There's a really nice article explaining upkeep mechanics on the strategy forum.
It's also available under Strategy Guides in the Civilopedia when you install the BUG mod.
To cut a long story short - the upkeep formula scales linearly with Number of Cities and Total Population.
The coefficients of this linear function depend on the Civic Upkeep ("None" vs. "Low" vs. "Medium" vs. "High") of each of the five civics you are running.
To make things extra complicated, there is a separate linear function for each Civic category, which sum up to make your total Civic Upkeep. Certain numbers (different in each civic category) are subtracted from "number of cities" and "total population" (the result is set to zero if it is negative). There is also a rounding step prior to summing the five Upkeep costs.
However, the easiest way to conceptualise the formula (if it weren't for the complicated rounding and floor functions) is that:
The upkeep you pay "for" each population AND "for" each city depends on the "sum" of your upkeep categories (with specific coefficients for none, low, medium, high). Small empires benefit from a "minimum threshold" on the first few cities/population points.
The rounding process and differing thresholds "soften out" this change.
