Evidence shows that the Sumerians, around 4000 years ago in Mesopotamia (modern-day Iraq and surrounding area), were possibly the first culture in the Earth's recorded history to formulate a formal solar calendar, which had 365 days. The Babylonians (after approximately 2500 BC) also devised an official calendar, but based it on solar and lunar cycles (luni-solar). The Hebrew calendar is also luni-solar and its origins are believed to be linked to the Babylonians.

The most accurate ancient lunar calendar may have been formulated by the Chinese after approximately 500 BC. Although based on lunar cycles, it's really a luni-solar calendar, like the Babylonian and Hebrew calendars; its starting point varies each year being roughly synchronized with the solar calendar/tropical year (about 365 days long).

The Maayan appeared to possess the most accurate calendar in recorded history up until around 1000 AD, varying less than 1 minute a year from our modern Gregorian calendar.

The Persian calendar in the Middle Ages around 1070 AD, thanks to astronomer Omar Khayyam, surpassed the accuracy of the Mayan model. This is not surprising, considering the Persians' and Arabs' superior scientific (especially astrological) contributions in the Middle Ages. After Omar Khayyam's Persian calendar corrections were officially adopted, this calendar was also more accurate than the Julian calendar, which preceded our current Gregorian calendar. Omar Khayyam calculated the solar year to be 365.24219858156 days long, accurate to the sixth decimal place.

The ancient Egyptians formed a calendar (12 30-day months plus five days to equal 365 days) before 2400 BC based on the star Sirius (they called this star Sothis). They noticed that this star would appear in the east just before sunrise every year around the time of the Nile's annual flood. A Sothic cycle is 1460 years and is defined by the heliacal rising of Sirius returning to the exact same point. Respected for its mathematical reliability, this calendar was used by astronomers in the Middle Ages.

The Egyptians' seasonal year, the time between the consecutive heliacal risings of the star Sirius, is remarkably close to the actual length of the solar year. However, the approximate six hour difference means that over just a couple of centuries their calendar would have been totally out of synch with the timing of the seasons in relation to the solar year. The Egyptian astronomers quickly identified this problem and apparently tried to compensate by using a second lunar calendar, which tied into the solar cycle. A Lunar calendar was also followed for festivals.

The Romans, under Julius Cesar, influenced by the astronomer Sisogenes of Alexandria Egypt, recognized the sophisticated astronomical skills of the Egyptians and adopted the Egyptian star (Sirius) calendar around 50 BC, and added one day to the calendar every four years (leap year) to adapt to the solar cycle. They abandoned their lunar calendar and the Julian calendar, forerunner to our modern Gregorian calendar, was born.

An aside, a Metonic cycle (invented by the 5th century BC Greek astronomer Meton) is 6940 days including 235 Lunar months comprising almost exactly 19 solar years. The 19-year cycle is significant as every 19 years the Moon and the Sun are aspected identically, on the same day of the year (the Metonic cycle's error rate is about 12 hours every 109.5 years: 19 tropical years = 6939.602 days and 235 Synodic months = 6939.688 days).

A Callippic cycle (presented in 4th century BC by the Greek astronomer Callippus) is a 76-year cycle equivalent to four Metonic cycles, less one day. It's a modification of the Metonic cycle. These cycles, widely used by ancient Egyptian and other astronomers before the Alexandrian calendar reform (under Julius Cesar), are important for sequential functions, and are superb cyclical timing considerations that can be used to outline fated life circumstances.

It's interesting that the Julian calendar's implementation took place in year 1 of a Metonic cycle, 19 years from a complete 76-year Callippic cycle, which suggests that the designers of the calendar were heavily influenced by the standards of the mathematical precision of the Metonic and Callippic cycles.

Even though the .25/day addition every year resulted in the Julian calendar being only about .00781 days from the true solar cycle, this difference yielded about a ten day error by the 1500's.

In 1582 the Gregorian calendar reform was adopted under the reign of Pope Gregory XIII to correct the inaccuracies of the Julian calendar. Striving for mathematical exactitude in calculating the length of the tropical year (the cycle of the seasons or solar year, defined as the time interval between vernal equinoxes), the scientists of that era dictated that the new universal calendar first drop 11 days from the old calendar as of October 4th, 1582 (making that day October 15th) and then initiated a leap year system adding a day every four years (except in century years evenly divisible by 400 or 4000). Although not perfect, this improved the solar calendar year to 365.2422 days, an error of about one day every 3300 years.