How to calculate the number of days in a period?

There is no way to do what you ask. The reason is that it is not possible from a Period to deduce the actual number of calendar days in the period. A Period is not tied to specific dates, once constructed in the way you show, it loses track of the actual calendar dates.

For example your first period represents a period of 1 month and 1 day. But the period does not care which month. It is simply a concept of "a month and a day".

If you need the number of days between two dates you should use ChronoUnit.DAYS.between as Saket Mittal writes.

From the documentation:

To define an amount of time with date-based values (years, months, days), use the Period class. The Period class provides various get methods, such as getMonths, getDays, and getYears.To present the amount >of time measured in a single unit of time, such as days, you can use the ChronoUnit.between method.

LocalDate today = LocalDate.now();
LocalDate birthday = LocalDate.of(1960, Month.JANUARY, 1);

Period p = Period.between(birthday, today);
long p2 = ChronoUnit.DAYS.between(birthday, today);
System.out.println("You are " + p.getYears() + " years, " + p.getMonths() +
                   " months, and " + p.getDays() +
                   " days old. (" + p2 + " days total)");

The code produces output similar to the following:

You are 53 years, 4 months, and 29 days old. (19508 days total)