UPDATE The formula has changed as of the March 2011 patch, it is now
(city population * 1.1) + (capital population * .15) - 1 for each city connected to the capital, not including the capital.
- The Machu Pichu wonder increases the modifier by 20%, to
(city population * 1.3) + (capital population * .15) - 1.
- Arabia increases the constant by 1, to
(city population * 1.1) + (capital population * .15) (thanks WillfulWizard).
The economic overview also gives a far better explanation of how it is calculated - in other words, this question is now trivially solved by simply looking at that economic overview :)
Original answer below.
Okay, I did a bit more testing, and bwarner's answer is almost accurate:
Each city, excluding the capital, provides (city's population * 1.25) + 0.01 gold per turn. Owning the Machu Pichu wonder increases the modifier by 20%, to (population * 1.5) + 0.01, for all the cities.
The capital does not provide any gold.
The 1.25 and 0.01 can be seen in the Assets\Gameplay\XML\GlobalDefines.xml file:
<Row Name="TRADE_ROUTE_BASE_GOLD">
<Value>1</Value>
</Row>
<Row Name="TRADE_ROUTE_CAPITAL_POP_GOLD_MULTIPLIER">
<Value>0</Value>
</Row>
<Row Name="TRADE_ROUTE_CITY_POP_GOLD_MULTIPLIER">
<Value>125</Value>
</Row>
The economic overview also demonstrates these values.
I couldn't find any other factor which affects these values, and I checked different difficulty levels, different distances between cities, different city route type (road vs railroad, road/railroad vs harbor), different city health and whether it is occupied. Looks like it's solely the population.
The supply limit based on your empire size is not related to the upkeep cost. Instead, if you exceed the supply limit, all your cities take a 10% production penalty. In most games, you will run out of money before you get to that point.
Best Answer
To directly answer the question, road maintenance is listed as "Tile Improvement Maintenance", when you mouse over your treasury/income in the top left. You can see a circled example in the screenshot below. As for the details:
Roads cost to maintain both inside and outside your borders
Because my conclusions are contrary to previous info we had about road maintenance in neutral territory... Pics Or It Didn't Happen!
Exibit 1: Prince Difficulty, some roads in, some out.
As you can see, I have 4 roads in my territory, and one outside, costing me a total of 5 maintenance. I have no other roads anywhere else. I wish I had taken a screenshot of the previous turn. The next time I find myself in this situation, I'll take a pair of screenshots and replace this single picture. Either way, remember you can always try it yourself to be sure. YaY Science!
Exibit 2: Settler Difficulty, all roads out.
Thanks to @DMA57361's questions, I checked a different difficulty and a different number of roads outside the borders, namely all of them. On Settler difficulty, building roads only outside of my borders, I still ended up with maintenance for the roads, so clearly they do cost.
Edited to account for difficulty, now that I've completed more extensive testing.
Roads cost the same to maintain in your own territory, and in neutral territory. How much varies by difficulty:
Road maintenance is only ever a whole number. In case of decimal remainder, always round down. For example, on Settler, 2 roads cost 0.68, which clearly got rounded down to 0.
To find each of these, I built roads either only inside, or only outside my borders at a time. This confirmed the same results for inside and out, but got me only close numbers. Then @Oak used his powers of XML scrying, and found the exact numbers for us.
Since so many difficulties are 1g, (and the ones that are not are the easier difficulties anyway,) and for our general happiness, I hereby declare "1g" an acceptable approximation for all further calculations relating to road maintenance. Hurray!
When next I can test, I'll re-test road's in another nation's borders, to clean up the next section! Same Bat-time. Same Bat-channel.
Roads DO NOT cost to maintain inside another nation's bordersEdit: This section is suspect until I complete further testing, since one road did not cause me maintenance. My mistake for not setting up a proper control. This still may be completely true, but I need to test on different difficulties and compare with similar numbers of roads in my borders and in neutral territory.
In the game these two pictures originated from, I had no roads, and built a road inside each another civilization's borders, and a city-state's borders. I can't verify that they were costing any gold to the land's owner (Rome's income was fluctuating quite a bit), but I can say for sure they were costing me nothing. This is likely what bwarner saw that caused the error.There may be other effects that change which roads cost to maintain, but these seem to be the major ones. Anyone found anything not explained by these.
PS As with any screenshot heavy post, I do my best to crop/scale the images to reasonable sizes without losing the important parts, such as the circled text. They still end up crowding the page, for which I'm sorry.