Editing Revised Julian calendar (section)

==Arithmetic==

The following are Gregorian minus Revised Julian date differences, calculated for the beginning of January and March in each century year, which is where differences arise or disappear, until AD 10000. These are exact arithmetic calculations, not depending on any astronomy. A negative difference means that the proleptic Revised Julian calendar was behind the [[proleptic Gregorian calendar]]. The Revised Julian calendar is the same as the Gregorian calendar from 1 March 1600 to 28 February 2800, but the following day would be 1 March 2800 (RJ) or 29 February 2800 (G); this difference is denoted as '+1' in the table. 2900 is a leap year in Revised Julian, but not Gregorian: 29 February 2900 (RJ) is the same as 28 February 2900 (G) and the next day will be 1 March 2900 in both calendars - hence the '0' notation.

{|class="wikitable" style="text-align:center"
|+ Revised Julian (RJ) minus Gregorian (G) date differences
|-
!scope="col"| Dates
!scope="col"| RJ − G
|rowspan="37" style="border-top:hidden;border-bottom:hidden;background:transparent;padding:0 2px"|
!scope="col"| Dates
!scope="col"| RJ − G
|rowspan="37" style="border-top:hidden;border-bottom:hidden;background:transparent;padding:0 2px"|
!scope="col"| Dates
!scope="col"| RJ − G
|-
|style="color:#999"| Mar BC   1 – Feb AD  200 ||  0 ||style="color:#999"| Mar AD 3600 – Feb AD 3800 || +1 ||style="color:#999"| Mar AD  7200 – Feb AD  7400 || +2
|-
|style="color:#999"| Mar AD  200 – Feb AD  400 || −1 ||style="color:#999"| Mar AD 3800 – Feb AD 4000 ||  0 ||style="color:#999"| Mar AD  7400 – Feb AD  7600 || +1
|-
|style="color:#999"| Mar AD  400 – Feb AD  600 ||  0 ||style="color:#999"| Mar AD 4000 – Feb AD 4200 || +1 ||style="color:#999"| Mar AD  7600 – Feb AD  7800 || +2
|-
|style="color:#999"| Mar AD  600 – Feb AD  800 || −1 ||style="color:#999"| Mar AD 4200 – Feb AD 4400 ||  0 ||style="color:#999"| Mar AD  7800 – Feb AD  8000 || +1
|-
|style="color:#999"| Mar AD  800 – Feb AD 1100 ||  0 ||style="color:#999"| Mar AD 4400 – Feb AD 4700 || +1 ||style="color:#999"| Mar AD  8000 – Feb AD  8300 || +2
|-
|style="color:#999"| Mar AD 1100 – Feb AD 1200 || −1 ||style="color:#999"| Mar AD 4700 – Feb AD 4800 ||  0 ||style="color:#999"| Mar AD  8300 – Feb AD  8400 || +1
|-
|style="color:#999"| Mar AD 1200 – Feb AD 1500 ||  0 ||style="color:#999"| Mar AD 4800 – Feb AD 5100 || +1 ||style="color:#999"| Mar AD  8400 – Feb AD  8700 || +2
|-
|style="color:#999"| Mar AD 1500 – Feb AD 1600 || −1 ||style="color:#999"| Mar AD 5100 – Feb AD 5200 ||  0 ||style="color:#999"| Mar AD  8700 – Feb AD  8800 || +1
|-
|style="color:#222"| Mar AD 1600 – Feb AD 2800 ||  0 ||style="color:#999"| Mar AD 5200 – Feb AD 6400 || +1 ||style="color:#999"| Mar AD  8800 – Feb AD 10000 || +2
|-
|style="color:#999"| Mar AD 2800 – Feb AD 2900 || +1 ||style="color:#999"| Mar AD 6400 – Feb AD 6500 || +2 ||style="color:#999"| Mar AD 10000 – Feb AD 10100 || +3
|-
|style="color:#999"| Mar AD 2900 – Feb AD 3200 ||  0 ||style="color:#999"| Mar AD 6500 – Feb AD 6800 || +1 ||style="color:#999"| Mar AD 10100 – Feb AD 10400 || +2
|-
|style="color:#999"| Mar AD 3200 – Feb AD 3300 || +1 ||style="color:#999"| Mar AD 6800 – Feb AD 6900 || +2 ||style="color:#999"| Mar AD 10400 – Feb AD 10500 || +3
|-
|style="color:#999"| Mar AD 3300 – Feb AD 3600 ||  0 ||style="color:#999"| Mar AD 6900 – Feb AD 7200 || +1 ||style="color:#999"| Mar AD 10500 – Feb AD 10800 || +2
|}

In 900 Julian years there are {{frac|900|4}} = 225 leap days. The Revised Julian leap rule omits seven of nine century leap years, leaving {{nowrap|1= 225−7 = 218}} leap days per 900-year cycle. Thus the calendar mean year is 365&nbsp;+&nbsp;{{frac|218|900}} days, but this is actually a double-cycle that reduces to 365&nbsp;+&nbsp;{{frac|109|450}} = 365.24{{overline|2}} days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term on ''average'' the Revised Julian calendar pulls ahead of the Gregorian calendar by one day in 3600 years.

The number of days per Revised Julian cycle = 900 × 365 + 218 = 328,718 days. Taking [[modulo operation|mod]] 7 leaves a remainder of 5, so like the Julian calendar, but unlike the Gregorian calendar, the Revised Julian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Revised Julian leap cycle with respect to the seven-day weekly cycle is seven times the cycle length = 7 × 900 = 6300 years.