Updated 12/6/2021

These are the dates for the Biblical Feasts in 2022.
All of them except Passover begin the prior evening.

Purim (Feast of Lots)
March 17, 2022
(Purim is not one of the Appointed Times in Torah)

This happened on the thirteenth day of Adar and on the fourteenth day they rested, making it a day of feasting and gladness. …The Jews established and took upon themselves, upon their descendants, and upon all who joined with them, that they would commemorate these two days in the way prescribed and at the appointed time every year. These days should be remembered and observed in every generation by every family and in every province and every city.
(Esther 9:17,27-28 TLV)

Passover
April 15, 2022

In the first month, on the fourteenth day of the month at twilight is the LORD’S Passover.
(Leviticus 23:5 NASB)

Unleavened Bread
April 16 – 22, 2022

Then on the fifteenth day of the same month there is the Feast of Unleavened Bread to the LORD; for seven days you shall eat unleavened bread. On the first day you shall have a holy convocation; you shall not do any laborious work. But for seven days you shall present an offering by fire to the LORD. On the seventh day is a holy convocation; you shall not do any laborious work.
(Leviticus 23:6-8 NASB)

First Fruits
April 17, 2022

When you enter the land which I am going to give to you and reap its harvest, then you shall bring in the sheaf of the first fruits of your harvest to the priest. He shall wave the sheaf before the LORD for you to be accepted; on the day after the sabbath the priest shall wave it.
(Leviticus 23:10-11 NASB)

Shavuot (Pentecost)
June 5, 2022

You shall also count for yourselves from the day after the sabbath, from the day when you brought in the sheaf of the wave offering; there shall be seven complete sabbaths. You shall count fifty days to the day after the seventh sabbath; then you shall present a new grain offering to the LORD.
(Leviticus 23:15-16 NASB)

Yom Teruah (Feasts of Trumpets)
September 26, 2022

In the seventh month on the first of the month you shall have a rest, a reminder by blowing of trumpets, a holy convocation. You shall not do any laborious work, but you shall present an offering by fire to the LORD.
(Leviticus 23:24-25 NASB)

Yom Kippur (Day of Atonement)
October 5, 2022

On exactly the tenth day of this seventh month is the day of atonement; it shall be a holy convocation for you, and you shall humble your souls and present an offering by fire to the LORD. You shall not do any work on this same day, for it is a day of atonement, to make atonement on your behalf before the LORD your God.
(Leviticus 23:27-28 NASB)

Sukkot and Shemini Atzeret (Feast of Tabernacles)
October 10 – 17, 2022

On the fifteenth of this seventh month is the Feast of Booths for seven days to the LORD. On the first day is a holy convocation; you shall do no laborious work of any kind. For seven days you shall present an offering by fire to the LORD. On the eighth day you shall have a holy convocation and present an offering by fire to the LORD; it is an assembly. You shall do no laborious work.
(Leviticus 23:34-36 NASB)

Hanukkah or Chanukah (Feast of Dedication)
December 19 – December 26, 2022
(Hanukkah is not one of the Appointed Times in Torah)

Then Judas and his brothers and all the assembly of Israel determined that every year at that season the days of the dedication of the altar should be observed with gladness and joy for eight days, beginning with the twenty-fifth day of the month Kislev.
(1 Maccabees 4:59 ESV)

Recommended Reading:

A Christian Guide to the Biblical Feasts by David Wilber
Feasts of the Bible pamphlet by Rose Publishing