Pixel Circle and Ellipse Generator

How the Circle Is Computed

For a circle with an odd diameter there is a centre block, and the generator uses the midpoint circle algorithm published by Jack Bresenham in 1977. It walks one-eighth of the circle starting at the top, (0, r), and at each step decides whether to move straight across or diagonally down by testing whether the midpoint between the two candidate squares lies inside the circle. A running decision value starts at 1 − r and is updated with additions only, then the other seven eighths are copied by symmetry.

The standard textbook example is r = 10: the first octant is (0, 10), (1, 10), (2, 10), (3, 10), (4, 9), (5, 9), (6, 8), (7, 7), which the generator reproduces, giving a 56-block outline 21 blocks across.

Even diameters and ellipses have no single centre block, so the generator uses the rule the algorithm approximates: a block is part of the shape when its centre lies inside the ellipse (x/a)² + (y/b)² ≤ 1. An outline keeps the inside blocks that touch an outside block along an edge; a thick ring removes a smaller ellipse from the middle.

Common Sizes

A filled 15-block circle uses 177 blocks, compared with π × 7.5² ≈ 177 for a true circle of that width, so the block version is a close match.

Building Tips

• Build in rows. Use the blocks-per-row list: each row is centred, so a row of 9 in a 15-wide circle leaves 3 empty blocks on each side.
• Odd sizes are easier. An odd width has a centre block to measure from; an even width centres on the line between two blocks.
• Domes and spheres. Stack circles of shrinking width, or use the ellipse option with a reduced height for each layer.
• Thick walls. A 2-block ring is easier to keep watertight in games and sturdier in real tiling than a 1-block outline.

Common Mistakes

• Counting the diameter from centre to edge. The width is the full number of blocks across, edge to edge.
• Mixing up rows and columns. The preview is drawn with rows top to bottom; the shape is symmetric, so turning it doesn’t matter for circles but does for ellipses.
• Expecting a perfect curve at small sizes. Below about 7 blocks, any block circle looks like a rounded square.

What This Generator Does Not Cover

It makes flat 2D shapes on a square grid. Spheres, cylinders with varying radius, and hexagonal or isometric grids need other tools; for the area or circumference of a real circle, use the circle calculator.

Frequently Asked Questions

How to Use This Calculator

1. Choose circle or ellipse — and the width (and height for an ellipse) in blocks.
2. Pick a style — 1-block outline, thick ring with a chosen thickness, or filled.
3. Generate — the grid preview shows every block.
4. Build row by row — using the blocks-per-row list and the total.