How to Calculate Day from any Given Date?

Calculating day from any given date is one of the amazing concepts as far as the calendar is concerned.

Before actually going into detail and calculating day, let's start with the basic calendar concepts as shown below:

1 day = 24 hours.

1 week = 7 days.

1 month = 28 / 29/ 30 / 31 days.

1 year = 12 months.

1 common year / ordinary year = 365 days.

1 leap year = 366 days.

February month in a leap year is of 29 days instead of 28 days.

Number of odd days in a common year / ordinary year = 1 day.

Number of odd days in a leap year = 2 days.

Number of odd days	Day
0	Sunday
1	Monday
2	Tuesday
3	Wednesday
4	Thursday
5	Friday
6	Saturday

If a year is exactly divisible by 4, then it is a leap year. This concept is applicable only in the case of a non-century year.

If a year is exactly divisible by 400, then it is a leap year. This concept is applicable only in the case of a century year [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, ……….].

Why every fourth year is a leap year with an additional day?

The time taken by the planet Earth to complete one revolution around the Sun is 365 days, 5 hours, 59 minutes, and 16 seconds. But only 365 days are considered out of this exact time, and the remaining time [5 hours, 59 minutes, and 16 seconds] keeps on adding every year.

Every fourth year this remaining time becomes:

[5 hours, 59 minutes, and 16 seconds] x 4

= 20 hours, 236 minutes, and 64 seconds

After changing the minutes to hours, and seconds to minutes, the above time becomes:

23 hours, 56 minutes, and 64 seconds => 23 hours, 57 minutes, and 4 seconds

This time is approximately equal to one day [24 hours], and this additional day is added every fourth year called leap year. Hence, February month in a leap year is of 29 days instead of 28 days.

Concept of number of odd days

Days left as remainder after dividing by 7 are called odd days. Number of odd days is an extremely important concept when it comes to calculating day from any given date.

A common year / ordinary year has 365 days. Dividing 365 days by 7 will give the remainder 1, hence the number of odd days in a common year / ordinary year is 1.

A leap year has 366 days. Dividing 366 days by 7 will give the remainder 2, hence the number of odd days in a leap year is 2.

In 100 years, there are 24 leap years and 76 ordinary years. Number of odd days will be 24x2 + 76x1 = 48 + 76 => 124, dividing 124 by 7 will give the remainder 5, hence the number of odd days in 100 years is 5.

In 200 years, there are 48 leap years and 152 ordinary years. Number of odd days will be 48x2 + 152x1 = 96 + 152 => 248, dividing 248 by 7 will give the remainder 3, hence the number of odd days in 200 years is 3.

In 300 years, there are 72 leap years and 228 ordinary years. Number of odd days will be 72x2 + 228x1 = 144 + 228 => 372, dividing 372 by 7 will give the remainder 1, hence the number of odd days in 300 years is 1.

In 400 years, there are 96 leap years and 304 ordinary years. Number of odd days will be 96x2 + 304x1 = 192 + 304 => 496, as 400 is a century leap year, so one additional day will be added in 496 and it becomes 497, now dividing 497 by 7 will give the remainder 0, hence the number of odd days in 400 years is 0.

Century years	Number of odd days
100	5
200	3
300	1
400	0
500	5
600	3
700	1
800	0
900	5
1000	3
1100	1
1200	0
1300	5
1400	3
1500	1
1600	0
1700	5
1800	3
1900	1
2000	0
2100	5
……….

 Note: As you can see in the above table, number of odd days in century leap year [400, 800, 1200, 1600, 2000, ……….] will be always 0.

Calculating day

Let start calculating day from any given date as shown in the example below:

11 Aug 1989

First check whether the given year is a leap year or not. To check this, divide the year by 4 in case of non-century year, and by 400 in case of a century year. Here 1989 is a non-century year and not exactly divisible by 4, so 1989 is not a leap year and the month of February is of 28 days.

Now split the given year in the following way:

[(Century year) + (last completed year of the given year) + (number of days completed on the given date (month wise))] divided by 7

[(1900) + (88) + (31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (Jun) + 31 (Jul) + 11 (Aug))] / 7

Now the main focus must be on finding the number of odd days because it is a key that help calculate the day from any given date. Number of odd days for century year 1900 is 1, please refer the table above.

In 88 years, there are 22 leap years and 66 ordinary years. Number of odd days will be 22x2 + 66x1 = 44 + 66 => 110, dividing 110 by 7 will give the remainder 5, hence the number of odd days in 88 years is 5.

Now put these values in the above equation as shown below:

[(1) + (5) + (223)] / 7

[229] / 7 => 5

Dividing 229 by 7 will give the remainder 5, so the number of odd days is 5 and the day on this given date is Friday. Please refer the table above regarding day corresponding to the number of odd days.

Hope you have understood this amazing calendar concept of calculating day from any given date.

Please try yourself with another example and in case of any issue, kindly provide your valuable comments.