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Which's the proper size of a floating island sailing through the sky? At first I thought that about 20km in diameter is totally uncomfortable and not viable, since it exceeds the size of the Troposphere.

According to these 2 images, one to see its real proportion and the other with its values in km for each atmosphere.

Taking into account also that the Everest mountain is almost 9km high and it is already difficult to breathe. It may not be recommended that you exceed 12km from the Troposphere.
Taking into account that the island does not maintain its own environment. And if it did, what would its new bearable height and size be?

Think volcano or Hawaii

EDIT
Think an aircraft carrier the size of Manhattan

It doesn't have to be super tall, but it can be super wide, like a fat disc or a top

If it was me, I wouldn't make it too big since the larger it might be the more ridiculous it would seem since it's defying the law of gravity. I wouldn't go beyond 750 metres diameter on an Earth sized world.

stratosphere sized

...

the game, stratosphere, sized.

The game is interesting, I didn't even know it existed. xD

If you wan't breathable air, you can't go much higher than 5 km. It's easier if the floating city has its own dome, so it can have a pressurized atmosphere.

But does it need to be realistic? I mean a floating city is not very realistic to begin with. Just use magic!