Prorated rent is the partial rent a tenant owes for a partial month, charged when they move in or move out part way through a billing period. You take the monthly rent, turn it into a daily rate, and multiply by the number of days the tenant actually occupies the unit.
In practice
Say the rent is $1,500 a month and a tenant moves in on the 18th of a 30-day month, so they occupy the unit for 13 days (the 18th through the 30th). The two common methods give close but different answers. Using the actual days in that month, the daily rate is $1,500 ÷ 30, which is $50, and 13 days comes to $650. Using a 365-day year averaged into a daily rate, $1,500 × 12 ÷ 365 is about $49.32 a day, and 13 days comes to about $641.10.
Both are defensible. What is not defensible is picking the method that happens to pay you more this time and a different one next time. Choose one method, write it into the lease, and apply it the same way at move-in and move-out. The first full month then bills at the normal $1,500 on its regular due date.
Why it matters to a small landlord
Proration almost always lands on a turnover, which is the messiest week of the year for record keeping. You are collecting a deposit, a partial month, and a first full month near the same date, and it is easy to log the partial payment as if it were the full rent. That one mislabel throws off the tenant's on-time history and your income totals for the year. Getting the move-out side right matters every bit as much, since a departing tenant only owes through their last day, and the same daily math sits underneath the turnover numbers you carry into the next lease. If you reconcile every month, a partial charge is far less likely to slip through; the ten-minute monthly close is where I catch mine.
Prorated rent is really one number anchored to two events. Pin down the move-in date with a move-in inspection so there is no argument about which day the clock started, log the partial charge as its own line in your rent ledger rather than folding it into the first full month, and the math stays clean from the first day to the last.