Conversion between the Julian date and the Julian calendar
The Julian date counts the days since January 1st, 4713 BC. Chr. (JD = 0) through. This date is based on the proleptic (advanced) Julian calendar , which was introduced later.
Current day
In this calculation, the day count since the beginning of the year, starting with 0, is called the current day (LT). LT = 0 for January 1st, LT = 364 (normal year) or LT = 365 (leap year) for December 31st .
The conversion between the date and the current day is given in the section "Calculation of the current day". The following leap year criterion must be taken into account (J = year number):
Schaltjahr, wenn Rest (J/4) = 1 (für vorchristliche Jahre) Schaltjahr, wenn Rest (J/4) = 0 (für nachchristliche Jahre)
Present year
In this calculation, the starting year of the Julian date is set to 4716 BC. Moved forward, since the leap years are then at the end of a 4-year cycle and the calculation is simplified. The current year (LJ) is the number of years from this starting year. For 4716 BC LJ = 0, for 4715 BC. Chr. Is LJ = 1 etc.
Julian calendar → Julian date
The current day (LT) is determined from the month (M) and day (T) taking into account the leap year criterion (see section "Calculating the current day").
Then the current year (LJ) is calculated from the year (J):
LJ = 4716 - J (für vorchristliche Jahre) LJ = 4715 + J (für nachchristliche Jahre)
To calculate the Julian date, the number of full 4-year cycles (N4) since the start year and the number of full years (N1) in the last, incomplete 4-year cycle are calculated:
N4 = LJ/4 (ganzzahlig) N1 = Rest dieser Division
The Julian date is then calculated as follows:
JD = 1461*N4 + 365*(N1-3) + LT
1461 is the length of a 4-year cycle, 365 is the length of a normal year. The 3 is deducted from N1 to compensate for the advance of the start year.
Julian date → Julian calendar
In order to calculate a date of the Julian calendar with a given Julian date, the number of full 4-year cycles (N4) since the start year and the number of days (R4) of the last, incomplete 4-year cycle are calculated:
N4 = (JD + 1095)/1461 (ganzzahlig) R4 = Rest dieser Division
By adding 1095 (3 * 365) the starting year is brought forward by three years.
Next, the number of full years (N1) of the incomplete 4-year cycle is calculated, as well as the current day (LT) in the last year:
N1 = R4/365 (ganzzahlig) LT = Rest dieser Division
N1 can be between 0 and 3. On the last day of the cycle, the calculation results in N1 = 4 and LT = 0. In this case, the values must be corrected:
falls (N1=4) setze N1=3 und LT=365
The current year LJ for the Julian date YD results in:
LJ = 4*N4 + N1
The calculation of the year (J) from LJ for the Julian calendar J results from:
J = (4716 - LJ) v. Chr. (für LJ ≤ 4715) J = (LJ - 4715) n. Chr. (für LJ > 4715)
To calculate the month (M) and day (D), see the section "Calculating the current day".
Calculation of the current day
To calculate the current day (LT) for a given month (M) and day (T), a month-dependent correction (MK) and a leap year correction (SK) are required. The leap year correction is:
SK = 1 (für Schaltjahre, wenn der Monat später als Februar liegt (M>2)) SK = 0 (sonst)
The monthly correction (MK) results from the table:
M MK Monatsname M MK Monatsname M MK Monatsname ---------------------- ---------------------- ---------------------- 1 -1 Januar 5 -1 Mai 9 +2 September 2 0 Februar 6 0 Juni 10 +2 Oktober 3 -2 März 7 0 Juli 11 +3 November 4 -1 April 8 +1 August 12 +3 Dezember
The current day is then calculated as follows:
LT = T + 30*(M-1) + (SK + MK)
The reverse (determination of the date for a given LT) is:
M = (LT+1)/30 + 1 (ganzzahlig) T = LT - 30*(M-1) - (SK + MK)
For some values of LT, the formula for M results in a value that is 1 too large. This is noticeable through M = 13 or T <1. In these cases the values for M and T have to be corrected:
falls (M>12) oder (T<1): vermindere M um 1, bestimme hierdurch bedingte neue MK und SK Werte und berechne T erneut.
Examples
Julian date → Julian calendar:
25.10.1917 JK: SK = 0
MK = 2
LT = T + 30*(M-1) + SK + MK
= 25 + 30*9 + 2
= 297
LJ = 4715 + J
= 6632
N4 = LJ/4
= 1658
N1 = 0 (Rest von LJ/4)
JD = 1461*N4 + 365*(N1-3) + LT
= 2422338 - 1095 + 297
→ 2421540 JD
24.3.5 v. Chr.: SK = 1 (da M>2 und 5/4 einen Rest 1 hat)
MK = -2
LT = T + 30*(M-1) + SK + MK
= 24 + 30*2 - 1
= 83
LJ = 4716 - J
= 4711
N4 = LJ/4
= 1177
N1 = 3 (Rest von LJ/4)
JD = 1461*N4 + 365*(N1-3) + LT
= 1719597 + 0 + 83
→ 1719680 JD
31.12.1600 JK: SK = 1
MK = 3
LT = T + 30*(M-1) + SK + MK
= 31 + 30*11 + 4
= 365
LJ = 4715 + J
= 6315
N4 = LJ/4
= 1578
N1 = 3 (Rest von LJ/4)
JD = 1461*N4 + 365*(N1-3) + LT
= 2305458 + 0 + 365
→ 2305823 JD
Julian calendar → Julian date:
2421540 JD: N4 = (JD + 1095)/1461
= 1658
R4 = 297 (Rest davon)
N1 = R4/365
= 0
LT = 297
LJ = 4*N4 + N1
= 6632
J = LJ - 4715
= 1917
M = (LT+1)/30 + 1
= 10
SK = 0
MK = 2
T = LT - 30*(M-1) - (SK + MK)
= 297 - 30*9 - 2
= 25
→ 25.10.1917 JK
1719680 JD: N4 = (JD + 1095)/1461
= 1177
R4 = 1178 (Rest davon)
N1 = R4/365
= 3
LT = 83
LJ = 4*N4 + N1
= 4711
J = 4716 - LJ (da LJ<4715)
= 5 v. Chr.
M = (LT+1)/30 + 1
= 3
SK = 1
MK = -2
T = LT - 30*(M-1) - (SK + MK)
= 83 - 30*2 + 1
= 24
→ 24.3.5 v. Chr.
2305823 JD: N4 = (JD + 1095)/1461
= 1578
R4 = 1460 (Rest davon)
N1 = R4/365
= 4
LT = 0
Korrektur, da N1=4:
N1 = 3
LT = 365
LJ = 4*N4 + N1
= 6315
J = LJ - 4715
= 1600
M = (LT+1)/30 + 1
= 13
Korrektur, da M>12:
M = 12
SK = 1
MK = 3
T = LT - 30*(M-1) - (SK + MK)
= 365 - 30*11 - 4
= 31
→ 31.12.1600 JK