Claus Tøndering –
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Miscellaneous questions

What day is the leap day?

It is 24 February!

Weird? Yes! This derives from the Roman calendar, and a detailed explanation is given in the section about the way Romans numbered their days.

From a numerical point of view, of course 29 February is the extra day. But from the point of view of celebration of feast days, the following correspondence between days in leap years and non-leap years has traditionally been used:

Non-leap yearLeap year
22 February22 February
23 February23 February
24 February (extra day)
24 February25 February
25 February26 February
26 February27 February
27 February28 February
28 February29 February

For example, the feast of St. Leander has been celebrated on 27 February in non-leap years and on 28 February in leap years.

In some countries the 25th rather than the 24th of February is considered the leap day.

Many countries are gradually changing the leap day from the 24th to the 29th. This affects countries such as Sweden and Austria that celebrate “name days” (i.e. each day is associated with a name).

What is the proleptic calendar?

The Julian calendar was introduced in 45 BC, but when historians date events prior to that year, they normally extend the Julian calendar backward in time. This extended calendar is known as the “Julian Proleptic Calendar”.

Similarly, it is possible to extend the Gregorian calendar backward in time before 1582. However, this “Gregorian Proleptic Calendar” is not commonly used.

If someone refers to, for example, 15 March 429 BC, they are probably using the Julian proleptic calendar.

In the Julian proleptic calendar, year X BC is a leap year, if X–1 is divisible by 4. This is the natural extension of the Julian leap year rules.

Has the year always started on 1 January?

In some ways, yes. When Julius Caesar introduced his calendar in 45 BC, the year started on 1 January, and it was always the date on which the Solar Number and the Golden Number were incremented.

However, the church didn’t like the wild parties that took place at the start of the new year, and in AD 567 the council of Tours declared that having the year start on 1 January was an ancient mistake that should be abolished.

Through the middle ages various New Year dates were used. If an ancient document refers to year X, it may mean any of 7 different periods in our present system:

  • 1 Mar X to 28/29 Feb X+1
  • 1 Jan X to 31 Dec X
  • 1 Jan X–1 to 31 Dec X–1
  • 25 Mar X–1 to 24 Mar X
  • 25 Mar X to 24 Mar X+1
  • Saturday before Easter X to Friday before Easter X+1
  • 25 Dec X–1 to 24 Dec X

Choosing the right interpretation of a year number is difficult, so much more as one country might use different systems for religious and civil needs.

The Byzantine Empire used a year starting on 1 Sep, but they didn’t count years since the birth of Christ, instead they counted years since the creation of the world which they dated to 1 September 5509 BC.

Since about 1600 most countries have used 1 January as the first day of the year. Italy and England, however, did not make 1 January official until around 1750.

In England (but not Scotland) three different years were used:

  • The historical year, which started on 1 January.
  • The liturgical year, which started on the first Sunday in advent.
  • The civil year, which
  • from the 7th to the 12th century started on 25 December,

    from the 12th century until 1751 started on 25 March,

    from 1752 started on 1 January.

It is sometimes claimed that having the year start on 1 January was part of the Gregorian calendar reform. This is not true. This myth has probably started because in 1752 England moved the start of the year to 1 January and also changed to the Gregorian calendar. But in most other countries the two events were not related. Scotland, for example, changed to the Gregorian calendar together with England in 1752, but they moved the start of the year to 1 January in 1600.

Then what about leap years?

If the year started on, for example, 1 March, two months later than our present year, when was the leap day inserted?

[The following information is to the best of my knowledge true. If anyone can confirm or refute it, please let me know.]

When it comes to determining if a year is a leap year, since AD 8 the Julian calendar has always had 48 months between two leap days. So, in a country using a year starting on 1 March, 1439 would have been a leap year, because their February 1439 would correspond to February 1440 in the January-based reckoning.

What is the origin of the names of the months?

A lot of languages, including English, use month names based on Latin. Their origin is listed below. However, some languages (Czech and Polish, for example) use quite different names.

January Latin: Januarius. Named after the god Janus.
February Latin: Februarius. Named after Februa, the purification festival.
March Latin: Martius. Named after the god Mars.
April Latin: Aprilis. The origin of the name is unknown. It may come from the Latin word aperire (“to open”), or – more likely – from the ancient Latin prefix apter- (“subsequent”).
May Latin: Maius. Named after the goddess Maia or the god Maius.
June Latin: Junius. Named after the goddess Juno.
July Latin: Julius. Named after Julius Caesar in 44 BC. Prior to that time its name was Quintilis from the word quintus, fifth, because it was the 5th month in the old Roman calendar.
August Latin: Augustus. Named after emperor Augustus in 8 BC. Prior to that time the name was Sextilis from the word sextus, sixth, because it was the 6th month in the old Roman calendar.
September Latin: September. From the word septem, seven, because it was the 7th month in the old Roman calendar.
October Latin: October. From the word octo, eight, because it was the 8th month in the old Roman calendar.
November Latin: November. From the word novem, nine, because it was the 9th month in the old Roman calendar.
December Latin: December. From the word decem, ten, because it was the 10th month in the old Roman calendar.

The Indiction of 2024:


What is the Indiction?

The Indiction was used in the middle ages to specify the position of a year in a 15 year taxation cycle. It was introduced by emperor Constantine the Great on 1 September 312 and ceased to be used in 1806.

The Indiction may be calculated thus:

Indiction = (year + 2) mod 15 + 1

The Indiction has no astronomical significance.

The Indiction did not always follow the calendar year. Three different Indictions may be identified:

  • The Pontifical or Roman Indiction, which started on New Year’s Day (being either 25 December, 1 January, or 25 March).
  • The Greek or Constantinopolitan Indiction, which started on 1 September.
  • The Imperial Indiction or Indiction of Constantine, which started on 24 September.

What is the correct way to write dates?

The answer to this question depends on what you mean by “correct”. Different countries have different customs.

Most countries use a day-month-year format, such as:

25.12.1998         25/12/1998         25/12-1998         25.XII.1998

In the U.S.A. a month-day-year format is common:

12/25/1998         12-25-1998

International standard ISO 8601 mandates a year-month-day format, namely either

1998-12-25   or   19981225.

This format is gaining popularity in some countries.

In all of these systems, the first two digits of the year are frequently omitted:

25.12.98         12/25/98         98-12-25

However, although the last form is frequently seen, it is not allowed by the ISO standard.

This confusion leads to misunderstandings. What is 02-03-04? To most people it is 2 March 2004; to an American it is 3 February 2004; and to a person using the international standard it could be 4 March 2002 (although a year specified with only two digits does not conform to the ISO standard).

If you want to be sure that people understand you, I recommend that you

  • write the month with letters instead of numbers, and
  • write the years as 4-digit numbers.

In calendrical calculations, we frequently use an operation call integer division.

Ordinarily we would say that, for example, 14 divided by 5 is 2.8. But when we use integer division, we discard the decimal fraction and simply state that 14 divided by 5 is 2.

We indicate that we use integer division by enclosing the division between the symbols   and   , for example thus:

  14/5   = 2

or thus:

= 2

When we perform integer division, the division leaves a remainder. In the case of 14 divided by 5, the remainder is 4: We can subtract 5 twice from 14, and this leaves us with 4.

We use the mathematical operator ‘mod’ to indicate the remainder. This is known as the modulo operator. We therefore have:

14 mod 5 = 4

If you want to use integer division in computer programs, you must realize that different programs use different notations for the operations. The following table shows how integer division and the modulo operator may be written:

Integer division Modulo
The Calendar FAQ   14/5   14 mod 5
Microsoft Excel (English) INT(14/5) MOD(14,5)
Visual Basic 14 \ 5 14 Mod 5
C, C#, C++ 14 / 5 14 % 5

NOTE: What is said here only applies to division of positive numbers. Different programming languages handle integer division of negative numbers differently; therefore the formulas in the Calendar FAQ avoid using these operations on negative numbers.