How do you calculate hospital payments by patient day level?

Unfortunately, there is no straightforward way to do this.

The hospital system in the United States is unique in the world for how incredibly complex and difficult it is to compute payments---and, probably not coincidentally, also unique in how expensive those payments end up being.

You can estimate how much you will end up paying for a given hospital stay using the chargemaster, an official document detailing the standard prices for each type of procedure, length of stay, etc.; but each hospital has its own chargemaster and they are often wildly different. I have linked the website the State of California uses to post all hospital chargemasters as an example; California does a good job of publishing all this data where it is easily accessible, but many states do not. Depending on the state you are interested in, you may be able to find all the chargemasters posted online---or you may not.

Even worse, the chargemaster is only a guideline. Hospitals frequently negotiate prices with different insurance providers that are considerably lower than their chargemaster prices. Medicare has what we economists call monopsony power---they comprise a substantial portion of the market by themselves, which gives them the power to negotiate even lower prices. Regulations established in Medicare Part D actually intentionally limited Medicare's capacity to negotiate lower costs. The argument was that the low prices were unfair to hospitals, but the costs for patients will almost certainly rise as a result.

In order to actually calculate the costs for a given patient, we need to know what hospital they are in, how long they stayed, and what procedures they received, and then we can look up all those expenses on the chargemaster. We may also need to know what sort of health insurance (or none) the patient has, and then what prices that insurance provider has negotiated with that particular hospital.

As a result of all this complexity and opacity in the system, prices can vary tremendously---by a factor of 10 or more---even for the same care in the same city. Depending on location and insurance, the same hospital stay can vary in price from as little as $10,000 to as much as $100,000.