# How to find the week day of (any) given date? [duplicate]

How to find the week day of any given date?

Say we need to know in which week-day was June $$25,2019$$?

## marked as duplicate by John Omielan, José Carlos Santos, Lee David Chung Lin, YuiTo Cheng, The CountJun 27 at 1:29

To determine the week-day of a given date, we need to:

• find out whether the given year is "common" or "leap".

• know $$\mod(a,b)$$.

• know $$\left \lfloor a \right \rfloor$$.

To find out whether the given year is "common" or "leap", we can use the following chart:

## $$\mod(a,b)$$ means the remainder when dividing $$a$$ by $$b$$. For example, when we divide $$17$$ by $$3$$, we get $$5$$ and the remainder is $$2$$. Therefore, $$\mod(17,3)=2$$.

For convince, $$\mod(a,100)=$$ the number formed by the last two digits of $$a$$. For example, $$\mod(13527,100)=27$$.

$$\left \lfloor a \right \rfloor$$ means the nearst integer less than or equal to $$a$$. For examples,

$$\left \lfloor 6.97 \right \rfloor=6$$,$$\left \lfloor -2.8 \right \rfloor=-3,\left \lfloor \frac{20}{4} \right \rfloor=5$$.

Suppose that the given date is of the form: MONTH $$d, y$$

We have to calculate the following:

• $$A=\mod(y,100)$$

• $$B=\left \lfloor \frac{A}{4} \right \rfloor$$

• $$C=\frac{y-A}{100}$$

• $$D = d$$ which is the given date.

• $$E =\left \lfloor \frac{C}{4} \right \rfloor$$

• $$F=0,3,2,5,0,3,5,1,4,6,2,$$ or $$4$$ depending on the given month (Jan, Feb, March, ..., or Dec) respectively.

• $$G=\left\{\begin{matrix} 0 & \text{if the month is not Jan nor Feb}\\ 1 & \text{for Jan or Feb in a common year}\\ 2 & \text{for Jan or Feb in a leap year} \end{matrix}\right.$$

• $$H=\mod(A+B-2C+D+E+F-G,7)$$

• The week-day depends on the $$H$$ value, $$0$$ for Sunday, $$1$$ for Monday, $$2$$ for Tuesday, $$3$$ for Wednesday, $$4$$ for Thursday, $$5$$ for Friday, and $$6$$ for Saturday.

Consider the example, June $$25,2019$$

Since $$2019$$ is not divisible by $$4$$, then $$2019$$ is a common year.

$$A=\mod(2019,100)=19$$

$$B= \left \lfloor \frac{19}{4} \right \rfloor=4$$

$$C=\frac{2019-19}{100}=20$$

$$D= 25$$ as given.

$$E= \left \lfloor \frac{20}{4} \right \rfloor=5$$

$$F=3$$ for June.

$$G=0$$ since the given month is neither Jan nor Feb.

$$H=\mod(19+4-2\times20+25+5+3-0,7)=\mod(16,7)=2=$$ Tuesday.

I noticed that many people ask about this. I posted this way because I think it is the simplest way for any given date , whatever the given century.

There are some simpler ways but for years between 2000 and 2099 only.

So it is a general way.