# Calculating City Size based on Population

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 fertile 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 dwellings can definitely be multi-story apartment-like buildings. They're very effective at building tall/strong glass buildings (their magic system helps with that and the tall palace is evidence of this). The dwellings are arranged so that 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 (farm and livestock land) and forests which surround the city.

Here are some useful bits of context:

• This is a world for a fantasy novel where the gods shaped the land to be suitable for this.
• The civilization is sitting somewhere around the 1800s in our own history as far as technological capabilities.
• 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.
• 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).
• They build most things out of glass (they get the sand from huge sand dunes in the east), but they do use metal (mines in the north) and wood for some things. The trees are within the boundary of the river.
• 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 people in the city also completely share resources. Everything comes to the administration buildings and is equally distributed. No "class" system. This means that everyone's homes will be the same size relative to the size of their families.

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).

Thanks!

• Hello and Welcome to worldbuilding. Boy have you chosen a complicated question to ask.... I'm not sure if we could answer it without a book. We've had a couple of these self-sufficient city questions asked before and they are usually closed because it is far too broad of a subject. Just a few clarifying questions? What technology level is this city? And does this sun powered magic contribute to society or can we ignore it? – Shadowzee Feb 11 '19 at 5:23
• At about 1800, the energy roughly divides out to about 20% human muscle, 20% animal muscle, and about 60% wood. This might help you work out some of the area relationships, though I'm not sure precisely how. The other problem you have is that you've not specified the environment. This could be anywhere -- the poles, the equator, or most anywhere. Production and the land required for it varies widely, I think, depending on many different factors. It may help get better answers if you add something about the climate and land type. – jonk Feb 11 '19 at 5:37
• This is not a duplicate but a question with some overlap and an answer that can apply to your question as well. worldbuilding.stackexchange.com/questions/121397/… – Cyn says make Monica whole Feb 11 '19 at 16:06
• the city I'm referring to is not fictitious (ancient yes but not fiction) - I would still search it because it solves (at least partial) a lot of the problems that comments are pointing out and it is very similar in design/isolation as your proposed city (it was a floating city on a lake) – LinkBerest Feb 11 '19 at 20:43
• When it comes to pure population density, look at two real-world examples, Riyadh (Saudi Arabia) and Manila (Phillipines) - The latter has a more than tenfold population density than the former. (46.000 vs. 3.600/km²) – tofro Feb 12 '19 at 10:31

I found this on farmland necessary to sustain some amount of people: How many people can you feed per square-kilometer of farmland? so using conventional farming (no hydroponics, magic, or crazy stuff), you'd get around 2350 people per km2. Flip it around and that's about 425 km2 for a million people.

Ok, then I looked up population density for one of the major US cities that I'm familiar with. About 3662 people / mi2 or 1400ish people / km2. That's about 715km2 for a million! This metric isn't ideal at all since medieval london was around 100 people/km2 which is a huge difference so you'll have to play around with this number. I read that ancient Rome (city of Rome) had around 1 million inhabitants so that might be a good reference as well

So, 425 + 715 = 1140km2 which is a circle with a diameter of 38km or 24mi. That's probably a solid start to the problem. You'd probably have to also look up how many farmers you'd need per km2 to help estimate that layer.

oh and the average human walking speed is about 3.1 mph so on a clear cross-cutting road, it'd take 8 hours to make it across with no breaks or obstacles.

• Your estimate for yield per km^2 assumes fairly modern (late 20th-century), crude oil based intensive farming methods. I don't think it's appliciable here. Also, according to en.wikipedia.org/wiki/List_of_urban_areas_in_the_European_Union and en.wikipedia.org/wiki/…, 1.400 people/km² appears to be on the lower end in regards to population density in cities of about 1 million people. If there are a lot of tall, "multi-story apartment like" buildings it might be a little low. But that depends on the specifics of the city. – nishuba Feb 12 '19 at 10:30
• Unless you intend to farm with purely human labor, you'll need draft animals to pull plows & wagons, and you'll need to feed them, too. – jamesqf Feb 12 '19 at 19:01

In the picture you provided the fields seem to be enclosed by walls and thereby probably count towards the city size.

Size with fields: 2312.32 km2

Size without fields: 312.32 km2

Why?:

Fields: For the field size I used this source; according to it, 4 people need 2 acres of land, which is about 8000 m2. This means 2000 m2 per person, times a million, gets us 2000 km2.

Rest of the city: I used London at the beginning of the 19th century (at that time it had a million in population) and encompassed 122 miles2 or 312.32 km2.

• Given that his pictured city includes sky scrapers, his city probably has a higher population density than turn of the 19th century London. But of course, this difference is small compared to the amount of farmland. – Shufflepants Feb 11 '19 at 16:24
• FYI, that puts it at a healthy 23 km radius. – Azor Ahai Feb 11 '19 at 17:06
• @AzorAhai Make that 27. – Mr Lister Feb 11 '19 at 18:18
• I think the problem of using London as a model is that it wasn't self-sustaining. For example, it was at the time the world's largest port. – jonk Feb 11 '19 at 20:23
• @Soan, note that your source for farm area is assuming modern high-density farming techniques and crops. Using 1800s technology, you might manage that density in someplace like the Nile Delta or Bangladesh, but for most of the rest of the world, you'd need to at least double the area needed. – Mark Feb 11 '19 at 22:47

Without consideration for comfort and open space you can look at the list and pick Manila as your model.

The highest density city in the world at 119,600 per square mile, you'd need less than 10 square miles for your city of 1million. The thing to note is that Manila isn't really high rise. It's very densely packed low and medium rise with minimal open space.

• I doubt that Manila grows any significant amount of food. – jamesqf Feb 11 '19 at 19:54
• @jamesqf, cropland wouldn't normally be considered within city bounds – Separatrix Feb 11 '19 at 20:58
• Normally, yes, but the OP states that everything (except metal from mines, and sand) comes from within the city boundary. Which (absent food-making magic) is utterly ridiculous. – jamesqf Feb 12 '19 at 18:47

Apartments or houses? Apartments are far more efficient when it comes to regards to their footprint. In the 1800, my guess is that the average household had about 4 to 5 people. Hence, you would need 200,000 to 250,000 housing units.

Class system will greatly influence the floor space per each housing unit. My lowest class, get about 40m2 apartment, or a 400m2 plot of land for a house. My 'rich' get 2500m2 plots for their houses.

My experimentation yielded that the housing 'efficiency' is between 65% to 75%, depending on class. What this means, is that for 100 poor houses (100 x 400m2 = 40,000m2), you would need an area of 61,540m2. Thad additional area is for your roads and streets.

My previous research yielded that a loaf of bread needs 1m2 of field space. A cow and a calf need about 1ha of grazing space. A chicken would need only 4m2 of space.

I hope this helps.

• Thanks for the feedback! Very helpful! I added into about the dwellings being tall apartments 👍 – kentcdodds Feb 11 '19 at 5:56