Day Calculator

Counting days between two dates is harder than it looks because the civil calendar is irregular by design. Months hold 28, 29, 30 or 31 days, and the Gregorian leap rule adds a day in years divisible by 4 except centuries not divisible by 400, which is why 2000 was a leap year and 1900 was not. That gives an average year of 365.2425 days against a tropical year of 365.2422, an error of one day in about 3,200 years. Rather than walk the calendar, the reliable method is the one used here: convert both dates to a linear count from a fixed epoch, subtract, and divide by 86,400,000 milliseconds per day. Leap years, varying month lengths and century exceptions are then handled automatically because they are already baked into the epoch mapping. Two conventions decide whether an answer is right. Exclusive counting returns the interval between the endpoints, so 1 January to 3 January is 2 days; inclusive counting counts both endpoints and returns 3. Contracts and court deadlines each specify one or the other, and a single day frequently matters. Calendar days also differ from business days, which exclude weekends and public holidays. Finance adds further conventions still: bond and loan interest is accrued using explicit day-count bases such as actual/365, actual/360 or 30/360, under which a period can be assigned a day count that does not match the calendar at all. A minor practical caveat is daylight saving time, which makes a local civil day 23 or 25 hours long twice a year.

The modern day count rests on two calendar reforms. Julius Caesar, advised by the Alexandrian astronomer Sosigenes, replaced the erratic Roman calendar in 46 BC with a solar year of 365 days plus one leap day every fourth year. That average of 365.25 days ran about 11 minutes and 14 seconds longer than the solar year, an error that accumulated to roughly ten days by the sixteenth century and pushed the date of the equinox away from the position assumed by the Church's calculation of Easter. Pope Gregory XIII issued the bull Inter gravissimas in February 1582, adopting the refined leap rule and deleting ten days so that 4 October 1582 was followed directly by 15 October. Catholic states switched immediately while Protestant and Orthodox ones took centuries: Britain and its American colonies adopted the reform in 1752, dropping 3 through 13 September, and Russia only in 1918. The resulting mess of local calendars is why the astronomer Joseph Justus Scaliger proposed the Julian Period in 1583, a simple continuous count of days from 1 January 4713 BC that astronomers still use as the Julian Day Number. Computing inherited the same idea in the form of an epoch count, notably the Unix epoch of 1 January 1970, and ISO 8601, first published in 1988, standardized the unambiguous year-month-day notation these calculations depend on.