Augustus corrected errors in the observance of leap years by omitting leap days until 8. Julian calendar dates before 8 are proleptic, and do not necessarily match the dates actually observed in the Roman Empire (Nautical almanac offices of the United Kingdom and United States, 1961, p. 411).
Dates near leap days that are observed in the Julian calendar but not in the Gregorian are listed in the table. Dates near the adoption date in some countries are also listed. For dates not listed, see below.
The usual rules of algebraic addition and subtraction apply; adding a negative number is the same as subtracting the absolute value, and subtracting a negative number is the same as adding the absolute value.
If conversion take you past a February 29 that exists only in the Julian calendar, then February 29 is counted in the difference.
No guidance is provided about conversion of dates before March 5, -500, or after March 28, 2100 (both being Julian dates).
Years not evenly divisible by 100, or evenly divisible by 400
For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the correct column. If converting from Julian to Gregorian, add the number from the "Difference" column. If converting from Gregorian to Julian, subtract. When adding, remember every year that this section applies to is a leap year in both calendars so February 29 must be included in the addition if applicable.
Years evenly divisible by 100 and not divisible by 400
Every year that fits into this section is a Julian leap year and a Gregorian common year. In the table these years are including a February 29 day in the Julian date column, and these dates are listed with emphasized rows. For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the right column.
When converting from Julian to Gregorian, add the number of days from the "Difference" column. If this date falls after the end of the Gregorian month, subtract the number of days of the Gregorian month and increment the month (and year if applicable). IF this date falls before the 1st day of the current month, then decrement the month (and year if applicable) and the number of days in this new month. Sometimes the difference column will be empty if the Julian date to convert is February 29 (it is in an emphasized row), meaning that the correction is not defined as a simple addition (in fact to convert it, first change February 29 into March 1 and add the Difference displayed on the previous row; this will give the equivalent Gregorian day in March, as listed in the Gregorian date column)
When converting from Gregorian to Julian, the process is just reversed, except that you lookup in the table the first date that comes before or at a date listed in the Gregorian column. Then you just need to substract the indicated number of days (counting them in the Gregorian Calendar) from your initial Gregorian date. But sometimes your date to convert will have no difference indicated in the table, and you can only use the date given in the Julian date column, which is a 29 February in the Julian calendar, for years that are leap in the Julian calendar, but not in the Gregorian calendar.
Nautical almanac offices of the United Kingdom and United States. (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (pp. 410–8 ). London: H. M. Stationery Office.