How does one calculate the Gregorian year from the Hebrew year (and the reverse)?
To calculate the Gregorian year from the Hebrew year, convert the Hebrew letters to numerals and add the number 1240 to that result. For the reverse, subtract the number 1240 from the Gregorian year and then convert the numerals to Hebrew letters. For a chart to convert the Hebrew alphabet to numbers, see here. If you are given the Hebrew year in numerals (e.g. 5774), exclude 5,000 in your calculation (see below) and add 1240 to the remaining numerals (e.g. 774).
1. Hebrew year: תרכד
ת is 400
ר is 200
כ is 20
ד is 4
Sum of numerals: 400 + 200 + 20 + 4 =624 (The year תרכד actually is the year 5624, but the 5,000 is left off for the purposes of the calculation and is assumed).
Add 624 to 1240: 624 + 1240 = 1864
2. English year: 2011
Subtract 1240: 2011 - 1240 = 771 (The year actually is 5771, but the 5,000 is assumed).
Convert to Hebrew letters: There is no Hebrew letter with the numerical equivalent as high as 700, but 700 is 400 + 300, ת and ש.
70 = ע
1 = א
From the time between the Hebrew New Year in the Fall to the Gregorian New Year in the Winter, the year is off by one, so this device is not always exact unless you know the month. This device generally though often proves helpful to librarians, who typically need to calculate the particular year in which a book was printed.
The JTS Library has many books on the topic of the Jewish calendar. For example, Judaism, Mathematics, and the Hebrew Calendar, by Hyman Gabai, presents a comprehensive, in depth analysis of the Hebrew calendar. The Jewish Calendar, by Rabbi David Feinstein, also offers a good overview of the calendar and Jewish holidays, as well as a section titled "Basic rules of calendar-based liturgies." Hebrew and Solar Calendar Every Day for 200 Years, by Victor E. Levy, and The Comprehensive Hebrew Calendar, by Arthur Spier, offer conversion charts and introductory explanations of the calendar system. Calendrical Calculations, by Edward M. Reingold, provides a mathematical explanation of the Julian, Gregorian, Jewish, and Muslim calendars. For a historical perspective, consult the book Palaces of Time: Jewish Calendar and Culture in Early Modern Europe, by Elisheva Carlebach.