How prorating works
When a tenancy begins or ends in the middle of a month, the tenant should only pay for the days they actually have the unit. The fair way to work that out is to divide the full monthly rent by the number of days in that specific month to get a daily rate, then multiply by the days occupied. Because months range from 28 to 31 days, calculating by the real month keeps the daily rate honest.
Move-in versus move-out
For a move-in, count from the move-in date to the last day of the month. For a move-out, count from the first of the month to the move-out date. The calculator handles both, and shows the days occupied, the days in the month, and the daily rate, so the number is easy to explain and easy to agree on.
Put it in writing
Prorated rent is one of those small details that causes friction when it is verbal and none when it is written down. Record the method, the daily rate, the days, and the total alongside the lease. Keeping rent and receipts and the lease record in one place means a partial first month never turns into a question three months later.