only when all four of its edge-sharing neighbours are also filled, so anything on the rim survives. Deriving it that way rather than running a second distance test means there is only one rule to get right, and the outline is always a subset of the fill with the same bounding box.

The result panel counts them for you, from the grid it actually drew rather than from a formula. A diameter of 10 is 80 blocks filled or 28 as an outline; a diameter of 25 is 489 filled or 68 as an outline. The outline is dramatically cheaper at larger sizes, which matters if you are gathering materials.

It is a rendering limit rather than a mathematical one. At 128 across the grid holds 16,384 cells, which a browser can lay out and a phone can still scroll. The rule would go on working at any size; the page would stop being usable, so it declines rather than hanging.

Because blocks are whole. Half a block is not something the grid can place, so accepting 7.5 would mean silently rounding it and answering a question you did not ask. The page says so instead.

Only one layer at a time. Each horizontal slice of a sphere is a circle of a different diameter, so you can build one by generating each layer separately, but this page produces a single flat layer and does not compute the sequence of radii for you.

It will not be the pattern, which is symmetric by construction at every size. Two things usually explain it: starting the build from a corner and losing count part way, or viewing a large circle from ground level, where perspective compresses the far side. Build outward from the centre row and count against the grid here.

No. The diameter and the pattern are computed by this page in your browser. Nothing is sent to a server, nothing is kept after you close the tab, and there is no account.