The document presents detailed calculations for determining the date of Easter using astronomical methods, including the Julian day number and adjustments for various lunar cycles. It contrasts these astronomical findings with traditional Catholic Easter dates, revealing that the two methods align in the majority of cases, with only a small percentage of discrepancies. The document also discusses the implications of these calculations within the context of biblical feasts and the timing of Easter celebrations.

1. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
Table-A Calculation Formula for Astronomical Easter Calculation, Gregorian Year JD# Method
A B C D E F G H I J
YR pEpact JD#1Jan JD#JanNM JD#PFM1 JD#Eqnx JD#PFM WkDy JD# Easter D#ck
-4000 24.3 260090.45 260113.8 260187.8 260170.2 260187.8 7 260188.8 1
2019 6.0 2458484.8 2458489.8 2458563.8 2458563.4 2458563.8 5 2458566.8 1
Yr pEPCT JD#Jan1.3 (B-1)+C 74.02+D F.3 or F.7 IF(E>=F,E,E+29.5) f.6(G)
IF(H=1,G+7,8-
INT(H)+G)
f.6(i)
The above Table-A is a tabulation of calculation steps for finding Astronomical date of Easter. The
example calculations use formula-2 of Table-B to determine moment of January New Moon for
selected year, expressed as astronomical Julian Day number, JD#. Alternatively one could use
any number of resources to arrive at a value for column B. Just be sure to express the moment as
an Astronomical formatted Julian Day Number, JD#. Julian calendar or Gregorian calendar dates
may be verified by the day of week. The numbers in column F, JD#.Equinox, are for equinox
moment by formula 4 of Table B. The month number and day-of-month may be determined in a
spreadsheet by adding two more columns and using formula 8 and 9,Table B, given that Year, Yr,
is stated as input in column-A. Alternatively, the Easter JD# may be converted back to Gregorian
Date by several free programs. This routine was compared by 70 dates. If using JMT in place of
GMT (UT), then add an offset of 0.098 days to step “I” and “J”.
A check was made against the WCC Easter dates table for years 2025 to 2001. Against that Table
this method using formula 2 and 4 reproduced their result. Other checked instances returned
results that matched either the Catholic Easter dates or alternative astronomical calculation
results. However the data of Ovidiu Vaduvescu did not confirm the astronomical values set forth in
the WCC document nor results of this calculation. If Equinox and PFM dates are closer than one
(1) day, verification by a more precise routine is advised. NEXT N3 1

2. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
Name (Nu) TABLE-B Excel Astronomical Name Formula: Yr-year; JD#-Julian Day
pEpact.Cassidy.f1 29.09-MOD(MOD(Yr,19)*11-INT((Yr-1502.57-12*MOD(Yr,19))/228),29.983)
pEpact.Cassidy.0.f1b 29.5-MOD(MOD(Yr,19)*11-INT((Yr-1584-12*MOD(Yr,19))/228),30)
pEpact.Lunation#.f2
IF((1+MOD((365.242454*(-4006-Yr)),29.5306))>=30,((1+MOD((365.242454*(-4006-
Yr)),29.5306))-30),(1+MOD((365.242454*(-4006-Yr)),29.5306)))
JD# Jan1.f3 257898.52-365.242454*(-4006-Yr)
JD# Equinox.f4
1st
Page
(2457102.448+(Yr-2015)*365.2422)+((-0.0005947871)*((Yr-2015)/1000)^4+(-
0.00392591)*((Yr-2015)/1000)^3+(0.013808751)*((Yr-
2015)/1000)^2+(0.1590901)*((Yr-2015)/1000))
March 1st Moon.f5 JD#.Jan1 + pEpact + 59
Day of Week.f6 (1+INT(MOD((1.5+JD#),7))) one is Sunday and 7 is Saturday, etc
JD#21March.f7 257978.00-365.242454*(-4006-Yr)
Day of Month.f8
1+INT(MOD(((INT(MOD(((INT(JD#+0.5)+(-
37+INT(0.5+0.75*INT((INT(JD#+0.5)-4479.5)/36524.25))))-
59.25),365.25)))+0.5),30.6))
Month Number.f9 ,
3=March, 4=April
1+MOD((2+INT(((INT(MOD(((INT(JD#+0.5)+(-
37+INT(0.5+0.75*INT((INT(JD#+0.5)-4479.5)/36524.25))))-
59.25),365.25)))+0.5)/30.6)),12)
2Next page

3. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
3
Look at 135 different years between 4000BC and
2038AD. The average lunar conjunction age at
4pm Easter Sunday was about 19. days, with a
minimum of 15.5 days and a max of 22.2 days.
Without the postponement rule, then some Easter
Sundays would land before a lunar age of 13.5 day
This gives a very early Lunar Good Friday of just
12.5 days. Application of the rule "Sunday
following the Paschal Moon" keeps Good Friday in
better alignment with the 14th lunar day. For at the
minimum found above, Good Friday falls more
closely on the 14th or 15th lunar day.
Recapping the "raised up on 3rd day", Good Friday
was day one by inclusive counting as Jesus was
laid in grave before sunset on the Sabbath. Then
day 2 was Friday after sunset to sunset Saturday,
and day 3 inclusive count was Saturday after
sunset unto about sunrise Sunday. Thus the
reason for sunrise Easter service is to memorialize
"Christ our Passover", "a feast by an ordinance for
ever." To the end that others may wish to abolish
this ".- feast by an ordinance for ever", they neglect
the blessings of the Almighty and sadly invite the
fires of judgment to blot their memory from off the
earth!
Adjustment to Jerusalem time can be
accomplished by adding 2.33 hours or 0.098 days
to the “if” statements and day of week calculations.
Why the Sunday after the Paschal Full Moon?
Take a look at either the proleptic Catholic or
Astronomical Easters for years 30 and 33AD. For these
dates, the proleptic Gregorian Easter dates are April 7
and April 3, respectively. Next determine the Lunar
Conjunction (astronomical new moon) age of 17.9 and
17.2 days, respectively, at 4pm Sunday. Given that Jesus
died before Friday sunset and was buried before sunset,
so 1 day back is, Saturday 4pm and another day back is
Friday 4pm. Thus at time of Jesus death, the Lunar days
are 15.9 and 15.2 respectively. Given that the visible new
crescent or sighted moon is some where about 1 day
after conjunction. So on Good Friday the lunar sighted
moon of these years is 14 days in age. Thus Good Friday
of years 30AD and 33AD would either be on Nissan 14 or
15. However, if this skip week, “after” were not used, then
sometimes the Easter would come early to the lunar
calendar.
Why the Postponement Rule?
From this it is seen that reckoning Easter by these
methods speaks of "Christ our Passover", Jn18:39, 19:14,
1Cor5:7, Heb11:28, Num9:13, Ex12:14.
Since the Catholic Easter concurs the Astronomical
Easter in about than 95% of the dates, keeping Good
Friday and Easter are keeping "Christ our Passover" as
"a memorial; and .... a feast to the LORD throughout your
generations; ... feast by an ordinance for ever." Ex12:14.
The postponement rule importance is illustrated by
calculation. NEXT

4. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
"And ye shall count unto you from the morrow after the
Sabbath, from the day that ye brought the sheaf of the wave
offering; seven Sabbaths shall be complete: Even unto the
morrow after the seventh Sabbath shall ye number fifty
days; and ye shall offer a new meat offering unto the LORD."
Lev 23: 15/16. The Fifty days were numbered from a
Saturday, so the 50th day falls always on a Sunday, 49days or
7 weeks after Easter Sunday
For Christians, the Easter Sunday sets the precedent to find
the Sunday in the 7th month. The earliest Easter being 22
March. By this the 7th lunar month starts around the last
week of September. The latest Easter falls on 25 April, by
which the 7th lunar month looks to fall on last week of
October. The 1st Sunday after and a 3rd Sunday would be a
logical memorial for the Autumn Feasts.
Effect of using Jerusalem as Principle Meridian
Exercise Caution when the Universal Time new moon
moment is on a Saturday night after 21:30 hours. As in 1998,
when the Full Moon moment was Saturday at 22:23. The
+2h21m offset between GMT and Jerusalem, gives a Paschal
full moon on 00:44 Sunday 12 Apr. This astronomical Easter
is delayed unto the following Sunday. Compared to a
Catholic and/or Universal Time Easter of 12April. This shows
the principle difference in the two methods. The Catholic
calculation is stepped in days and weeks. The Astronomical
method is a moment defined calculation. Thus it depends
upon the details of complex astronomical calculations.
NEXT
Frequency of Variation
For 24 years, from 2001 to 2025, only once did the
Astronomical Easter differ from the Catholic Easter. That
being 2019, with Astro Easter on 24March, and Catholic
Easter on 21April. Many of the tabulated dates of the
table were evaluated for known difficult dates likely to
offer discrepancy between the two methods. Even so, only
11 of 60 years show variance between the methods. So
most likely, better than 95% of years will show the
Catholic Easter and Lunar Easter are same.
Other Feasts: Pentecost, Tabernacles, and The Lord's Supper
The other two of the three main feasts were Pentecost
and Tabernacles. For Christians, Pentecost (7 weeks after
Easter) celebrates the Holy Spirit. The feast of Tabernacles
celebrates being freed from bondages of the flesh, the
world, and eternal death, thru election by God the Father.
By celebrating these 3 feasts, Passover (hope of a more
better resurrection thru Jesus Christ), Pentecost (hope of
continual renewal by Holy Spirit), and Tabernacles (hope
of election and freedom from bondage thru grace of
Father God), the Holy Trinity can be honored by Christians.
Because Jesus initiated the Holy Communion, then
communion on these days should be held in high esteem.
The 1st of the first and seventh lunar months are seen as
special days or Sabbath's. Also, the middle of these
months are feasts of remembrance.
Pentecost is by the definition, always on a Sunday by
virtue of the week count, 7th Sunday after Easter.
4

5. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
Comparison of Three Major Hebrew Feasts
The Table at right compares the three feasts set forth by
Moses. Two of these feast weeks are routinely celebrated
in most churches. The first is Easter Holy week. That starts
with Palm Sunday, followed by Good Friday, and lastly,
Resurrection Sunday or Easter Sunday. The first of these
two Holy Days of Palm Sunday and Good Friday, correspond
approximately to the 10th and 15th days of a lunar month.
This provisioned that the 1st day of the lunar month falls
upon a Friday, the 8th day being a Friday also, the 10th day is
then a Sunday, and the 15th day being a Friday. It is
provisioned that Jesus died on a Friday and His empty
tomb found early Sunday; thus the term Holy Week.
The feast of Pentecost is celebrated in most churches 7
weeks after Easter. These first two Mosaic Feasts being
celebrated, begs the question? If two are celebrated, then
why not the 3rd and if so, then how so? If one remembers
the words of the blessed Savior, “When you Fast” they
were not in the permissive sense but in the imperative
instance. The 40 days of Lent could be taken as something
dealing with fasting. However the Master was noted to
have kept the Feast of Tabernacles. So then does it not
seem proper for churches to also remember this 3rd Feast?
The Sunday following Passover is typically Catholic Easter
Sunday. As Easter is the Sunday following the first full moon
after Spring Equinox, then the start of the lunar month is
about 2 weeks prior.
A lunar month is about 28.5 days in length. Six lunar
months are then 171 days or 24.4 weeks.
The 3 Mosaic Feasts of 1
st
month, 7
th
Month Ex23:14, and Pentecost
Reference Nissan, Lev23, Nu28:16
Pentecost,
Du16:16-17
Trumpets -Tishari
MonthDay/
date+-
March/April May/June Ex23:14 September/Oct.
1st
Day-A
Sabbath
Sabbath, 1st
Day of 1st
Month
15th
Nissan + 49D,
Easter + 49 days
Sabbath & blow
Trumpets 1st
of 7th,
New Moon & sin
offering
7th
Day
A Sabbath Lev23:8,
Ex12:6
A Sabbath
10th pick passover Lamb,
Psalm Sunday
9th
evening to 10th
evening
day of atonement,
fasting
14th
Passover: sunset
Deut16:6, kill lamb,
Ex12:6
15th
unleven bread 7 days,
15th
is Good Friday &
17th
Easter
Tabernacles for 7
days, start with a
Sabbath
21st
evening end unleven
22nd
offering for 7 day
23rd
Assembly
Taking out the two and a fraction of weeks elapsed unto
Easter, then 22 weeks after Easter corresponds to nearly the
start of the seventh lunar month. A comparison of dates 22
weeks after Easter to 1 Tishrei shows the two dates agree
within a few days. The odd exceptions being when Hebrew
calendar postponement rules are applied. One possible
church memorial to this time would be Eucharist 22 and 24
weeks after Easter. BACK NEXT
5

6. 6
Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
First. Page
Easter
by UTC UTC
YR Astro Cath this astro Full Moon Equinox
2038 28Mr 25Ap 28-Mar 2465503.59 2465503.03
2019 24Mr 21Ap 24-Mar 2458563.57 2458563.42
1998 19Ap 12Ap 19-Apr 2450915.43 2450893.33
1967 02Ap 26Mr 2-Apr 2439575.64 2439570.82
1962 25Mr 22Ap 25-Mar 2437744.83 2437744.60
1954 25Ap 18Ap 25-Apr
1943 28Mr 25Ap 28-Mar 2430805.42 2430805.00
1927 24Ap 17Ap 24-Apr
1876 16Ap 09Ap 9-Apr 2406353.32 2406333.76
1845 23Mr 30Mr 30-Mar 2395014.35 2395011.24
1829 19Ap 26Ap 26-Apr 2389167.08 2389167.36
1825 03Ap 10Ap 10-Apr 2387719.77 2387706.39
1818 22Mr 29Mr 29-Mar 2385151.09 2385149.70
1805 14Ap 21Ap 21-Apr 2380425.49 2380401.54
1802 18Ap 25Ap 25-Apr 2379333.61 2379305.83
1744 29Mr 05Ap 29-Mar
1724 09Ap 16Ap 9-Apr
1700 04Ap 11Ap 4-Apr
550 26Ap 19Ap 26-Apr 1922022.20 1922022.43
-61 me26Mr NoCalc 26-Mar 1698859.401 1698859.395
97 YR's Astro v Catholic Easter Variants
2038AD-1AD
Only one application offers astronomical or
‘uniform’ Easter calculation. Kalendis has not
been ported to mobile devices. This Excel
spreadsheet will find the Astronomical Easter
for years between 4007BC and 3027AD. In Table
to right, are differences between this calc and
others Astro-Easter. For these, exact values of
full Moon and Equinox are input. In all evaluated
points, this excel sheet was verified by Kalendis
to be correct. The below chart shows variations
of my Full Moon Date to Kalendis. The normal
range is +/- 1.5 hours for about 7000 years.
Beware, not all implementations of mobile Excel
have the needed numerical accuracy to evaluate
these complex expressions. Only IOS-Numbers
and MS-Excel routines could accurately execute
these complex calculations.

7. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
Excel Formula for Catholic Easter by Julian Day Number for Calendar Converter or direct Excel Cell
C var !. Single Input of Gregorian Year, if BC then 1-Yr.BC & find Easter in 7 steps, i.e. 30AD=> 30
.f10 P' =MOD(-8-11*MOD(Yr,19)+INT((Yr-1600)/100)-INT((Yr-1600)/400)-INT((8*INT((Yr-1400)/100))/25),30) 14
.f11 P =P'-IF(P'=29,1,IF((1+MOD(Yr,19))>11,IF(P'=28,1,0),0)) 14
.f12 D.1 =118+INT(365.25*(Yr+4712))-INT(0.75*INT(((Yr)/100)+49)) 1732097
.f13 D.2 =D.1+P 1732111
.f6 D.3 =1+INT(MOD((1.5+D.2),7)) 5
.f14 D.4 =IF(D.3=1,D.2+7,8-D.3+D.2)&"Catholic Easter as Julian Day Number" 1732114
end Estr use D.4 to get Day_of_Month, f.9, &Month#, f.8, &day_of_Week,f.6 as =D&f.n&… D7M4wkd1
Here is the Catholic Easter formulation using Gregorian Year
as input to find Easter Date as a Julian Day Number. This
simplifies several steps as compared to other methods. The
resultant JD# may be used to rapidly find Pentecost Sunday
or any number of Easter dependant days. The JD# can be
rapidly changes to calendar dates via formula f.6, f.8, & f.9
for historical or future dates. Beware excel dates do not
display for years prior to 1901. Thus the above work around.
The Easter JD# can be ported to excel date system for years
1901 forward. Simply determine the offset to Excel date
number and JD#, then subtract offset to other dates. Apply
this method when a wide range of dates are to be reviewed.
Most Easter routines are only valid for a few hundred years
after 1901. This is substantial since Christ our Passover was
slain from the foundation of the world. Thus there has
been a perpetual Easter since the day this world was
founded. That date was when Adam sinned, 4000 years
prior to Jesus Baptism at river Jordan by Saint John. The
day of resurrection was hidden by God and revealed by
Christ earthly Easter day in 30AD.
The following list dates when Astronomical Easter is not
same date as the Catholic Easter, about 1 in 12 years.
Next page
7

8. Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15
This tabulation covers from years 2050 back to 60BC. A
span of about 2100 years. As seen in the above
Tabulation some centuries have few discrepancy than
others. The cycle of 391-19 or 372 years can be seen
in some skip sequences. The average is about 11 of 12
years agree and 1 in 12 years are not in agreement
between the two Easter Methods. However the
pattern is not uniform. Some centuries have fewer
concurrences than others. Next page
Variant Astro Easter Years to Catholic Variant Astro Easter Years to Catholic
2049 1700 1457 1206 915 543 254 1903 1558 1351 1074 716 384 73
2045 1693 1453 1199 895 536 242 1900 1552 1332 1061 685 367 66
2038 1685 1446 1182 881 523 235 1876 1551 1331 1030 634 343 42
2019 1680 1429 1162 861 519 218 1873 1527 1328 1003 614 323 22
1981 1666 1427 1155 854 516 216 1845 1514 1313 998 607 320 15
1974 1629 1419 1142 846 509 191 1829 1507 1311 979 590 313 -5
1967 1622 1409 1135 837 496 188 1825 1503 1308 960 588 303 -19
1962 1609 1408 1128 827 489 178 1818 1487 1294 959 587 292 -29
1954 1598 1402 1111 817 482 171 1805 1484 1284 941 570 289 -32
1943 1590 1389 1108 810 474 168 1802 1483 1277 935 569 273 -49
1927 1582 1375 1101 783 469 144 1778 1473 1237 932 563 269 -53
1924 1578 1370 1088 736 438 137 1744 1465 1226 922 550 262 -56
1923 1571 1362 1081 729 411 124 1724 1463 1218
Given the primitive nature of physics and astronomy at
the time of the original formulation of the Easter
Calendar, the Catholic method mostly agrees with the
Astronomical formulation. That being stated, the
Paschal Moon of the Catholic Easter is not a true
moon. In fact it has a striking similarity to the Molad of
the calculated Hebrew Calendar. But the molad event is
timed to start around the autumn equinox vs. around
or about the Spring Equinox for the Catholic Easter. 8