How To Calculate The Day Of The Week

ELREY'S REVISED METHOD

 Century number
 16 = 0    
 17 = 5
 18 = 3 
 19 = 1
 20 = 0 
 21 = 5

 Month number
 144025036146 
 JFMAMJJASOND

 1234560      -  Day of week number (the remainder when divided by 7 )
 SSMTWTF      -  Day of week

 Formula:   ( Month number   + day  + Century number + year + year / 4 )  mod 7 =>  day of week number
                 |                          |                                               |
                 v                          v                                               v
             144025036146               16 = 0                                            1234560
             JFMAMJJASOND               17 = 5                                            SSMTWTF 
                                        18 = 3 
                                        19 = 1
                                        20 = 0      

• If Leap year and Jan or Feb, minus 1. (previous day)

• mod means 'remainder when divided by ...'

• Example July 18, 1990

   July   28     19    90     1/4 of 90
 (   0  + 28 +    1 +  90  +    22        ) mod 7  =  
 (                141                     ) mod 7  = 1  (Sat)  

• May 27, 2015

   May     27      20      15    1/4 of 15
  (  2  +  27   +   0  +   15 +   3           )  mod 7 =    5  (Wed)

• May 8, 2015

   May      8     20      15    1/4 of 15
  (  2  +   8   +  0  +   15 +      3        )  mod 7 =    0  (Fri)

• Sep 18, 2016

   
   Sep   18    20    16      1/4th of 16
  ( 6  + 18  +  0  + 16 +       4        ) mod 7 =  2 (Sunday)

• Jan 31, 1883

     Jan      31    18     83
   ( 1  +    31 +   3  + 83  +  20  ) mod 7 =
                           138        mod 7 =  5 (Wed)