Introduction to Calendars

John P. Pratt

What is a Calendar?

A calendar is a system for keeping track of time, usually tied to some sort of celestial repeating cycles. The simplest calendars simply keep track of days in a continuous count. Modern astronomers keep a Julian Day Count, which is simply a continuous count of days starting from an arbitrary date before recorded history. For example, Oct. 9, 1995, was Julian Day number 2,450,000. The Mayans also had a continuous day count, called the "long count." The Julian Day number is useful to astronomers to easily calculate a time interval between two events, but it is not useful in everyday life which we like to arrange in cycles, such as the week, month, and year. When would we celebrate birthdays or anniversaries if all we had was a continuous day count?

Solar Calendars

A solar calendar keeps track of the sun. The sun has an annual seasonal cycle of long days in the summer and short days in the winter. It's very important for farmers, skiers, and campers to known when the seasons will be, so we have a solar calendar to tell us. Formerly, we used the Julian Calendar and today we use the Gregorian calendar. Let's look at each.

Julian Calendar

The Julian Calendar is named for Julius Caesar, who introduced it in 45 B.C. It has 365 days, divided into twelve months, beginning on Jan. 1. It adds a leap day on Feb. 29th every 4 years, so that the years average 365.25 days each. That is very close to the true value of 365.242 days for the length of the earth's orbit around the sun, so it makes an excellent calendar. It was used until 1582, when it was discovered that the little error of .008 days every year had added up to 10 full days, so that the first day of spring on the calendar was getting too close to being in the summer. Don't confuse it with the Julian Day used by astronomers, named after Julian Scaliger.

Gregorian (or "New Style") Calendar

The correction that Pope Gregory XIII made was to skip the leap year in three out of every four century years. Thus, the years 1700, 1800, and 1900 were not leap years, but 2000 will be a leap year. That is a very minor correction, but it makes the average year be 365.2425 days which is very close to the true value. This keeps the spring equinox, when the sun rises most nearly due east, either on March 20 or 21 every year. It is also called the "New Style" calendar.

Today virtually the entire world uses the Gregorian calendar, but they didn't all switch at once. The Catholic countries of Italy, France and Spain began in 1582 with the Pope, but Protestant countries were not anxious to follow his lead. Finally in 1751 England and her colonies made the switch. Other countries did not do so until this century, especially those of the Eastern Orthodox religion, who switched about 1940. Our family recently had some Russian professors stay at our home, who invited us to their Easter service. We were all disappointed because their church in our country had switched over to the Gregorian calendar, so they celebrated Easter on a different day!

"Old Style" Calendar

Before 1751 the English had their own version of the Julian Calendar, called the "Old Style" calendar, in which the year began on March 25. That is, the day after March 24, 1710 was March 25, 1711. That was very confusing in a world where everyone else changed the year on Jan. 1. They solved the problem by putting both years down for dates in Jan., Feb., and March (before the 25th). That is, newspapers would give the date as February, 1730/31, with both the old style and new style years. The same was true for the colonies: George Washington was born on Feb. 11, 1731 (Old Style), which we celebrate as Feb. 22, 1732 on the Gregorian Calendar.

Lunisolar Calendars

Calendars which track both the sun and moon are called lunisolar ("luni" = moon, "solar" = sun), and most of the world's early calendars were lunisolar. They use the months to keep track of the moon ("moonths") and years to keep track of the sun. Although virtually every country uses the Gregorian calendar for commerce, many countries and religions keep a lunisolar calendar for certain holidays. For example, the Chinese calendar and Hebrew calendar are lunisolar.


On our Gregorian calendar, the months are merely arbitrary divisions of the year. On a lunisolar calendar, every month begins at the new moon, when the moon is invisible, or on the first night when it is barely visible in the west after sunset as a very thin crescent. It takes 29.53 days for the moon to complete its cycle of phases, so lunar months approximately alternate between 29 and 30 days so that they average 29.53 days in length. On a lunisolar calendar, simply knowing the day was the 15th of the month tells you that it was within a day of the full moon.


A lunisolar calendar also needs to have a year length equal to the seasonal cycle of 365.24 days, but 12 lunar months only total 354 days, which is about 11 days short of a year! It cannot use "leap days" to make the year come out right, because they are being used for the month. It was because this problem seemed hard and because people decided they didn't care where the moon was that led them to abandon the lunisolar calendar and switch to the Julian Calendar.

But the problem is not all that hard. One simply inserts an entire "leap month" when necessary to make the year come out right on the average. If 12 lunar months are about 11 days short of a year, then 36 would be about 33 days short, so about every three years a lunisolar calendar inserts ("intercalates") an entire 13th month. The Hebrew Calendar inserts 7 extra months every 19 years in what is called the Metonic Cycle, after a Greek astronomer. That gives an average year of 365.247 days which is better than the Julian Calendar but not as accurate as the Gregorian.

What is implied in a lunisolar calendar is that it is more important to know where the moon is than to have every season begin on exactly the same solar day every year. In reality, there is a lot of variation in just when seasons actually begin every year, so in practice a one month variation in the beginning of the year is not a problem for most farming efforts. In our modern world, however, there are other endeavors for which we would like more precision in the length of a year (such as financial dealings), so it is preferred to use the Gregorian solar calendar for commerce.

Other differences between the Hebrew calendar and the Gregorian are that the Hebrew day begins at 6:00 p.m. (formerly at the appearance of the third star after sunset), and the year begins in the fall, usually in September (on Rosh Hashanah). The Chinese year begins in January /February.

The Week

The week is a continuous cycle of seven days, which forms an uninterrupted day count. It turns out that seven days is the best length for a day count for a lunisolar calendar, because 7 approximately divides into the length of the month (28 is near 29.53) and also the year (52 weeks = 364 days is close to 365.24). The Hebrew calendar is tied to the week in that the Hebrew year can only begin on 4 of the 7 week days. On the other hand, the Gregorian calendar is not really tied to the week at all. That is, even though we arrange the Gregorian days in a blocks of seven days, the Gregorian calendar is really totally separate from the week (except for holidays which tend to be on Mondays). When we switched from the Julian Calendar to the Gregorian, the week was not interrupted. That is, when the ten-day shift was made, Thursday, Oct. 4, 1582 (Julian), was followed by Friday Oct. 15 (Gregorian).

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