How to find day of a date

Question

As previously there were a method to find the date from the year 1893 to 2032 , which is very difficult to take a list of table always . Is there any other easy way to find the day of any date ?

Answer 1

Compute the number of days, modulo 7. Add the result to your present day.

For instance, today is Thursday, August 22, 2013.

August 23, 2014 is 366 days away.

$$366 \equiv 2 \bmod 7,$$

so August 23, 2014 is a Saturday.

Computing the number of days between dates is tedious, but not difficult.

Answer 2

Here is a method to convert between the Gregorian Calendar and the Julian Day Number.

Suppose the year, month, and date are given by $(Y,M,D)$ where January and February are included in the previous year, and March is month $0$ of its year. Thus, January 1, 2000 would be $(1999,10,1)$. Then the Julian Day Number that starts at noon GMT on that day would be $$ \text{JDN} = 365Y + \left\lfloor\frac Y4\right\rfloor - \left\lfloor\frac Y{100}\right\rfloor + \left\lfloor\frac Y{400}\right\rfloor + \left\lfloor\frac{153M+2}5\right\rfloor + D + 1721119 $$ To get the day of the week, $\text{DOW}$, use $\text{JDN}+1 \equiv \text{DOW} \pmod7$ where $$ \begin{align} 0 &= \text{Sunday}\\ 1 &= \text{Monday}\\ 2 &= \text{Tuesday}\\ 3 &= \text{Wednesday}\\ 4 &= \text{Thursday}\\ 5 &= \text{Friday}\\ 6 &= \text{Saturday} \end{align} $$ The inversion of this process is a bit more complicated. To convert from $\text{JDN}$ to $(Y,M,D)$, use the following: $$ \begin{align} Q_1 &= \left\lfloor\dfrac{\text{JDN}-1721120}{146097}\right\rfloor\\ R_1 &= (\text{JDN}-1721120) - 146097 Q_1\\ Q_2 &= \min\left(\left\lfloor\frac{R_1}{36524}\right\rfloor,3\right)\\ R_2 &= R_1 - 36524 Q_2\\ Q_3 &= \left\lfloor\frac{R_2}{1461}\right\rfloor\\ R_3 &= R_2 - 1461 Q_3\\ Q_4 &= \min\left(\left\lfloor\frac{R_3}{365}\right\rfloor,3\right)\\ R_4 &= R_3 - 365 Q_4\\[18pt] Y &= 400 Q_1 +100 Q_2 + 4 Q_3 + Q_4\\[6pt] M &= \left\lfloor\frac{5R_4+2}{153}\right\rfloor\\ D &= R_4 - \left\lfloor\frac{153M+2}5\right\rfloor + 1 \end{align} $$

Answer 3

There is a very handy formula which, when memorized, will allow you to compute the day of the week on which a date falls in your head. The formula for the 2000's is as follows:

1. Take the last two digits of the year, divide by four, disregard the remainder. Add the quotient thus determined to the last two digits of the year.
2. Add a number for the month based on the following: January 1, February 4, March 4, April 0, May 2, June 5, July 0, August 3, September 6, October 1, November 4, December 6, except in a leap year, it is 0 for January and 3 for February.
3. Add the number of the month.
4. Add 6.
5. Divide the result by seven. The remainder indicates the day of the week. For example, if the remainder is 3, the date falls on the third day of the week, or Tuesday. If the remainder is 0, the date falls on the seventh day of the week, or Saturday.

For example, determine the day of the week on which September 30, 2017, falls. 17 divided by 4 equals 4, disregarding the remainder. Adding 17 and 4 equals 21. Add 6 for September gives us 27. Adding 30 for the day gives us 57. Adding 6 gives us 63. 63 divided by 7 is 9 with a remainder of zero. Since the remainder is zero, September 30, 2017, falls on the seventh day of the week, or Saturday, which is true.

This formula works for any date in the 2000's. For the 1900's, omit Step 4. For the 1800's, Step 4 should be "Add 2," and for the 1700's, it should be "Add 4," but bear in mind that prior to September 14, 1752, Great Britain, including her American colonies, observed the Julian Calendar. Also, prior to 1750, the British calendar year began on March 25 and ended on the succeeding March 24.

This formula is taken from the 1939 edition of Funk & Wagnall's College Standard Dictionary (entry for the word "calendar").