Easter Date worksheet

1. Orthodox Easter Sunday: Sunday, April 30, 2000

1. The Orthodox method uses the older Julian calendar. Start with the year's place in the 4-year leap cycle (a), the week (b) and the 19-year moon cycle (c)

   $\text{a, b, c}$$=\text{2000 mod 4, 2000 mod 7, 2000 mod 19}$$=\text{0, 5, 5}$

2. Find d, the number of days from March 21 to the church's full moon on the Julian calendar

   $\text{d =}110\text{mod 30}$$=20$

3. Find e, which counts the days from the full moon to the next Sunday, minus 1

   $\text{e =}34\text{mod 7}$$=6$

4. Add d and e to 114. Dividing by 31 gives the month, and the remainder plus 1 gives the day on the Julian calendar

   $20+6+114$$=140$

5. That is April 17 on the Julian calendar, which runs behind today's calendar

   $\text{Julian date}$$=\text{April 17, 2000}$

6. Add the gap between the two calendars, which is 13 days in 2000. It grows by one day in most century years

   $\text{gap =}\text{⌊}\frac{\text{2000}}{100}\text{⌋}-\text{⌊}\frac{\text{2000}}{400}\text{⌋}-2$$=13$

7. So Orthodox Easter falls on April 30 on the calendar used today

   $\text{Easter}$$=\text{Sunday, April 30, 2000}$

2. Western Easter Sunday: Sunday, April 21, 2250

1. Find where the year sits in the moon's 19-year cycle. Moon phases repeat on almost the same dates every 19 years

   $\text{a =}\text{2250}\text{mod 19}$$=8$

2. Split the year into its century (b) and its last two digits (c)

   $\text{b, c}$$=\text{22, 50}$

3. Work out the century fixes. The values d and e track skipped leap days. The values f and g correct the slow drift of the moon

   $\text{d, e, f, g}$$=\text{⌊22 ÷ 4⌋, 22 mod 4, ⌊30 ÷ 25⌋, ⌊22 ÷ 3⌋}$$=\text{5, 2, 1, 7}$

4. Find h, the number of days from March 21 to the church's full moon. Each year in the cycle moves the moon 19 days around a 30-day month

   $\text{h =}177\text{mod 30}$$=27$

5. So the church's full moon falls on Wednesday, April 17, 2250. Easter is the first Sunday after it

   $\text{full moon}$$=\text{Wednesday, April 17, 2250}$

6. Find l, which counts the days from the full moon to the next Sunday, minus 1. It uses where the year falls in the week (i and k)

   $\text{l =}31\text{mod 7}$$=3$

7. Check the rare fix-up m. It is 0 this year, so nothing changes

   $\text{m =}\text{⌊}\frac{371}{451}\text{⌋}$$=0$

8. Add h and l to 114, then take away 7 for each week that m moves Easter back. Dividing by 31 gives the month (3 is March, 4 is April), and the remainder plus 1 gives the day

   $27+3+114-7\times 0$$=144$

9. 144 ÷ 31 is 4 with 20 left over, so Easter is April 21

   $\text{Easter}$$=\text{Sunday, April 21, 2250}$

3. Western Easter Sunday: Sunday, April 11, 1700

1. Find where the year sits in the moon's 19-year cycle. Moon phases repeat on almost the same dates every 19 years

   $\text{a =}\text{1700}\text{mod 19}$$=9$

2. Split the year into its century (b) and its last two digits (c)

   $\text{b, c}$$=\text{17, 0}$

3. Work out the century fixes. The values d and e track skipped leap days. The values f and g correct the slow drift of the moon

   $\text{d, e, f, g}$$=\text{⌊17 ÷ 4⌋, 17 mod 4, ⌊25 ÷ 25⌋, ⌊17 ÷ 3⌋}$$=\text{4, 1, 1, 5}$

4. Find h, the number of days from March 21 to the church's full moon. Each year in the cycle moves the moon 19 days around a 30-day month

   $\text{h =}194\text{mod 30}$$=14$

5. So the church's full moon falls on Sunday, April 4, 1700. Easter is the first Sunday after it

   $\text{full moon}$$=\text{Sunday, April 4, 1700}$

6. Find l, which counts the days from the full moon to the next Sunday, minus 1. It uses where the year falls in the week (i and k)

   $\text{l =}20\text{mod 7}$$=6$

7. Check the rare fix-up m. It is 0 this year, so nothing changes

   $\text{m =}\text{⌊}\frac{295}{451}\text{⌋}$$=0$

8. Add h and l to 114, then take away 7 for each week that m moves Easter back. Dividing by 31 gives the month (3 is March, 4 is April), and the remainder plus 1 gives the day

   $14+6+114-7\times 0$$=134$

9. 134 ÷ 31 is 4 with 10 left over, so Easter is April 11

   $\text{Easter}$$=\text{Sunday, April 11, 1700}$

4. Western Easter Sunday: Sunday, April 2, 1600

1. Find where the year sits in the moon's 19-year cycle. Moon phases repeat on almost the same dates every 19 years

   $\text{a =}\text{1600}\text{mod 19}$$=4$

2. Split the year into its century (b) and its last two digits (c)

   $\text{b, c}$$=\text{16, 0}$

3. Work out the century fixes. The values d and e track skipped leap days. The values f and g correct the slow drift of the moon

   $\text{d, e, f, g}$$=\text{⌊16 ÷ 4⌋, 16 mod 4, ⌊24 ÷ 25⌋, ⌊17 ÷ 3⌋}$$=\text{4, 0, 0, 5}$

4. Find h, the number of days from March 21 to the church's full moon. Each year in the cycle moves the moon 19 days around a 30-day month

   $\text{h =}98\text{mod 30}$$=8$

5. So the church's full moon falls on Wednesday, March 29, 1600. Easter is the first Sunday after it

   $\text{full moon}$$=\text{Wednesday, March 29, 1600}$

6. Find l, which counts the days from the full moon to the next Sunday, minus 1. It uses where the year falls in the week (i and k)

   $\text{l =}24\text{mod 7}$$=3$

7. Check the rare fix-up m. It is 0 this year, so nothing changes

   $\text{m =}\text{⌊}\frac{158}{451}\text{⌋}$$=0$

8. Add h and l to 114, then take away 7 for each week that m moves Easter back. Dividing by 31 gives the month (3 is March, 4 is April), and the remainder plus 1 gives the day

   $8+3+114-7\times 0$$=125$

9. 125 ÷ 31 is 4 with 1 left over, so Easter is April 2

   $\text{Easter}$$=\text{Sunday, April 2, 1600}$

5. Western Easter Sunday: Sunday, April 13, 1800

1. Find where the year sits in the moon's 19-year cycle. Moon phases repeat on almost the same dates every 19 years

   $\text{a =}\text{1800}\text{mod 19}$$=14$

2. Split the year into its century (b) and its last two digits (c)

   $\text{b, c}$$=\text{18, 0}$

3. Work out the century fixes. The values d and e track skipped leap days. The values f and g correct the slow drift of the moon

   $\text{d, e, f, g}$$=\text{⌊18 ÷ 4⌋, 18 mod 4, ⌊26 ÷ 25⌋, ⌊18 ÷ 3⌋}$$=\text{4, 2, 1, 6}$

4. Find h, the number of days from March 21 to the church's full moon. Each year in the cycle moves the moon 19 days around a 30-day month

   $\text{h =}289\text{mod 30}$$=19$

5. So the church's full moon falls on Wednesday, April 9, 1800. Easter is the first Sunday after it

   $\text{full moon}$$=\text{Wednesday, April 9, 1800}$

6. Find l, which counts the days from the full moon to the next Sunday, minus 1. It uses where the year falls in the week (i and k)

   $\text{l =}17\text{mod 7}$$=3$

7. Check the rare fix-up m. It is 0 this year, so nothing changes

   $\text{m =}\text{⌊}\frac{289}{451}\text{⌋}$$=0$

8. Add h and l to 114, then take away 7 for each week that m moves Easter back. Dividing by 31 gives the month (3 is March, 4 is April), and the remainder plus 1 gives the day

   $19+3+114-7\times 0$$=136$

9. 136 ÷ 31 is 4 with 12 left over, so Easter is April 13

   $\text{Easter}$$=\text{Sunday, April 13, 1800}$

6. Orthodox Easter Sunday: Sunday, April 6, 2200

1. The Orthodox method uses the older Julian calendar. Start with the year's place in the 4-year leap cycle (a), the week (b) and the 19-year moon cycle (c)

   $\text{a, b, c}$$=\text{2200 mod 4, 2200 mod 7, 2200 mod 19}$$=\text{0, 2, 15}$

2. Find d, the number of days from March 21 to the church's full moon on the Julian calendar

   $\text{d =}300\text{mod 30}$$=0$

3. Find e, which counts the days from the full moon to the next Sunday, minus 1

   $\text{e =}42\text{mod 7}$$=0$

4. Add d and e to 114. Dividing by 31 gives the month, and the remainder plus 1 gives the day on the Julian calendar

   $0+0+114$$=114$

5. That is March 22 on the Julian calendar, which runs behind today's calendar

   $\text{Julian date}$$=\text{March 22, 2200}$

6. Add the gap between the two calendars, which is 15 days in 2200. It grows by one day in most century years

   $\text{gap =}\text{⌊}\frac{\text{2200}}{100}\text{⌋}-\text{⌊}\frac{\text{2200}}{400}\text{⌋}-2$$=15$

7. So Orthodox Easter falls on April 6 on the calendar used today

   $\text{Easter}$$=\text{Sunday, April 6, 2200}$

7. Orthodox Easter Sunday: Sunday, April 16, 2400

1. The Orthodox method uses the older Julian calendar. Start with the year's place in the 4-year leap cycle (a), the week (b) and the 19-year moon cycle (c)

   $\text{a, b, c}$$=\text{2400 mod 4, 2400 mod 7, 2400 mod 19}$$=\text{0, 6, 6}$

2. Find d, the number of days from March 21 to the church's full moon on the Julian calendar

   $\text{d =}129\text{mod 30}$$=9$

3. Find e, which counts the days from the full moon to the next Sunday, minus 1

   $\text{e =}49\text{mod 7}$$=0$

4. Add d and e to 114. Dividing by 31 gives the month, and the remainder plus 1 gives the day on the Julian calendar

   $9+0+114$$=123$

5. That is March 31 on the Julian calendar, which runs behind today's calendar

   $\text{Julian date}$$=\text{March 31, 2400}$

6. Add the gap between the two calendars, which is 16 days in 2400. It grows by one day in most century years

   $\text{gap =}\text{⌊}\frac{\text{2400}}{100}\text{⌋}-\text{⌊}\frac{\text{2400}}{400}\text{⌋}-2$$=16$

7. So Orthodox Easter falls on April 16 on the calendar used today

   $\text{Easter}$$=\text{Sunday, April 16, 2400}$

8. Orthodox Easter Sunday: Sunday, April 25, 2500

1. The Orthodox method uses the older Julian calendar. Start with the year's place in the 4-year leap cycle (a), the week (b) and the 19-year moon cycle (c)

   $\text{a, b, c}$$=\text{2500 mod 4, 2500 mod 7, 2500 mod 19}$$=\text{0, 1, 11}$

2. Find d, the number of days from March 21 to the church's full moon on the Julian calendar

   $\text{d =}224\text{mod 30}$$=14$

3. Find e, which counts the days from the full moon to the next Sunday, minus 1

   $\text{e =}24\text{mod 7}$$=3$

4. Add d and e to 114. Dividing by 31 gives the month, and the remainder plus 1 gives the day on the Julian calendar

   $14+3+114$$=131$

5. That is April 8 on the Julian calendar, which runs behind today's calendar

   $\text{Julian date}$$=\text{April 8, 2500}$

6. Add the gap between the two calendars, which is 17 days in 2500. It grows by one day in most century years

   $\text{gap =}\text{⌊}\frac{\text{2500}}{100}\text{⌋}-\text{⌊}\frac{\text{2500}}{400}\text{⌋}-2$$=17$

7. So Orthodox Easter falls on April 25 on the calendar used today

   $\text{Easter}$$=\text{Sunday, April 25, 2500}$

9. Western Easter Sunday: Sunday, April 18, 2500

1. Find where the year sits in the moon's 19-year cycle. Moon phases repeat on almost the same dates every 19 years

   $\text{a =}\text{2500}\text{mod 19}$$=11$

2. Split the year into its century (b) and its last two digits (c)

   $\text{b, c}$$=\text{25, 0}$

3. Work out the century fixes. The values d and e track skipped leap days. The values f and g correct the slow drift of the moon

   $\text{d, e, f, g}$$=\text{⌊25 ÷ 4⌋, 25 mod 4, ⌊33 ÷ 25⌋, ⌊25 ÷ 3⌋}$$=\text{6, 1, 1, 8}$

4. Find h, the number of days from March 21 to the church's full moon. Each year in the cycle moves the moon 19 days around a 30-day month

   $\text{h =}235\text{mod 30}$$=25$

5. So the church's full moon falls on Thursday, April 15, 2500. Easter is the first Sunday after it

   $\text{full moon}$$=\text{Thursday, April 15, 2500}$

6. Find l, which counts the days from the full moon to the next Sunday, minus 1. It uses where the year falls in the week (i and k)

   $\text{l =}9\text{mod 7}$$=2$

7. Check the rare fix-up m. It is 0 this year, so nothing changes

   $\text{m =}\text{⌊}\frac{330}{451}\text{⌋}$$=0$

8. Add h and l to 114, then take away 7 for each week that m moves Easter back. Dividing by 31 gives the month (3 is March, 4 is April), and the remainder plus 1 gives the day

   $25+2+114-7\times 0$$=141$

9. 141 ÷ 31 is 4 with 17 left over, so Easter is April 18

   $\text{Easter}$$=\text{Sunday, April 18, 2500}$

10. Orthodox Easter Sunday: Sunday, April 20, 3000

1. The Orthodox method uses the older Julian calendar. Start with the year's place in the 4-year leap cycle (a), the week (b) and the 19-year moon cycle (c)

   $\text{a, b, c}$$=\text{3000 mod 4, 3000 mod 7, 3000 mod 19}$$=\text{0, 4, 17}$

2. Find d, the number of days from March 21 to the church's full moon on the Julian calendar

   $\text{d =}338\text{mod 30}$$=8$

3. Find e, which counts the days from the full moon to the next Sunday, minus 1

   $\text{e =}42\text{mod 7}$$=0$

4. Add d and e to 114. Dividing by 31 gives the month, and the remainder plus 1 gives the day on the Julian calendar

   $8+0+114$$=122$

5. That is March 30 on the Julian calendar, which runs behind today's calendar

   $\text{Julian date}$$=\text{March 30, 3000}$

6. Add the gap between the two calendars, which is 21 days in 3000. It grows by one day in most century years

   $\text{gap =}\text{⌊}\frac{\text{3000}}{100}\text{⌋}-\text{⌊}\frac{\text{3000}}{400}\text{⌋}-2$$=21$

7. So Orthodox Easter falls on April 20 on the calendar used today

   $\text{Easter}$$=\text{Sunday, April 20, 3000}$