How to Find the Day of the Week in Any Year of the Twentieth or Twenty-First Century

Tom Wayburn

Let D = the difference between the year numbers.

Let L be the day of the week in the later year of the day that has the same date as the day that you seek in the earlier year modulo 7 where Monday is 1.

Let E be the day of the week of the day you seek in the earlier year modulo 7. 

Let G equal the greatest integer in D/4*.

Let S equal the quantity (G + δ) modulo 7 where δ is obtained from the table below:

 

Earlier year \ Later year

Not leap year

Before leap day

After leap day

Not leap year

0

0

1

Before leap day

1

0

X

After leap day

0

X

0

 

The table is not needed if we remember that, if the earlier year is a leap year and the day is before leap day or if the later year is a leap year and the day is after leap day, δ = 1.  Otherwise, δ = 0.

E is the number of the day of the week with Monday equal to 1.

The day of the week of the earlier year is found from the equation E = L S D mod 7.

For example, my birthday was March 24, 1934.  March 24 is a Saturday this year, which is a 6.  I will be 73, so Δ = 73.  Neither 1934 nor 2007 is a leap year, so δ = 0.

S = [GINT(73/4) + 0] (mod 7) = 4

and

E = L S D (mod 7) = 6 4 3  = 6,

which is a Saturday.

*Note:  Unfortunately, 1900 was not a leap year.  My formula does not account for that, but it is easily remedied.  See http://www.jimloy.com/math/day-week.htm.