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DayOfWeek

As of Version 10.0, calendar functionality is built into the Wolfram Language »

DayOfWeek[{year,month,day}]

gives the day of the week on which the given date {year,month,day} occurred.

DayOfWeek[{year,month,day,hour,minute,second}]

gives the day of the week for the given date.

Details and Options

Examples

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Basic Examples  (6)Summary of the most common use cases

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-iuyy1z

The Declaration of Independence was signed on a Thursday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-zgeew
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-cee0ih

The Bastille was stormed on a Tuesday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-c4adgp
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-kclh4i

Canada became an independent nation on a Monday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-gl8ew1
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-qybs3

Wolfram Research began on a Saturday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-c3jhzk
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-c6uoof

This gives the day of the week at the time the formula was input:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-hxxuv1
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-cddyld

Hours, minutes, and seconds do not affect the day of the week:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-dq1yms
Out[2]=2

Options  (5)Common values & functionality for each option

Calendar  (5)

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-wxptf

Dates in Catholic countries after October 14, 1582 and before September 14, 1752 require the Gregorian option. Louis XIV was born on a Sunday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-fulllb
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-fdayrn

Russian Orthodox dates require the Julian option. Russian Orthodox Christmas 2000 was on a Sunday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-d73mz4
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-bczndn

The Islamic calendar begins on a Friday:

In[2]:=2
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https://wolfram.com/xid/0tr52ut8z27i-sn1mn
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-o2lprt

This date corresponds to one attribution of the Hegira, July 16, 622, in the Western (Julian) calendar:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-ddz06u
Out[2]=2
In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-b8ja97

By definition, Yom Kippur cannot fall on a Friday or Sunday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-cjhtr3
Out[2]=2

Because the Jewish calendar has a leap month preceding Passover, the Wolfram Language uses a numbering starting with Nisan, the month of Passover, and Tishrei, the first month of the Jewish year, is number 7:

In[3]:=3
✖
https://wolfram.com/xid/0tr52ut8z27i-nybx4q

Applications  (2)Sample problems that can be solved with this function

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-kp01d6

By definition, the Western calendar rules follow a 400-year cycle. This cycle also includes days of the week, since:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-ekw9l2
Out[2]=2

That is, the 400-year cycle has an integral number of weeks (otherwise, the cycle would have 2800 years).

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-cg3v4v

A century never begins on a Sunday:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-kkjfrf
Out[2]=2

No matter how the beginning of a century is defined:

In[3]:=3
✖
https://wolfram.com/xid/0tr52ut8z27i-drlizh
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-bky9yd

The Western calendar was modified from Julian to Gregorian for better accuracy. The change deleted 10 days in October 1582 in Catholic countries and deleted 11 days in September 1752 in Britain and her colonies. By default, the Wolfram Language applies the British (American) version. These calendar changes did not affect the day of the week, so there is an issue for DayOfWeek concerning dates after October 14, 1582 and before September 14, 1752. For British dates, the default gives the correct answer. For dates in Catholic countries, it is necessary to use the Gregorian option for Calendar.

The calendar change did not affect days of the week:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-reuh0
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0tr52ut8z27i-b03eyn
Out[3]=3

George Washington was born on a Tuesday:

In[4]:=4
✖
https://wolfram.com/xid/0tr52ut8z27i-bg9krn
Out[4]=4

Voltaire was born on a Sunday:

In[5]:=5
✖
https://wolfram.com/xid/0tr52ut8z27i-d1ap6q
Out[5]=5

Dates after September 2, 1752 and before September 14, 1752 are not accepted by the Automatic option. Use the Gregorian or Julian option for these dates (valid only for non-British Western countries):

In[6]:=6
✖
https://wolfram.com/xid/0tr52ut8z27i-v58jf
Out[6]=6

Neat Examples  (1)Surprising or curious use cases

In[1]:=1
✖
https://wolfram.com/xid/0tr52ut8z27i-fc6iiy

This computes the number of times each day of the week occurs as a 13th of the month over the complete 400-year cycle of the Western (Gregorian) calendar:

In[2]:=2
✖
https://wolfram.com/xid/0tr52ut8z27i-b8zt4o
Out[2]=2

The 13th of the month falls more often on a Friday than on any other day of the week.