With land connection:
C = (100 + DF + (4 * BTV) + (.004 * P)) * (1 + I)
C = cost to convert
BTV = Base tax value
DF = distance factor
P = Population
I = inflation
DF seems to range from 0 – 10 ducats, depending. I am not sure exactly how it is computed, but it is higher further away from your capital. Even maxed, it is not very material to the cost of the conversion.
Example:
Wales has a population of 25,850 and a base tax value of 6. Inflation is 20 percent and the distance factor is 2. Cost to convert is calculated as follows:
C = (100 + DF (4 * BTV) + (.004 * P)) * (1+I)
C = (100 + 2 + (4*6) + (.004*25850)) * (1+0.20)
C = (100 + 2 +24 + 103.40) * 1.20
C = 274
Very simple. Slightly more complicated (and expensive) for overseas provinces.
Here is the formula for converting cost with no land connection to the capital. Please note this includes all islands as well as provinces on the same land mass separated by other countries provinces, including your own vassals.
C = (175 + DF + (7 * BTV) + (.007 * P)) * (1 + I)
C = cost to convert
DF = distance factor
BTV = Base tax value
P = Population
I = inflation
Same as above but the costs are higher. Also, I am not sure exactly how the distance factor is calculated for provinces lacking a land connection. It appears to be a function of how far away the province is from the capital, since moving the capital changes the factor. It tends to be from 0 - 50d depending. For example, British-controlled Massachusetts is an extra 21d for the distance factor. Since there is no perfect way to calculate it, it is going to have to be estimated in most cases. Importantly, it is not a multiplier but a lump sum cost added, so it is usually not so important.
Example:
Delaware has a population of 15,250 and base tax value of 5. Inflation is at 10 percent and the distance factor is 24.
C = (175 + DF + (7 * BTV) + (.007 * P)) * (1 + I)
C = (175 + 24 + (7*5) + (.007*15,250)) * (1+0.10)
C = (175 + 24 +35 + 106.75) * 1.10
C = (340.75) * 1.10
C = 374.825