Days in Month Calculator

Gregorian month lengths are fixed by convention rather than by any astronomical cycle: seven months carry 31 days, four carry 30, and February carries 28 or 29. Only February varies, under a three-part rule - a year is a leap year if divisible by 4, except that century years must also be divisible by 400. That rule tracks the mean tropical year of about 365.2422 days. The Julian scheme of one leap year in four assumes 365.25 days and runs fast by roughly 11 minutes a year, about three days every four centuries; dropping three leap days per 400 years brings the Gregorian mean year to 365.2425 and leaves a residual error of only about one day in 3,000 years. The weekday breakdown depends on the starting weekday as well as the length. A 31-day month spans four full weeks plus three days and therefore contains 21 to 23 weekdays and 8 to 10 weekend days; a 30-day month contains 20 to 22 weekdays; a 28-day February always contains exactly 20 weekdays and 8 weekend days, while a 29-day February contains 20 or 21. These counts exclude public holidays, which are jurisdiction-specific, so they are an upper bound on working days rather than a payroll answer. The total-hours figure assumes every day is exactly 24 hours, which fails in months containing a daylight saving transition - in the United States, March has one 23-hour day and November one 25-hour day. Financial day-count conventions such as 30/360 add a further wrinkle, treating every month as 30 days regardless of the calendar.

The uneven month lengths are a Roman inheritance. The addition of January and February to an earlier ten-month calendar is traditionally credited to Numa Pompilius around 713 BC, producing a 355-day year kept roughly in step with the seasons by inserting an intercalary month at the discretion of the pontiffs, a discretion abused for political ends until the calendar had drifted badly. Julius Caesar, advised by the Alexandrian astronomer Sosigenes, imposed the solar reform that took effect in 45 BC, fixing the month lengths close to their modern values and adding one leap day every fourth year; the transitional year 46 BC was stretched to 445 days and is remembered as the year of confusion. Quintilis was renamed for Caesar, and Sextilis for Augustus in 8 BC. The familiar story that Augustus stole a day from February so that his month would not be shorter than July traces to the medieval writer Sacrobosco in the thirteenth century and is treated with scepticism by modern scholars. The Julian year of 365.25 days was itself too long, and by the sixteenth century the vernal equinox had slipped about ten days from its position at the Council of Nicaea in 325. The correction, designed largely by Aloysius Lilius and elaborated by the Jesuit mathematician Christopher Clavius, was promulgated by Pope Gregory XIII in the bull Inter gravissimas of February 1582; October 4 was followed directly by October 15. Adoption was slow and religiously divided: Britain and its colonies did not switch until September 1752, when eleven days were dropped.