A calendar is any system that uses observations of cyclic motions of celestial bodies and/or the climate seasons on Earth to schedule or record the activities of human beings, or one that uses mathematics to approximate such observations.
Calendars have been in use throughout recorded history. The Bible tells us  that the use of a calendar goes back to antediluvian times. Ancient Egypt had a calendar, as did virtually every superpower in the ancient world.
Rome's calendar came to dominate the ancient world at the points of the swords and spears of Rome's legendary legions. Julius Caesar's reforms of that calendar made it one of the most useful of the ancient calendars; Pope Gregory IX would reform the calendar further more than a millennium and a half later. Muhammad, the great general and "prophet" of the Arab world, invented a calendar of his own and spread that throughout the Middle East at the points of the scimitars of his own armies. China has always had a calendar of its own and has never totally abandoned it.
In the eighteenth century AD, the French mathematician Joseph Lagrange, as head of the French Revolutionary weights-and-measures committee, devised an observed solar calendar with months named for growing, harvesting, and climate seasons, not for Roman numbers (September, October, November, December) or dead Roman emperors (July, August) or gods (January, February, March, June, etc.). But he also abandoned the seven-day week of the Julian and Gregorian calendars in favor of a ten-day week (called a décade in French). Perhaps this feature more than any other made the calendar impractical. (The Biblical model is clearly a week of six days of labor and one day of rest; see Genesis 1 .) In any event Emperor Napoleon I switched back to the Gregorian calendar in 1806, probably to retain the favor of the Popes of Rome as he continued his attempts to conquer the world. A short-lived political movement called the Paris Commune would revive the French republican calendar toward the end of the nineteenth century but would then abandon it two years later.
In summary, calendars have tended to come into being as much for ideological reasons, or the vanity of any particular ruler, as for practical reasons. Likewise, they tend to fall out of popular use as much on account of military conquest as on account of the relative fidelity of any given calendar to the seasons or astronomical cycles it is supposed to chart.
Thus the Gregorian calendar owes its dominant acceptance worldwide as much to the spread of Christianity as to its actual utility. Nor is that dominance complete; the Chinese, for example, maintain a calendar of their own, as do most Muslim nation-states. At the opposite extreme is the French republican calendar, a calendar born in ideology and later abandoned after a later ruler found the calendar not merely impractical but also politically imprudent to retain.
The prophet Daniel predicted  that a totalitarian world leader would make one final change of the calendar before God would return and, among other things, decree His own calendar as part of His direct Millennial rule. (See Revelation 19-20 .)
Types of calendars
Observed versus calculated
A calendar can be either observed or calculated. An observed calendar relies on regular adjustment by some designated human authority that receives reports of astronomical and/or seasonal observations. The briefly-used French republican calendar was an observed calendar, in that the officials in charge of weights and measures declared leap years when necessary to begin the calendar, without fail, on the autumnal equinox as observed in Paris. The ancient Hebrews, in Biblical days, also used an observed calendar prior to their Captivity.
Astronomical calendars (not to be confused with astronomical dating) use the orbital periods of the earth and the moon, the apparent motions of the sun, and sometimes the periods and motions of the stars and other celestial bodies (including Jupiter with its synodic year of slightly more than 399 days). The Egyptian calendar allegedly used an astronomical body called Sothis, though its precise identification remains an unsettled controversy. The Bible tells us that God specifically created the sun, moon, and stars to help humankind reckon the seasons and years.
Lunar calendars synchronize the months with the synodic period of the moon. A purely lunar calendar would be about 354 days long, because the average synodic month (that is, the period of the moon's appearance in the sky of earth) is less than 30 days. Typical lunar calendars have twelve months in a year, alternating between 30 and 29 days.
Failure to adjust such a calendar causes it to cycle without regard to the seasons. The Islamic calendar is the one remaining true lunar calendar in widespread use; its failure to have a seasonal corrective is a matter of speculation. The ancient Roman calendar was subject to seasonal adjustment, but the repeated failures of various chiefs of the Roman state religion to attend to this adjustment finally led Julius Caesar to change Rome's calendar from lunar to solar.
Solar calendars synchronize strictly to the apparent motions of the sun. Phases of the moon tend to occur almost at random within any given month, but solar calendars tend to track faithfully with agricultural seasons over many years. The Julian calendar and its successor the Gregorian calendar are the two solar calendars in most widespread use today.
Luni-solar calendars begin and end their months by the phases of the moon, but adjust themselves to track the sun as well. The modern Hebrew calendar is the best-known luni-solar calendar in use today. The Biblical calendar was supposed, by Sir Isaac Newton, to be a luni-solar calendar. But in fact it was probably a luni-seasonal calendar that relied on the ripening of a particular crop to signal the first month of spring.
Agricultural or seasonal calendars are far less common than the astronomical. These calendars track various growing or harvesting seasons. Such a calendar might vary from year to year on account of the mildness or harshness of winter or, less commonly, summer. But a seasonal calendar would always stay more-or-less true to solar or stellar apparent motions on average.
Though no pure seasonal calendar is in common use today, the Biblical calendar was probably a luni-seasonal calendar until the Babylonian captivity, when the Hebrews came under the influence of the Babylonians, arguably the foremost astronomers of their day.
The French republican calendar pretends to be an agricultural-meteorological seasonal calendar, with its months named for the seasons of growing, harvesting, or climate. But it is not a true seasonal calendar, because it makes no allowances for adjustment from agricultural or meteorological observations.
- Walker, John. "Fourmilab Calendar Converter." Fourmilab Switzerland. Accessed April 9, 2008.
- "Chronologie, eres, et calendriers" (Chronology, Eras, and Calendars). Institut de mécanique célèste et de calcul des éphémerides (Institute of Celestial Mechanics and Ephemeral Calculation), Paris, France. Accessed April 9, 2008.
- Genesis 7
- Daniel 7:25
- Newton, Sir Isaac. The Chronology of Ancient Kingdoms Amended. Reproduced by Project Gutenberg. Accessed April 3, 2008.
- Genesis 1:16-18
- Jones, Floyd N. The Chronology of the Old Testament, 16th ed. Green Forest, AR: Master Books, 1993-2007 (ISBN 9780890514160), pp. 106-109