Months have either 30 or 31 days. Patterns can be simple, i.e. 30:31 and 31:30, quarter-based, i.e. 31:30:30, 30:31:30 and 30:30:31, more complicated ,or totally irregular as in the Gregorian calendar.

On the one hand, six times 61 makes 366 days, thus either a 31st or a 30th day must be left out in leap years. On the other hand, four time 91 makes 364 days, thus either a 31st or a 32nd day must be added in common years, and another 31st, 32nd or 33rd in leap years, or a leap week has to be introduced which may make one month 37 or 38 days long in leap years.

End-of-year leap day[edit | edit source]

Month lengths in days, values for leap years shown in parentheses
Month J/G 31:30 30:31 31:30…30:31 30:31…31:30 31:30:30 30:31:30 30:30:31
January 31 ±0 −1 ±0 −1 ±0 −1 −1
February 28 (29) +2 (+1) +3 (+2) +2 (+1) +3 (+2) +2 (+1) +3 (+2) +2 (+1)
March 31 ±0 −1 ±0 −1 −1 −1 ±0
April 30 ±0 +1 ±0 +1 +1 ±0 ±0
May 31 ±0 −1 ±0 −1 −1 ±0 −1
June 30 ±0 +1 ±0 +1 ±0 ±0 +1
July 31 ±0 −1 −1 ±0 ±0 −1 −1
August 31 −1 ±0 ±0 −1 −1 ±0 −1
September 30 +1 ±0 ±0 +1 ±0 ±0 ±0
October 31 −1 ±0 ±0 −1 ±0 −1 −1
November 30 +1 ±0 ±0 +1 ±0 +1 ±0
December 31 −2 (−1) −1 (±0) −1 (±0) −2 (−1) ±0 (+1) ±0 (+1) +1 (+2)
Month starts in ordinal days, values for leap years shown in parentheses
Month J/G 31:30 30:31 31:30…30:31 30:31…31:30 31:30:30 30:31:30 30:30:31
January 001 ±0 ±0 ±0 ±0 ±0 ±0 ±0
February 032 ±0 −1 ±0 −1 ±0 −1 −1
March 060 (061) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +1 (±0)
April 091 (092) +2 (+1) +1 (±0) +2 (+1) +1 (±0) +1 (±0) +1 (±0) +1 (±0)
May 121 (122) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +1 (±0) +1 (±0)
June 152 (153) +2 (+1) +1 (±0) +2 (+1) +1 (±0) +1 (±0) +1 (±0) ±0 (−1)
July 182 (183) +2 (+1) +2 (+1) +2 (+1) +2 (+1) +1 (±0) +1 (±0) +1 (±0)
August 213 (214) +3 (+2) +1 (±0) +1 (±0) +2 (+1) +1 (±0) ±0 (−1) ±0 (−1)
September 244 (245) +2 (+1) +1 (±0) +1 (±0) +1 (±0) ±0 (−1) ±0 (−1) −1 (−2)
October 274 (275) +1 (±0) +1 (±0) +1 (±0) +2 (+1) ±0 (−1) ±0 (−1) ±0 (−1)
November 305 (306) +1 (±0) +1 (±0) +1 (±0) +1 (±0) ±0 (−1) −1 (−2) −1 (−2)
December 335 (336) +1 (±0) +1 (±0) +1 (±0) +2 (+1) ±0 (−1) ±0 (−1) −1 (−2)
31:30...30:31 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 31 001 ±0 ±0
February 30 032 +2 (+1) ±0
March 31 062 ±0 +2 (+1)
April 30 093 ±0 +2 (+1)
May 31 123 ±0 +2 (+1)
June 30 154 ±0 +2 (+1)
July 30 184 −1 +2 (+1)
August 31 214 ±0 +1 (±0)
September 30 245 ±0 +1 (±0)
October 31 275 ±0 +1 (±0)
November 30 306 ±0 +1 (±0)
December 30 (31) 336 −1 (±0) +1 (±0)
30:31...31:30 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 30 001 −1 ±0
February 31 031 +3 (+2) −1
March 30 062 −1 +2 (+1)
April 31 092 +1 +1 (0)
May 30 123 −1 +2 (+1)
June 31 153 +1 +1 (±0)
July 31 184 ±0 +2 (+1)
August 30 215 −1 +2 (+1)
September 31 245 +1 +1 (±0)
October 30 276 −1 +2 (+1)
November 31 306 +1 +1 (±0)
December 29 (30) 337 −2 (−1) +2 (+1)
31:30 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 31 001 ±0 ±0
February 30 032 +2 (+1) ±0
March 31 062 ±0 +2 (+1)
April 30 093 ±0 +2 (+1)
May 31 123 ±0 +2 (+1)
June 30 154 ±0 +2 (+1)
July 31 184 ±0 +2 (+1)
August 30 215 −1 +2 (+1)
September 31 245 +1 +1 (±0)
October 30 276 −1 +2 (+1)
November 31 306 +1 +1 (±0)
December 29 (30) 337 −2 (−1) +2 (+1)
30:31 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 30 001 −1 ±0
February 31 031 +3 (+2) −1
March 30 062 −1 +2 (+1)
April 31 092 +1 +1 (0)
May 30 123 −1 +2 (+1)
June 31 153 +1 +1 (±0)
July 30 184 −1 +2 (+1)
August 31 214 ±0 +1 (±0)
September 30 245 ±0 +1 (±0)
October 31 275 ±0 +1 (±0)
November 30 306 ±0 +1 (±0)
December 30 (31) 336 −1 (±0) +1 (±0)
31:30:30 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 31 001 ±0 ±0
February 30 032 +2 (+1) ±0
March 30 062 −1 +2 (+1)
April 31 092 +1 +1 (±0)
May 30 123 −1 +2 (+1)
June 30 153 ±0 +1 (±0)
July 31 183 ±0 +1 (±0)
August 30 214 −1 +1 (±0)
September 30 244 ±0 ±0 (−1)
October 31 274 ±0 ±0 (−1)
November 30 305 ±0 ±0 (−1)
December 31 (32) 335 ±0 (+1) ±0 (−1)
30:31:30 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 30 001 −1 ±0
February 31 031 +3 (+2) −1
March 30 062 −1 +2 (+1)
April 30 092 ±0 +1 (±0)
May 31 122 ±0 +1 (±0)
June 30 153 ±0 +1 (±0)
July 30 183 −1 +1 (±0)
August 31 213 ±0 ±0 (−1)
September 30 244 ±0 ±0 (−1)
October 30 274 −1 ±0 (−1)
November 31 304 ±0 −1 (−2)
December 31 (32) 335 ±0 (+1) ±0 (−1)
30:30:31 Month lengths with changes from Julian/Gregorian in days, values for leap years shown in parentheses
Month Length Start Length Position
January 30 001 −1 ±0
February 30 031 +2 (+1) −1
March 31 061 ±0 +1 (±0)
April 30 092 ±0 +1 (±0)
May 30 122 −1 +1 (±0)
June 31 152 +1 ±0 (−1)
July 30 183 −1 +1 (±0)
August 30 213 −1 ±0 (−1)
September 31 243 ±0 −1 (−2)
October 30 274 −1 ±0 (−1)
November 30 304 ±0 −1 (−2)
December 32 (33) 334 +1 (+2) −1 (−2)

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