What is the formula for city connection income?

Question

In Civ 5 connecting cities to your capital earns you income, but each road costs 1G to maintain, so you don't want to connect cities too early. What is the formula for calculating how much gold you will get by linking cities?

From my experience it seems to be related to the population of the cities, but there also seems to be a benefit to having lots of trade routes. So connecting a second city of roughly the same size seemed to give me more then double the income from a single city. I now have 6 cities in the "network" and despite them being farther away, my trade income is more than paying for the roads.

Answer 1

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.

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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.

Answer 2

Looking at the economy details screen shows how much you are making from trade routes to each city. Currently I seem to be making population * 1.25 from each city (where population is the target city's population). Not sure where the 1.25 comes from or what might modify it.

Answer 3

Sadly the Manual entry for trade routes is not very useful, but confirms population is involved:

Each trade route is worth a certain amount of gold each turn, the amount determined by the population of the connected city.

EDIT: The Civilpedia is only slightly more forthcoming, saying that the population of both cities matters, not just the connected city.

Answer 4

If you look at the Economic Overview/General Information screen you can see the gold for each city connection. These values for the individual city connections exactly equal the formula of population * 1.1 + ((.15 * Capital Population)-1). If you have Machu Pichu multiply the result by 1.25.

HOWEVER, if you add up the detail for the City Connections in this screen they will add up to more than the aggregate shown. The difference is that the aggregate shown does not include the portion of the City Connection value represented by the Capital.

I think the programmers made an error here. I think in calculating the value of the aggregate City Connections they plugged in the aggregate value of the populations of the connected Cities rather than add up the individual values of each City Connection, thereby losing the small increment value which the Capital adds. In Civs with many cities this can add up to a significant error.