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Road Maintenance /Road/Turn
Difficulty | Your Land | Neutral
-----------|-----------|--------
Settler    |     1/3g  |   1/3g
Chieftain  |     1/2g  |   1/2g
Warlord    |    7/10g  |  7/10g
Prince     |       1g  |     1g
5-7*       |       1g* |     1g*
Deity      |       1g  |     1g

In the case of fractions, multiply by your number of roads, then round down.

To find each of these, I built roads either only inside, or only outside my borders at a time. Warlord's 7/10g is an odd number, but that's the best fit (rounding down all fractions when totaling maintenance) after building a full 10 roads, both inside and outside my borders. I did not build enough roads to be certain of 1/3 or 1/2, but those are close enough numbers to see the trend, and I'm not bothered by some small error on those numbers. (If anyone would like to test those more fully, I would be happy to post the exact number.)

Also, I was quite surprised that Deity had a 1g still. I checked that I was really playing on Deity and built several roads, all costing another 1g, so that's what I'm going with. I'm still open to someone finding a mistake in my test, since that's such an odd result.

*Having found 1g at Deity, I skipped testing the in-between difficulties, since they would not be anything BUT 1g. As long as no mistakes are found in Prince-Deity all costing 1g/road/turn, 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 will double check Deity again, then re-test road's in another nation's borders, to clean up the next section! Same Bat-time. Same Bat-channel.

Road Maintenance /Road/Turn
Difficulty | Your Land | Neutral
-----------|-----------|--------
Settler    |    0.34g  |  0.34g
Chieftain  |    0.50g  |  0.50g
Warlord    |    0.75g  |  0.75g
Prince     |    1.00g  |  1.00g
5-7*       |    1.00g  |  1.00g
Deity      |    1.00g  |  1.00g

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.

This is contrary to what bwarner writes, so ... Pics Or It Didn't Happen!

However, either the difficulty or being outside changed the cost/tile, meaning I needed 3 tiles to produce 1g maintenance. This requires more testing, and makes the screenshots I posted for the next section suspect. (I made them from the same save game)

Because my conclusions are contrary to previous info we had about road maintenance in neutral territory... Pics Or It Didn't Happen!

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 /Road/Turn
Difficulty | Your Land | Neutral
-----------|-----------|--------
Settler    |     1/3g  |   1/3g
Chieftain  |     1/2g  |   1/2g
Warlord    |    7/10g  |  7/10g
Prince     |       1g  |     1g
5-7*       |       1g* |     1g*
Deity      |       1g  |     1g

In the case of fractions, multiply by your number of roads, then round down.

To find each of these, I built roads either only inside, or only outside my borders at a time. Warlord's 7/10g is an odd number, but that's the best fit (rounding down all fractions when totaling maintenance) after building a full 10 roads, both inside and outside my borders. I did not build enough roads to be certain of 1/3 or 1/2, but those are close enough numbers to see the trend, and I'm not bothered by some small error on those numbers. (If anyone would like to test those more fully, I would be happy to post the exact number.)

Also, I was quite surprised that Deity had a 1g still. I checked that I was really playing on Deity and built several roads, all costing another 1g, so that's what I'm going with. I'm still open to someone finding a mistake in my test, since that's such an odd result.

*Having found 1g at Deity, I skipped testing the in-between difficulties, since they would not be anything BUT 1g. As long as no mistakes are found in Prince-Deity all costing 1g/road/turn, 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 will double check Deity again, then re-test road's in another nation's borders, to clean up the next section! Same Bat-time. Same Bat-channel.

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

This is contrary to what bwarner writes, so ... Pics Or It Didn't Happen:

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!

Roads DO NOT cost to maintain inside another nation's borders

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.

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

This is contrary to what bwarner writes, so ... 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.

However, either the difficulty or being outside changed the cost/tile, meaning I needed 3 tiles to produce 1g maintenance. This requires more testing, and makes the screenshots I posted for the next section suspect. (I made them from the same save game)

Roads DO NOT cost to maintain inside another nation's borders

Edit: 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.