Day of the Week Calculator

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The stars have fascinated humankind forever. Watching the constellations move across the sky, and observing the sun and moon have motivated mythologies, beliefs, religions, mathematics, metaphysics and philosophy.

Day of the Week Calculator

Wondering what day of the week Mum’s birthday falls on this year, or whether the public holiday in September might fall on a Friday and give you a 3 – day weekend?

Perhaps you’d like to know whether you’re Monday child or Thursday child? This calculator will help you solve these little riddles quickly and easily, even for a date in the distant future. The days of the week are based on the formula behind the Gregorian Calendar.

The Gregorian Calendar is used in most parts of the world. The Calendar, which we use to this day, was named after Pope Gregory XIII and is designed to space the leap years in such a way that the average year is 365,24 days long. The reason this average is required is that this is an approximation for the tropical year. A tropical year or solar year is the time it takes the sun to return to the same position as seen from the Earth in terms of the four seasons. For example, it is the time it takes from one seasonal solstice to the same solstice in the following year. Since we know the earth does not travel around the sun in exactly 365 days, leap years (and indeed a complicated formula) compensate for this.

The Julian Calendar, released by Julius Ceasar in 46 B.C miscalculated the solar year by 11 minutes, and by the time Pope Gregory XIII introduced the Gregorian Calendar in 1582, the dates had fallen entirely out of sync with the seasons! What bothered Gregory though, was the reality that Easter was moving further and further away from the Spring Equinox.

So where does this gap come from?

The earth’s axis is at a slight tilt, but like a spinning top, this orientation is very slowly but continuously changing.

For the earth, the axis of rotation takes some 25 772 years. This introduces the concept of the precession of the equinoxes, in that they move westwards relative to the stars. Ergo, the appearance of the stars changes over millennia. This term, ‘the precession of the equinoxes’ however, is one of ancient astronomy and does not hold relevance in technical conversations about astronomy today.

It was Hipparchus who concluded that the equinoxes were moving through the zodiac and that a full cycle would take 36 000 as the rate of precession was not less than 1° in a century. At this time, however, it was still probably thought that the heavens were in motion around a still Earth! 

The Mayan calendar, or Mesoamerican Long Count Calendar which represents roughly 30 000 years is also thought by some to trace the precession of the equinox, although this is by no means widely accepted by scholars of Mayan culture.

How does the Formula work?

While the Julian Calendar included an extra day in February every four years, it was found that this made the calendar a little too long and this would have an impact over time.

It was Aloysus Lilius, an Italian scientist and the man who designed the Gregorian Calendar, who added the variation that adds leap days in years divisible by four, unless the year is also divisible by 100. If, however, the year is also divisible by 400 a leap year is added regardless.  This is still off though by 26 seconds. It is calculated that by the year 4909, the Gregorian Calendar will be a full day ahead of the tropical or solar year. 
In the Gregorian Calendar, in 400 years there will be 97 leap years and 303 normal years.

January 1st in year N occurs on the same weekday as January 1st in year 400 + N. The leap year pattern then also takes place in 400-year cycles. There is a complicated algorithm based on a table of 400 elements, and this is the easiest way to calculate the day of the week by date. It’s like the back-end of the Gregorian Calendar!

The formula is as follows:


But this may still require a computer! Why not use our handy calculator.
If you’re still committed to checking it using mental arithmetic, this is a step by step mental calculation based on this algorithm:

1.	Take the last two digits of the year
2.	Divide by four and discard fractions
3.	Add the day of the month
4.	Add the month’s value based on the following key:

    Jan 	 1
    Feb     4
    Mar 	4
    Apr	0
    May	2
    Jun	5
    Jul	0
    Aug	3
    Sep	6
    Oct	 1
    Nov	4
    Dec	6

5.	If it is January or February of a leap year, subtract 1.
6.	If the date you’re trying to calculate is a date on the Gregorian Calendar, add 0 for 1900, 6 for 2000s, 4 for 1700s, 2 for 1800s
7.	Add the last two digits of the year
8.	Divide by 7 and take the remainder.

The number indicates the day of the week where Sunday – 1 and so on.

Other Fun Facts about how the calendar which governs our lives came about:
The adoption of the Gregorian Calendar was by no means universal or instant! A few interesting facts about the start of the Calendar year include the reality that in Britain, it wasn’t until 1752 that January 1st was taken to be the first day of the year.

Although this was the start of the year in the Julian Calendar, in the middle ages, peoples’ festivals centered around more religious holidays. In Britain, March 25th was the first day of the Calendar year.

This day was known as Lady Day, to celebrate the Virgin Mary. When the Gregorian Calendar was finally adopted in Britain, January 1st become the first day of the year once more.

How the days of the week were named

The names of the days of the week are linked to celestial bodies, and to the gods of the Romans. Although the Romantic Languages still reflect this, as these names have moved through the ages, the final forms are influenced by Germanic and Norse cultures and Languages too.

Monday, or Moon’s Day, is named after the moon. The French Lundi, and Spanish Lunes are derived from the Latin for moon, luna.

Tuesday is derived from the Old English Tiw’s day, where Tiw is the Germanic God of War and the Sky. Tiw is linked to Mars, the Roman God, where the Latin term for Tuesday was Dies Marti, the day of Mars.

Wednesday, Dies Mercurii, the Day of Mercury is the Day of Odin or Woden in Norse or Germanic culture. Odin, the supreme god, is equated with Mercury. From Wodensdæg to Humpday – how far the mighty have fallen!

Thursday is Jupiter’s Day, Dies Jovis. Jupiter, the Roman god of the sky and thunder was brother of Pluto. In the Old English, Thuresdæg, the ‘Day of Thunder’ was named after Thor, the Germanic god of thunder.

The word Friday is derived from the Old English Frigedæg, or Frigg’s Day, Named after Frigga, wife of the Supreme God Odin. She is the goddess off married love. In Roman Mythology, Thursday, Dies Veneris is named after the Roman goddess of love, Venus. In French, the Latin derivation is still clear in the term Vendredi.

Saturday derives its name from Saturn, Dies Saturni in Latin. Saturn was the Roman god of Agriculture.

Sunday is named for the Sun, from the Old English ‘Sunnandæg’ and the Latin ‘Dies Solis’.

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