To easily convert between the Gregorian and Julian calendars, use the calendar converter at Fourmilab.ch. Enter the relevant Gregorian date at the top of the page, click Calculate, and scroll down to the Julian Calendar heading to see the resulting Julian calendar date.
Fourmilab's calendar converter also converts between many other calendar systems, including Hebrew, Islamic, Mayan and Indian calendars. Enter the desired date in any of the available date boxes, click Calculate, and scroll through the other calendar headings to see the equivalent date.
The Julian and Gregorian calendars are 13 days out of sync, as of 2015. When Pope Gregory XIII introduced the Gregorian calendar in 1582 it was 10 days out of sync with the Julian calendar. The Gregorian calendar more closely matches the orbit of the Earth around the Sun than the Julian calendar. However, the Gregorian calendar is not perfect and is off by one day for every 3,236 years.
To stay in sync, the Gregorian calendar removes leap years in years divisible by 100 but not divisible by 400. The Julian calendar simply defines leap years as those divisible by 4. Thus, 2100 is the next Julian leap year that is not a Gregorian leap year, at which point the two calendars become 14 days out of sync.