I suspect there has been (and will be) a lot of difficulty answering this question because there is no real specific size for a “medieval city”. I know AskHistorians doesn’t like questions that are looking for one specific example, but I think the only way to look at this is by giving several examples!

The actual physical size of a city would depend on several other factors. How old is the city? Where is it? Does it have defensive walls? Is it a trade or administrative centre?

Many medieval cities were very, very old. Many of them had been founded when they were part of the Roman Empire, so in the Middle Ages they were already a thousand years old or more, but that’s just the ones in northwestern Europe. Cities in the Mediterranean were even older than that, and in the Near East some cities have been occupied since before recorded history. The age of the city is important because if they’re that old, they’re probably relatively small (and therefore easier to defend), and they’re probably on a river or a coast, which made trade and communication easier but may have limited how far the city could expand.

Some cities were certainly bigger than others, and they might have had something like suburbs too, but you don’t really see anything like massive urban sprawl like we have now. And new cities were certainly built where there had been no cities before, especially in parts of Europe that hadn’t been part of the Roman Empire. But let’s say, in general, what you probably imagine as a “medieval city” was probably on a river or a coast, and had been there since Roman times or even earlier.

One example is London, which was built by the Romans at a strategic point on the north bank of the Thames. Eventually it was surrounded by a wall, and the amount of land encompassed by the Roman (or later medieval) wall is a good way to measure the physical size of a city. London’s wall enclosed about 3 km^(2). Today, “London” is enormous if we include all the other cities and boroughs that make up Greater London, but technically, only this very small area is “the City”. Of course, as the administrative centre and the usual residence of the king, there was a lot more going on in medieval London outside the walls too, which is why it’s difficult to define a “city” like this. There were lots of urban buildings outside the walls, including royal and government buildings not far away in Westminster, and dozens of smaller towns and villages in the surrounding rural areas.

Paris is a similar example. Paris was also an old Roman city, like London built at a strategic point on a river, and it had a wall as well, but unlike London the centre of Paris shifted a bit over the centuries. The shape of medieval Paris was really determined by the walls built by Philip II in the late 12th/early 13th centuries - the Île de la Cité and the north (right) and south (left) banks of the Seine, unlike London which only covered the north bank of the Thames. So, Paris was a little bit bigger, but because of the river, it probably still covered the same amount of land as London, about 3 km^(2). And like London there were urban areas outside the walls, and plenty of villages and farms.

Some cities were much more massive, like the capital of the Roman/Byzantine Empire, Constantinople. It’s on a peninsula that is surrounded by water on the north (the Golden Horn), south (the Sea of Marmara), and east (the Bosporus), which made it relatively easy to defend, and it was at the perfect location for trade and communication between Europe and Asia. It was much older than the Empire, since there had been an ancient Greek colony at the tip of the peninsula, but it was expanded by emperor Constantine in the 4th century. By the 5th century the land border to the west was defended by the massive Land Walls (or the Theodosian Walls), which were really a series of three walls. There were smaller walls surrounding the coastal sides of the city too. The walls enclosed about 30 km^(2) - 10 times bigger than London or Paris. And there were other cities across the Golden Horn and the Bosporus so the whole area was almost like a modern urban metropolis.

So, the size of a city could vary greatly depending on where it was, and how important it was. What about a “regular” city, not the royal residence or a major capital? Well the best example that springs to mind is also in France, the city of Nantes...simply because I used to live there. I always wandered around exploring the remnants of the Roman wall, so the dimensions of the city were actually the first thing I thought of when I saw this question, haha. Nantes was built at the confluence of the Loire and Erdre rivers, on a waterway for easy communication and trade, and at a relatively easy to defend spot. The Roman wall followed the banks of the Loire and the Erdre and enclosed about 1.5 km^(2). Around the same time as the new walls were being built in Paris, the walls of Nantes were rebuilt too. They crossed the Erdre to the west, to enclose the suburb that had developed on that side of the river, and now covered about 2.6 km^(2) - almost the same size as Paris and London.

What about new cities, that hadn't already been enclosed by Roman walls? Ghent is an example of this - it was actually very old as well, but didn't have any previously-existing defensive structure that it either had to fit into or expand out of. So in that sense it was relatively new, for a medieval city. Ghent and other cities in Flanders experienced massive growth in the 13th and 14th centuries, thanks to the extremely lucrative textile trade. Ghent grew to over 6 km^(2) by the 14th century. It was twice as big as Paris, although still not nearly as big as Constantinople.

I’m sure we could continue to find example after example…I haven’t even thought about the cities like Cordoba, Baghdad, Cairo, Jerusalem, not to mention cities in China, or Africa, or even cities in the Americas during the same period. So I hope these are a good start. Let’s say very generally that a medieval western European city would probably be an old Roman (or earlier) city on a waterway with walls that enclosed 1-3 km^(2), but depending on the circumstances they could be much larger.

Sources:

Francis Sheppard, London: A History (Oxford University Press, 1998)

John W. Baldwin, Paris, 1200 (Stanford University Press, 2010)

Paul Bois, ed., Histoire de Nantes (1977)

Jonathan Harris, Constantinople: Capital of Byzantium (Continuum, 2007)

David Nicholas, Medieval Flanders (Routledge, 1992)

David Nicholas's two-part series, The Growth of the Medieval City and The Later Medieval City (Routledge, 1997)

I assume you are talking about the size of a city within the walls, and not it’s surrounding countryside and farmlands to support the city. The problem with giving a specific answer is that cities expand based off of waterways & roads which are older than the city itself. It’s a naturally growing response to environment and the draw that brought people there in the first place. Paris for example, begins as a fortified town on the Seine, with several famous sieges as the Carolingian Franks fought “Vikings” to control the river. The Ile de la Cite was the only part of the city that was fortified. The island itself is tiny, but the city expanded beyond to both banks of the Seine and continued outwards.

As Paris expands, both in importance and population, various Kings of France want protect more and more of the city. The first series of walls on both banks of the Seine were completed by Phillip II and covered approximately 5,500 meters, and the area within was approximately 2.5 square kilometers. In the 14th century the area of the city covered by walls was 4.4 square kilometers. At the time, this is one of the largest cities in Western Europe with an extremely wealthy benefactor in the Capetian Kings of France. Unlike the earlier Carolingians, much of the Capetian power base is in Paris and the immediate surrounding area.

However, it is crucial to understand that a city is not bound by its physical defenses, which are based around natural strong points and the wealth of those interested in protecting it. Cities expand significantly beyond their walls with markets, farming villages, and woodland. Your city can only scale along with production and transport of available food. For example, the city of Rome at its height influenced agricultural production as far away as Carthage & Egypt as the state was rich enough to ship grain in from across the Mediterranean. It was also significantly cheaper to move by water than by land.

For this reason, there will be large populations outside of the walls of any medieval city, even among people who would be considered to live to there. You can see in these two maps that there is an extensive network of farms and population beyond the walls along a network of roads. The density of this population will decrease as you get further from the city center and walls, as you get further and further into farming villages and perhaps smaller market towns. Considering the logistics of travel, there probably will not be much interaction between people further than a day’s journey from the city. About 30 kilometers by road, and significantly further by river. Those living directly outside the walls will be very involved in the day to day existence of the city, and will likely provide crucial goods for its continued existence.

As an aside, if you want an excellent source for the look and shape of European cities in the Middle Ages, check out the Historic Cities Project which has hundreds of beautiful city maps.

So, to get back to your original question, the area within a walled city would only be a couple to several square kilometers. The layout and organization of the city depends on the terrain, such as rivers and hills. However, beyond those walls there will be bunches of dense population for several kilometers along roads and rivers, with decreasing density as you go along those transportation networks towards smaller farming villages, surrounded by plots and fields.

edit: u/WelfOnTheShelf has given you an excellent write up on the size of individual cities within their walls, which better answers your question. However, it's crucial to remember that walls do not define a city, but for the purposes of a game provide a good visual distinction.