How the shape is worked out
Each block is a square on the grid. A block is part of the shape when its middle falls inside a true circle (or ellipse, or sphere) of the size you chose. An odd size has one middle block; an even size has a middle of 2 by 2, which the plan outlines. The dashed lines are the two axes through the middle, so you can count out from them.
Thin, thick or filled
Thin outline is the usual one-block ring: where the curve steps in, the blocks meet corner to corner, with no block more than the ring needs. A diameter of 7 takes 16 blocks. Thick outline fills each of those steps so every block touches the next by a side (24 blocks at 7), which reads as a smoother wall, gives every block a side to be placed against, and makes a path you can walk along the top. Filled is every block, for floors and solid builds. In both outlines a block that is not needed is left out, so the very tip of a long, narrow ellipse can come out a little flatter than the filled shape.
Spheres and domes, layer by layer
A sphere is built as a stack of flat layers. Move through them with the slider or the arrow buttons; layer 1 is the bottom. Show the layer below draws the previous layer faintly underneath, so you can see where this one steps in or out. A hollow sphere's layer is its ring plus whatever has to be filled so you cannot see in from above or below, which is why the layers near the top and bottom are solid. A dome is the top half of the sphere, standing on its widest layer.
Counting blocks
The counts show the blocks in the layer you are looking at and in the whole shape, and how many stacks of 64 that is. The numbers at the edge of the grid are how many blocks each row and column of the layer holds. Point at a block, or tap it, to see how far it is from the middle: an even size has no single middle block, so the two blocks either side of the centre line are both 1 away from it.
Ticking off what you have built
Tap or click a block to mark it placed; tap again to take the mark off. On a keyboard, the arrow keys move around the plan and Space marks a block. Marks are kept for each layer while the page is open, and are not saved anywhere; changing the shape, size or style starts a fresh plan.
Sharing and saving a plan
The address in the bar keeps your settings, for example #sphere-25-thin-layer-7, so Copy link gives a link that opens the same plan. Download PNG saves the layer you are looking at as a picture with the counts written on it, to keep on a second screen or print. The plan is worked out in this page and nothing is sent anywhere.
Questions
Is this the same in Java and Bedrock?
Yes. A circle or sphere is the same blocks in either edition, and both stack most blocks to 64. Some items stack to 16 or not at all, so the stack count is for ordinary building blocks.
How big can I go?
Up to 256 blocks across. In both editions the Overworld is 384 blocks tall, from y −64 up to y 319, so a 256 sphere fits if you start low enough. Big plans need zooming in to read; the row counts at the edge show once the squares are large enough to label.
Thin or thick: which should I use?
Thin uses the fewest blocks and is what most circle charts show. Nothing walks or flows through a corner join, so a thin ring still holds water and keeps mobs out. Pick thick when you want a wall with no stepped corners, a ring you can walk around on top, or blocks that each have a neighbour to be placed against.
Do the layers of a thin sphere touch each other?
Not always by a face. As in a thin ring, where the shell curves a block can sit diagonally off the one below it, touching only along an edge; other sphere generators work the same way. The shell still has no hole you can see or walk through. A thick sphere uses thick rings in every layer, so the steps within each layer are filled and the shell is more solid.
Why are the top and bottom layers of a hollow sphere solid?
Near the poles each layer is much smaller than the one next to it. The blocks between the two rings are what keeps the shell closed, so they are part of the plan.
Should I pick an odd or even size?
An odd size has a single middle block, which is easier to start from: place it, then count out along the axes. An even size has a middle of 2 by 2. Both are worked out exactly, so pick whichever fits your build.