On Jan 18, 2015, hcs wrote:
To calculate mentally the number of days in a year for a given date is known since Dionysius Exiguus.

I give an English source in my Encyclopedia of weekday calculation on p. 48 "[2] Thomas Harrington: „The Magic of Memory: Phonetic Mnemonics”, “The numbers of the days throughout the year” and “date to day”, p. 13-15; Lybrary.com, 2007".
Subtract the numbers of two days (for two dates in a year) gives one the result asked for.
DinY = 30(M - 1) + M' + D

On Jan 19, 2015, Scott Cram wrote:
Here are a couple of online links that may help, as well:

http://powertoolsandtips.blogspot.com/20......nce.html

http://powertoolsandtips.blogspot.com/20......orm.html

The Thomas Harrington approach mentioned by Hans Solka is good, as he uses some very simple mnemonics. However, once you realize that each month is approximately 30 days, you know your multiples of 30 up to 11 (0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330), and get familiar with the actual number of days preceding each month, you'll find that you don't need the mnemonics as much anymore.

Just for fun, here's a polynomial equation that generates the number of days before any month, where the month is given as a number 1 (January) through 12 (December). I even worked out a version for leap years!