Every paid time off policy comes down to one line of arithmetic: a rate, multiplied by the time that has passed, added to whatever you had already banked. The confusion comes from the units, because policies are written in hours per paycheck, days per year, or hours earned per hour worked, and the number on your pay stub is almost always in hours.
The formula
PTO balance = starting balance + (hours accrued per pay period x pay periods completed)
Worked example
Take an offer letter that promises 15 paid days a year, paid every two weeks. First convert the days to hours: 15 days at 8 hours each is 120 hours a year. Then divide by the 26 biweekly paychecks in a year, which gives 4.62 hours added to your balance every payday. Six months in, after 13 paychecks, you have banked 60 hours, or 7.5 days off.
The calculator above does this for any combination of rate and pay frequency, and it counts only whole completed pay periods, which is how balances actually post. It does not subtract time off you have already taken, so if you have used days since the start date you set, take those hours off the result yourself.