I’m trying to make a digital version of Monopoly, and it would be easiest for me if I could use the base rent of a property to determine the rent with any number of houses. Is there a formula/equation that can be used to do so?
There is no formula that the game uses, different properties go up at different rates, and not always a consistent rate. You'll need to hard code the per property rent values into your system unfortunately.
Here are the Rents for all of the Monopoly properties that can be developed, with their names in both the traditional Atlantic City version as well as the London England version: