Question: I'm trying to determine how large (geographically) my city will have to be to accommodate for 1 million people.

I have a city that was basically formed by the gods to be fertal land with a good climate for crops (there are all four seasons) and to look like this:

That's not exactly how the river runs around the city, but the basic idea is that the land spirals from the place where the river enters the city down to where it exits.

The city is split by the river into 8 octants, each octant is almost completely identical to the others. In the middle is a huge palace where 8 rulers live, surrounding the palace is the octant "administration building" then immediately out from that is where other normal city buildings are (textile shops, hospitals, etc.).

From there you get to people's dwellings. The people who work in the center of the city first, then people who work further out second. Then you get to the second layer of normal city buildings (so there's an inner hospital and an outer hospital for each octant).

Finally you get to a third set of dwellings for the people who work out in the fields and forests which surround the city.

An important thing to note about this city is optimized for efficiency, not citizen's enjoyment. So sports and things like that don't have a place here and therefore wont take up space.

Also, they use the river to travel and transport goods throughout the city (as I mentioned, the drawing is imperfect because it doesn't really communicate how this works very well).

So what I need to determine is what the diameter of the city would need to be to accommodate ~1 million people. How big would the fields need to be in relation to the dwellings etc. I need to know this so I can accurately describe how long it would take someone to travel from the palace to the outside of the city given various modes of transportation (walking, riding in a carriage, and riding on a barge on the river).

Another thing to note is that the city is completely self-sustaining. With the exception of mines that are out in the mountains to the north and sand dunes to the east (the entire city is built out of especially strong glass to enable the sun-powered magic), everything the people need to survive and thrive exists within the boundary of the river. The city also completely sharing resources. Everything comes to the adminstration buildings and is equally distributed. No "class" system.

Also, the civilization is sitting somewhere around the 1800s in our own history as far as technological capabilities.

Thanks!