Friday
the 13^{th} – Non Leap Year

Days to the 13th 
Sun 
Mon 
Tues 
Wed 
Thurs 
Fri 
Sat 
13Jan 
13 
6 
0 
1 
2 
3 
4 
5 
13Feb 
44 
2 
1 
4 
5 
6 
0 
1 
13Mar 
72 
2 
1 
4 
5 
6 
0 
1 
13Apr 
103 
5 
4 
0 
1 
2 
3 
4 
13May 
133 
0 
6 
2 
3 
4 
5 
6 
13Jun 
164 
3 
2 
5 
6 
0 
1 
2 
13Jul 
194 
5 
4 
0 
1 
2 
3 
4 
13Aug 
225 
1 
0 
3 
4 
5 
6 
0 
13Sep 
256 
4 
3 
6 
0 
1 
2 
3 
13Oct 
286 
6 
5 
1 
2 
3 
4 
5 
13Nov 
317 
2 
1 
4 
5 
6 
0 
1 
13Dec 
347 
4 
3 
6 
0 
1 
2 
3 
This table is for a year that is a non leap
year. Using mod 7 we can see from the
above table which months will have a Friday the 13^{th}. The value of 6 represents the value 6 mod 7
and this value shows the months where the 13^{th} falls on a
Friday. We can see that for a year in
which January 1 falls on a Thursday, there will be three months that have a
Friday the 13^{th} and that for these years, there will be back to back
months, February and March, where this will occur. This is the only time that this will
happen. Since February in non leap years
has 28 days, which is an even multiple in mod7, March will have the same dates
on the same days as does February. Since
all other months are either 30 or 31 days, there will be a remainder in mod 7,
and successive months will have the 13^{th} on a different day than the
preceding month. The starting day for the next year’s calendar in a non leap
year will be the previous year’s starting day plus 1. This table was made with Excel and used the
formula feature that calculated the mod 7 values shown in the table.