1. Why do calendar months have different numbers of days?
If you count the days in a calendar from January to December, you will find 7 months with 31 days, 4 months with 30 days, and February with 28 days. Adding these up (31 × 7 = 217, 30 × 4 = 120, plus 28) gives 365 days. It would look neat if they alternated, but July and August both have 31 days.
To remember which months have 30 days, some people use a wordplay phrase. In Japanese, the phrase "Nishi Muku Samurai" helps recall the months: "Nishi" (West) represents February, April, June, and September, while "Samurai" splits into characters for 10 and 1 to represent November. This is a known mnemonic [9]. The fact that people created such wordplay suggests the uneven pattern is difficult to memorize. Is this uneven arrangement the result of a single design?
2. How the moon's 29.5-day cycle and the early 10-month Roman calendar shaped month lengths
The average cycle of the moon’s phases (the synodic month) is about 29.53 days [6]. Therefore, calendars based on the moon usually have months of 30 days ("long months") or 29 days ("short months"). In actual lunar movement, long months can sometimes occur in a row [6]. Repeating 29.53 days 12 times gives about 354 days, which is more than 10 days short of the solar year (about 365 days).
The oldest Roman calendar is said to have started in March and had only 10 months, totaling 304 days [1]. This calculation works out as 4 months of 31 days and 6 months of 30 days (31 × 4 + 30 × 6 = 304). According to tradition, King Numa later added January and February to make 12 months [2]. Since this is tradition, it cannot be stated as historical fact. When months were added, something strange happened to the day counts.
Note: The average cycle of the moon’s phases (the synodic month) is about 29.53 days [6].
3. Why King Numa's odd-numbered months left only February with an even number of days
According to tradition, King Numa reduced the 30-day months by one day to make them 29 days. He set January to 29 days and February to 28 days, making the year 355 days long [2]. This length is close to 12 cycles of the moon’s phases (about 354 days).
Roman priests are said to have considered even numbers unlucky, and it is explained that they aligned the months to odd numbers like 29 or 31 days [2]. However, if you add 12 odd numbers together, the total is always even. Since 355 is an odd number, at least one month had to be even to make the math work. That month was February with 28 days.
There is an explanation that February was the month for honoring the dead, so it was acceptable for it to be unlucky [2]. However, this is just one theory from that time. We cannot say for certain that February is short *because* it is unlucky. This created a 355-day calendar, but it still left a difference of about 10 days from the solar year.
4. How Caesar added 10 days to fix the calendar's drift from the seasons
Because the 355-day calendar was about 10 days shorter than the solar year, it drifted out of sync with the seasons. To fix this, an intercalary month (Mercedonius) of 27 or 28 days was supposed to be added every 2 to 3 years [4]. However, the priests decided when to add it, and the process became chaotic, causing further drift [4].
Julius Caesar ended this confusion. In 46 BC, he extended one year to 445 days for adjustment. Then, starting in 45 BC, he introduced the Julian calendar [1][2]. To make the year 365 days, he added 10 days to the 355-day calendar.
According to sources, Caesar did not touch the months that already had 31 days (March, May, July, October) or February. Instead, he distributed the 10 extra days among the 7 months that had 29 days. Calculating from these descriptions, January, August, and December gained 2 days each to become 31 days, while April, June, September, and November gained 1 day each to become 30 days. This adds up to 10 days (2 × 3 + 1 × 4 = 10), bringing the total to 365 days [3]. One explanation for not touching February is related to superstition. This arrangement matches our current calendar. But where did the story about February and August come from?
5. Is there any evidence that Emperor Augustus took a day from February?
There is no basis for the claim that "Emperor Augustus took a day from February to make his month 31 days." Some point out that this story may have been created by the 13th-century scholar Sacrobosco [1][5]. August (originally named Sextilis) is said to have become 31 days during Caesar’s calendar reform, increasing from 29 days [5]. However, the Royal Observatory of Belgium does not clearly state when August became 31 days [2]. Because sources disagree, it is safer to read these claims as "it is said that."
The month Sextilis was renamed "Augustus" in 8 BC. The reason cited in a senate decree, quoted by the ancient author Macrobius, was that Augustus had first become consul in this month. It does not mention changing the number of days [5].
The explanation that "Caesar arranged it so odd months had 31 days and even months had 30 days" is also considered a fabrication with no basis [1]. July and August both having 31 days is simply the result of how the Julian calendar assigned days. July originally had 31 days, and August gained 2 days to reach 31 days. The Roman calendar took its current form this way. How did Japan handle "long" and "short" months?
6. How long and short months changed every year in Japan's old calendar
In Japan’s old calendar (lunisolar) until the Edo period, long months had 30 days and short months had 29 days, with an intercalary month added every 2 to 3 years. Because the next year’s calendar was calculated anew each year, the pattern of long and short months changed every year [7].
To help people know this changing pattern, a tool called the "Daisho-reki" (Major/Minor Calendar) became very popular in the Edo period [7]. These calendars wove the long and short months into pictures and text, sometimes competing in cleverness and humor [9]. Since the pattern changed annually, new versions were needed every year.
In Meiji 5, an imperial edict on November 9 decided to switch to the solar calendar. December 3 of Meiji 5 became January 1 of Meiji 6 [8]. From the decision to the implementation, there were only about 3 weeks, meaning December effectively ended in 2 days. With the adoption of the solar calendar, the Daisho-reki was no longer needed and stopped being made [8].
7. How to check the Roman calendar's day totals with simple addition
You can verify the numbers in this article using paper and pencil. Try calculating these three totals: 1) Do 4 months of 31 days and 6 months of 30 days equal 304 days? 2) Do 7 months of 29 days, 4 months of 31 days, and February with 28 days equal 355 days? 3) Does adding 10 to 355 equal 365? If your answers match, you have confirmed the article’s numbers yourself.
If you want to compare sources, you can choose based on your interest. For the Daisho-reki, look at the National Diet Library’s "Japanese Calendar" and the National Astronomical Observatory’s "Major and Minor Months." For the Meiji reform, check the observatory’s explanation of the Japanese calendar. For the Roman calendar, consult Claus Tøndering and the Royal Observatory of Belgium. There are explanations based on tradition for why the Romans avoided even numbers. Compare how different sources describe these differences.