0

# How do the days of a date in the Gregorian calendar change through the years?

Updated: 9/24/2023

Cigmorfil

Lvl 1
9y ago

Each year, the day a date can have goes forward one day, however, on a leap year it goes forward two days; due to the leap years, the days a date can have follows a 28 day cycle:

{Mo, Tu, We, Th}, {Sa, Su, Mo, Tu}, {Th, Fr, Sa, Su}, {Tu, We, Th, Fr}, {Su, Mo, Tu, We}, {Fr, Sa, Su, Mo}, {We, Th, Fr, Sa}

where each block of 4 represent sequential days before a missed day when the leap year occurs. Note that each day appears exactly 4 times, once in each position (each time in a different block) so that each day starts one of the blocks. If the date is after 28 February, the jump occurs in a leap year, but for those before 1 March, the jump occurs in the year after a leap year.

A century is one hundred years long, which means that each year will take 25 blocks from the above cycle to complete: 3 complete cycles plus the first 4 blocks. Numbering the blocks from 0 to 6 in the sequence above:

block 0: {Mo, Tu, We, Th};

block 1: {Sa, Su, Mo, Tu}; ...

block 6: {We, Th, Fr, Sa}

and assuming a date was a Monday in the first year of a leap century, then the blocks used in that century would be:

0123456 0123456 0123456 0123

(If the first day was another day, then the sequence would start from the block which starts with that day, eg if it was a Tuesday, then the block sequence would be: 3456012 3456012 3456012 3456.)

In the Gregorian Calendar a century is only a leap year if the century is divisible by 400. Thus 2000 was a leap year, but 1900 was not. Thus the above cycle of 28 days jumps for 3 out of 4 centuries when the day of the date at the start of the next century follows the day of the last year of the current century.

So carrying on from the above, as the century was a leap year, the next block must start with the day following the last day of the last block, ie the day after the last day of block 3 which is Friday, the block starting with Saturday - block 1; thus the next century would have the block sequence:

1234560 1234560 1234560 1234

Which is one block along from the previous century. So the complete sequence for 4 years starting from a leap century would be:

0123456 0123456 0123456 0123

1234560 1234560 1234560 1234

2345601 2345601 2345601 2345

3456012 3456012 3456012 3456

As the next century would start with a leap year, it starts with the next block in the cyclic sequence, which is block 0 again - the same sequence occurs for every block of 4 centuries starting with a leap century!

From this a complete list of days for every year of any date can be worked out, by changing the start block for the 4 century cycle above.

One this to note is that as the leap day is inserted after 28 February, the years for which the above cycles are appropriate will be slightly different:

For dates after the leap day (ie 1 March and later), the days jump in the leap year itself, so the sequence is appropriate for years starting with the leap century itself, ie the first block relates to the years xx00-xx03, the second to xx04-xx07, etc.

For dates before the leap day (ie 28 February and earlier) the jump occurs the year after the leap year, so the sequence is appropriate for years starting with the year after the leap century, ie the first block relates to the years xx01-xx04, the second to xx05-xx08, etc.

For the leap day itself, that follows the sequence of missing days:

{Tu, Su, Fr, We, Mo, Sa, Th}

Again with jumps on non-leap centuries:

0123456 0123456 0123456 0123

2345601 2345601 2345601 234

3456012 3456012 3456012 345

4560123 4560123 4560123 456

(0 =Tu, 1 = Su, etc).

Wiki User

9y ago

Earn +20 pts
Q: How do the days of a date in the Gregorian calendar change through the years?
Submit
Still have questions?
Related questions

### Why the change from the Julian to the Gregorian calendar?

The Julian calendar looses a day every 128 years. The Gregorian calendar looses a day every 3200 years.

### What event marks the start of Gregorian calendar?

The calendar is intended to mark the number of years since the death of King Herod the Great. The Roman abbot Dionysus Exiguus devised the new Christian calendar in 533. He knew that it was impossible to say when Jesus was born, but he knew, or thought he knew, when Herod died. So, he chose to begin his Christian calendar on the year of Herod's death, and he based this on the reign of the Roman emperor Augustus. Unaware that Augustus only adopted that name four years after his reign began, going by his birth name of Octavius until then, Exiguus commenced his calendar just 4 years too late.

### What do the Gregorian calendar and Julian calendar have in common?

almost everything... The major difference between the two calendars is the Julian calendar has 100 leap years in every 400 years, and the Gregorian calendar has 97 leap years in every 400 years. That makes the average length of a Julian calendar year 365.25 days and the average length of a Gregorian calendar year 365.2425 days. As a result, it takes only about 128 years for the Julian calendar to accumulate a full day of error, but for the Gregorian calendar to accumulate a full day of error takes about 3200 years.

### What is the Gregorian Calendar based on?

It is a reform of the Julian calendar, which loses a day every 128 years. The Gregorian calendar loses a day every 3200 years, making it 25 times more accurate.

### How often does the Islamic calendar synchronize with the solar year?

The term "synchronize" is unclear. The Islamic Calendar has a year of only 354 days, so it can never be the same length as a solar year (usually calculated with the Gregorian Calendar with an average of years length of 365.24 days). However, the date on the Islamic Calendar and on the Gregorian Calendar will correlate every 34 Islamic Calendar Years which correspond to 33 Gregorian Calendar Years.

### How many days off is the Gregorian calendar?

The Gregorian calendar takes about 3200 years to accumulate one day of error, as opposed to the Julian calendar, which accumulated an additional day of error every 128 years.

Thailand

### What was new years day on the gregorian calendar?

the 1st of January

### Who has more leap years Julian or Gregorian calendars?

The Julian calendar has more leap years. Every 400-year period of the Julian calendar is three days longer than the same period in the Gregorian calendar.

All of them

### When did the Gregorian calendar become standard in its country?

Italy, Spain, Portugal and Poland were the first four countries to switch from the Julian calendar, the calendar reformation commissioned by Julius Caesar in 46 BCE, to the Gregorian calendar, the calendar reformation commissioned by Pope Gregory XIII in 1582. They started using the Gregorian calendar on the 15th of October 1582.The last country to switch from the Julian calendar to the Gregorian calendar was Turkey, more than 344 years later.

### Was the year 1237 a leap year?

No, odd-numbered years are never leap years in either the Gregorian calendar or the Julian calendar.