Month length

12 months

Systematic month lengths in 12-month calendars

Year	Half	Third	Quarter	Sixth	Month	Irregular						61-day double-month												91-day quarter																					30-day month
						Greg/Jul						common				31:30		30:31		31:30*		30:31*		common			31:30:30			30:31:30			30:30:31			5:4:4			4:5:4			4:4:5
Y	H1	T1	Q1	S1	M01	365⁺	181⁺	120⁺	90⁺	59⁺	31	366⁻	183	122	61	92	31	91	30	92	31	91	30	364⁺	182	91	122	61	31	121	61	30	121	60	30	126	63	35	119	63	28	119	56	28	360⁺	180	120	90	60	30
					M02						28⁺						30		31		30		31						30			31			30			28			35			28						30
				S2	M03					61	31				61		31		30		31		30					61	30		60	30		61	31		63	28		56	28		63	35					60	30
			Q2		M04				91		30					91	30	92	31	91	30	92	31			91			31			30			30			35			28			28				90		30
		T2		S3	M05			123		61	31			122	61		31		30		31		30				121	60	30	122	61	31	121	61	30	119	56	28	126	63	35	119	63	28			120		60	30
					M06						30						30		31		30		31						30			30			31			28			28			35						30
	H2		Q3	S4	M07		184		92	62	31		183		61	92	31	91	30	91	30	92	31		182	91		61	31		61	30		60	30		63	35		63	28		56	28		180		90	60	30
					M08						31						30		31		31		30						30			31			30			28			35			28						30
		T3		S5	M09			122		61	30			122	61		31		30		30		31				121	61	30	121	60	30	122	61	31	119	63	28	119	56	28	126	63	35			120		60	30
			Q4		M10				92		31					91	30	92	31	92	31	91	30			91			31			30			30			35			28			28				90		30
				S6	M11					61	30				61		31		30		30		31					60	30		61	31		61	30		56	28		63	35		63	28					60	30
					M12						31						30		31		31		30						30			30			31			28			28			35						30

Ordinal start dates in 12-month calendars

Year	Half	Third	Quarter	Sixth	Month	Irregular	61-day double-month				91-day quarter						Constant
						Greg/Jul	31:30	30:31	31:30*	30:31*	31:30:30	30:31:30	30:30:31	5:4:4	4:5:4	4:4:5	30
Y	H1	T1	Q1	S1	M01	001	001	001	001	001	001	001	001	001	001	001	001
					M02	032	032	031	032	031	032	031	031	036	029	029	031
				S2	M03	060+	062	062	062	062	062	062	061	064	064	057	061
			Q2		M04	091+	093	092	093	092	092	092	092	092	092	092	091
		T2		S3	M05	121+	123	123	123	123	123	122	122	127	120	120	121
					M06	152+	154	153	154	153	153	153	152	155	155	148	151
	H2		Q3	S4	M07	182+	184	184	184	184	183	183	183	183	183	183	181
					M08	213+	215	214	214	215	214	213	213	218	211	211	211
		T3		S5	M09	244+	245	245	245	245	244	244	243	246	246	239	241
			Q4		M10	274+	276	275	275	276	274	274	274	274	274	274	271
				S6	M11	305+	306	306	306	306	305	304	304	309	302	302	301
					M12	335+	337	336	336	337	335	335	334	337	337	330	331

Comparison to legacy months in common years of 12-month calendars

Difference		61-day double-month				91-day quarter						Constant
		31:30	30:31	31:30*	30:31*	31:30:30	30:31:30	30:30:31	5:4:4	4:5:4	4:4:5	30
length	+3…+7	–	1	–	1	–	1	–	4	4	4	–
	+2	1	–	1	–	1	–	1	–	–	–	1
	+1	2	2	–	4	1	1	2	–	–	–	–
	±0	6	5	10	1	6	5	4	1	0	1	4
	−1	3	4	1	6	4	5	5	–	–	–	7
	−2…−3	–	–	–	–	–	–	–	7	8	7	–
offsets	+3…+6	–	–	–	–	–	–	–	6	2	–	–
	+2	8	3	5	6	2	1	–	2	2	–	–
	+1	2	7	5	4	4	4	4	2	2	2	1
	±0	2	1	2	1	6	5	4	2	2	2	3
	−1	–	1	–	1	–	2	4	–	1	1	3
	−2…−5	–	–	–	–	–	–	–	–	3	7	5

13 months

Systematic month lengths in 13-month calendars

Year	Month	4-week
Y	M01	364⁺	28
	M02		28
	M03		28
	M04		28
	M05		28
	M06		28
	M07		28
	M08		28
	M09		28
	M10		28
	M11		28
	M12		28
	M13		28

14 months

Systematic lengths in 14-month calendars

Year	Half	Seventh	Month	common		(regular)		4-week
						26		3–4		3–4*		4–3		4–3*
Y	H1	S1	M01	364⁺	182	52	26	56	28	56	28	56	28	56	28
			M02				26		28		28		28		28
		S2	M03			52	26	49	21	49	28	49	28	49	21
			M04				26		28		21		21		28
		S3	M05			52	26	56	28	56	28	56	28	56	28
			M06				26		28		28		28		28
		S4	M07			52	26	49	21	49	21	49	21	49	21
	H2		M08		182		26		28		28		28		28
		S5	M09			52	26	49	28	49	28	56	28	56	28
			M10				26		21		28		28		28
		S6	M11			52	26	56	28	56	28	49	21	49	21
			M12				26		28		28		28		28
		S7	M13			52	26	49	28	49	28	49	28	49	28
			M14				26		21		21		21		21

10 months

Systematic lengths in 10-month calendars

Year	Half	Fifth	Month	(alternating)						(constant)				5-week
				common		36:37		37:36		36⁺				common		1st		2nd		3rd		4th		5th
Y	H1	F1	M01	365⁺	73	182	36	183	37	360⁺	180	72	36	364⁺	182	77	42	77	35	70	35	70	35	70	35
			M02				37		36				36				35		42		35		35		35
		F2	M03		73		36		37			72	36			70	35	70	35	77	42	77	35	70	35
			M04				37		36				36				35		35		35		42		35
		F3	M05		73		36		37			72	36			77	35	70	35	70	35	70	35	77	42
	H2		M06			183	37	182	36		180		36		182		42		35		35		35		35
		F4	M07		73		36		37			72	36			70	35	77	42	77	35	70	35	70	35
			M08				37		36				36				35		35		42		35		35
		F5	M09		73		36		37			72	36			70	35	70	35	70	35	77	42	77	35
			M10				37		36				36				35		35		35		35		42

11 months

Systematic month lengths in 11-month calendars

Year	Month	equal				2 longer
		33		leap month			3–4–4	4–3–4	4–4–3
Y	M01	363⁺	33	350 (385)	35	365⁺	33	33	33
	M02		33		35		33	33	33
	M03		33		35		33	33	33
	M04		33		35		33	34	34
	M05		33		35		33	33	33
	M06		33		35		33	33	33
	M07		33		35		34	33	33
	M08		33		35		33	33	34
	M09		33		35		33	33	33
	M10		33		35		33	33	33
	M11		33		(35)		34	34	33

10+1 months

A calendar with ten regular and one leap month, where each month has exactly five weeks of seven days, has years either 350 or 385 days long. This can only be compatible with leap cycles that have a number of days divisible by five, i.e. not the popular 293 and 400-year cycles (146097 and 107016 days respectively).