# A History of Calendars and The International Fixed Calendar

A couple of weeks ago, I was tasked with coming up with an
interesting fact for our daily standup meeting at work. I decided to
do a bit of Wikipedia research on calendars because they seemed kind
of interesting and I didn’t know *that* much about their
history. It turns out that the origins of our Gregorian calendar can
be traced back to earlier than the Roman kingdom. However, I had to
start somewhere and the first Roman calendar seemed like a good place
to start.

### The Romulan Calendar

The so-called Romulan calendar is attributed to Romulus, the first king and namesake of Rome. It consisted of 10 months starting with Martius and ending in December. The names of the months were named after Roman or Greek gods, or numbers. There were a total of 38 weeks, each lasting eight days. As these weeks only sum to 304 days, the remaining days were simply a period of time that spanned winter. This period would often last around 50 days.

However, there appear to be many differing accounts of how this calendar was actually organised so take this with a grain of salt. Note the names and lengths of each month are not so different from what they are today.

Month | Meaning | Length in Days |
---|---|---|

Martius | Month of Mars | 31 |

Aprilis | Month of Aphrodite | 30 |

Maius | Month of Maia | 31 |

Iunius | Month of Juno | 30 |

Quintilis | Fifth Month | 31 |

Sextilis | Sixth Month | 30 |

September | Seventh Month | 30 |

October | Eighth Month | 31 |

November | Ninth Month | 30 |

December | Tenth Month | 30 |

### The Roman Republican Calendar

The second king of Rome, Numa Pompilius, must have gotten sick of this “period of winter” business because the calendar was reformed around the year 450 BCE. The changes made to the calendar would (on average) bring the calendar year closer to the length of the tropical year (the time taken for the Earth to take one revolution of the Sun). Two months were added to the end of the calendar: Ianuarius and Februarius. Also, an intercalary month, Intercalaris, was added after Februarius every other year.

The Republican calendar would follow a four year cycle: common year, leap year, common year, and leap year. Intercalaris would occur on every leap year and Februaris would have a different number of days depending on which year in the cycle it occurred. This would bring the average number of days per calendar year to 365.75 days per year (there are 365.24219 days in a tropical year). This was due to the number of days in each year being either 355, 376, or 377.

At some point during the use of this calendar the three new months snuck into the front of the calendar instead of remaining at the end.

Month | Meaning | Length in Days |
---|---|---|

Ianuarius | Month of Janus | 29 |

Februarius | Month of Februa | 22, 23, or 28 |

Intercalaris | Intercalary Month | 27 |

Martius | Month of Mars | 31 |

Aprilis | Month of Aphrodite | 29 |

Maius | Month of Maia | 31 |

Iunius | Month of Juno | 29 |

Quintilis | Fifth Month | 31 |

Sextilis | Sixth Month | 29 |

September | Seventh Month | 29 |

October | Eighth Month | 31 |

November | Ninth Month | 29 |

December | Tenth Month | 29 |

### The Julian Calendar

The next major change of the calendar was made by non other than Julius Caesar. In the year 46 BCE, the roman general ordered the calendar to be reformed in order to bring it closer to the length of a tropical year. The year would now be 365.25 days long on average. The intercalary month was struck from the calendar and a single leap day was added to the end of Februarius (ideally) every four years. Days were added and removed from the other months as well.

A period of time was required for the new calendar to realign with the tropical year. Because of this, two intercalary months were added and the year 46 BCE was 445 days long!

In 44 BCE the month of Quintilis was renamed to “Julius” in honour of Julius Caesar. Similarly, in 8 BCE the month of Sextilis was renamed to “Augustus” after Augustus Caesar.

This calendar looked very similar to our current system and lasted the following 1500 years.

Month | Meaning | Length in Days |
---|---|---|

Ianuarius | Month of Janus | 31 |

Februarius | Month of Februa | 28 or 29 |

Martius | Month of Mars | 31 |

Aprilis | Month of Aphrodite | 30 |

Maius | Month of Maia | 31 |

Iunius | Month of Juno | 30 |

Julius | Month of Julius | 31 |

Augustus | Month of Augustus | 31 |

September | Seventh Month | 30 |

October | Eighth Month | 31 |

November | Ninth Month | 30 |

December | Tenth Month | 31 |

### The Gregorian Calendar

In 1582 Pope Gregory XIII introduced a reform of the Julian calendar. Due to the error between the length of the Julian year and the tropical year, the Julian calendar would fall behind about one day every 128 years. At this point in time, the Julian calendar was roughly two weeks behind.

The only change to the Julian calendar was to skip three leap days every 400 years. This was enough to bring the average length of the Gregorian year to 365.2524 days long. This will cause one day of error every 3000 years or so which is acceptable for common use. The Gregorian calendar is listed below with English month names.

Month | Meaning | Length in Days |
---|---|---|

January | Month of Janus | 31 |

February | Month of Februa | 28 or 29 |

March | Month of Mars | 31 |

April | Month of Aphrodite | 30 |

May | Month of Maia | 31 |

June | Month of Juno | 30 |

July | Month of Julius | 31 |

August | Month of Augustus | 31 |

September | Seventh Month | 30 |

October | Eighth Month | 31 |

November | Ninth Month | 30 |

December | Tenth Month | 31 |

Many countries and religions adopted the Gregorian calendar within a year of its introduction. Some took several hundreds of years to switch, including Russia which switched in 1918. Other countries adopted the Gregorian calendar from other calendar systems. An example of this is Saudi Arabia which switched from the Hijiri (Islamic) calendar in 2016.

Eastern Orthodox churches have used the Revised Julian calendar since 1923. The Revised calendar skips over many leap years so that each years is 365.2422 days long.

### The International Fixed Calendar

So all this background brings us to the calendar that got me interested in this topic in the first place: the international fixed calendar. It is sometimes known as the Cotsworth plan, the Eastman plan, or the international fixed calendar.

It was first devised in 1902 by Moses B. Cotsworth, a British accountant and business analyst who realised monthly accounting was complicated by each month having a different number of weeks. This was later championed by George Eastman, the founder and CEO of Kodak, who adopted it for his company between 1928 and 1989. This remains the most widespread and mainstream use of the international fixed calendar to date (pun intended).

The calendar maintains some compatability with its Gregorian counterpart by sharing the same year and leap year rules. There are 13 months and each month has four weeks. Each week (and by extension, each month and year) starts on a Sunday. The new month, Sol, occurs between June and July.

If you do the maths on this you will realise that this only accounts for 364 days each year. To make up for this extra day there is a special day added to the end of December called Year day. It doesn’t have a day of the week associated with it (i.e. the day before Year day is a Saturday and the day after is a Sunday). There is a similar situation for Leap day which occurs at the end of June on a Gregorian leap year.

The advantages of using this calendar are obvious for everyday use: - it is easier to mentally reason about, - each week, month, and year is predictable (i.e. the 13th is always a Saturday), - because most months have the same number of days, financial forecasting will become more accurate.

Month | Length in Days |
---|---|

January | 28 |

February | 28 |

March | 28 |

April | 28 |

May | 28 |

June | 28 or 29 |

Sol | 28 |

July | 28 |

August | 28 |

September | 28 |

October | 28 |

November | 28 |

December | 29 |

I was unable to find a nice printable version of this calendar so I thought I’d give making my own a go. I’ve made it using LaTeX and provided the source for the curious. Here is the result:

In fact, because it is a perennial calendar, the same calendar can be used for any year (although an extra day is required for leap years). So I’ve also provided links to the versions without the year printed on them as well. You can download the calendars using the links below:

- InternationalFixedCalendar_2021.pdf
- InternationalFixedCalendar.pdf
- InternationalFixedCalendar_LeapYear.pdf
- InternationalFixedCalendar.tex

I’m also thinking of making a version with some pictures on the reverse side of each month so it can be bound and hung on a wall. However, this will be a project for another day.

Here are the links where I got the information for this post: