|Centuries:||16th century – 17th century – 18th century|
|Decades:||1610s 1620s 1630s – 1640s – 1650s 1660s 1670s|
|Years:||1642 1643 1644 – 1645 – 1646 1647 1648|
|1645 by topic:|
|Arts and Science|
|Architecture - Art - Literature - Music - Science|
|Lists of leaders|
|Colonial governors - State leaders|
|Birth and death categories|
|Births - Deaths|
|Establishments and disestablishments categories|
|Establishments - Disestablishments|
|Ab urbe condita||2398|
|English Regnal year||20 Cha. 1 – 21 Cha. 1|
|Chinese calendar||甲申年 (Wood Monkey)
4341 or 4281
— to —
乙酉年 (Wood Rooster)
4342 or 4282
|- Vikram Samvat||1701–1702|
|- Shaka Samvat||1567–1568|
|- Kali Yuga||4746–4747|
|Japanese calendar||Shōhō 2
|Julian calendar||Gregorian minus 10 days|
|Minguo calendar||267 before ROC
|Thai solar calendar||2187–2188|
|Wikimedia Commons has media related to 1645.|
1645 (MDCXLV) was a common year starting on Sunday (dominical letter A) of the Gregorian calendar and a common year starting on Wednesday (dominical letter E) of the Julian calendar, the 1645th year of the Common Era (CE) and Anno Domini (AD) designations, the 645th year of the 2nd millennium, the 45th year of the 17th century, and the 6th year of the 1640s decade. Note that the Julian day for 1645 is 10 calendar days difference, which continued to be used from 1582 until the complete conversion of the Gregorian calendar was entirely done in 1929.
- January 3 – The Long Parliament adopts the Directory for Public Worship in England, Wales, Ireland and Scotland, replacing the Book of Common Prayer (1559). Holy Days (other than Sundays) are not to be observed.
- January 10 – Archbishop of Canterbury William Laud is executed for treason on Tower Hill, London.
- January 14 – English Civil War: Fairfax is appointed Commander-in-Chief.
- January 29 – English Civil War: Armistice talks open at Uxbridge.
- February 2 – Battle of Inverlochy: The Covenanters are defeated by Montrose.
- February 15 – English Civil War: The New Model Army is officially founded.
- February 28 – English Civil War: Uxbridge armistice talks fail.
- March 4 – English Civil War: Prince Rupert leaves Oxford for Bristol.
- March 31 – Fearing the spread of the Black Death (plague), Edinburgh Town Council prohibits all gatherings except weddings and funerals.
- April 3 – The House of Lords passes the Self-denying Ordinance, requiring members of the Parliament of England to resign commissions in the armed services.
- April 10 – Because of the plague, the Edinburgh town council orders that the college graduation ceremony should be brought forward so that students can leave the city (on November 19, teaching resumes in Linlithgow).
- April 23 (St George's Day) – English Civil War: One hundred and fifty Irish soldiers bound for service with King Charles I of England are captured at sea by Parliamentarians and killed at Pembroke in Wales.
- May 9 – Battle of Auldearn: Scottish Covenanters are defeated by Montrose.
- June 1 – English Civil War: Prince Rupert's army sacks Leicester.
- June 10 – English Civil War: Oliver Cromwell is confirmed as the Lieutenant-General of the Cavalry.
- June 14 – English Civil War – Battle of Naseby: 12,000 Royalist forces are beaten by 15,000 Parliamentarian soldiers.
- June 28 – English Civil War: The Royalists lose Carlisle.
- July 2 – Fight at Alford, Aberdeenshire.
- July 10 – English Civil War – Battle of Langport: Cromwell wins in Somerset.
- July 21 – Qing dynasty regent Dorgon issues an edict ordering all Han Chinese men to shave their forehead and braid the rest of their hair into a queue identical to those of the Manchus.
- July 23 – Tsar Alexei Mikhailovich of Russia comes to the throne.
- August 13 – The Treaty of Brömsebro is signed between Sweden and Denmark–Norway, ending the Torstenson War and ceding Jemtland, Herjedalen, Gotland and Ösel (Saaremaa) to Sweden, which also holds the province of Halland for a period of 30 years as a guarantee.
- September 10 – English Civil War: Prince Rupert surrenders Bristol.
- September 13 – Battle of Philiphaugh: Covenanters defeat Montrose at Selkirk.
- September 24 – English Civil War – Battle of Rowton Heath: Parliamentarians defeat the Royalist cavalry.
- October 8–October 14 – English Civil War: Third siege of Basing House by Cromwell results in its destruction.
- October 8 – Jeanne Mance founds the Hôtel-Dieu de Montréal, the first hospital in North America.
- October 11 – English Civil War: Re-fortification of Bourne Castle in Lincolnshire against a threatened Royalist attack begins.
- November 20 The then Colegio de Santo Tomas, was elevated by Pope Innocent X into the University of Santo Tomas in his brief In Supreminenti. It has the oldest extant University Charter in the Philippines, as well as the whole of Asia.
- Bamana forces from Ségou invade the Mali heartland, destroying the Mali Empire after its 400 years as a unified state.
- The Stolberg-Wernigerode branch of the family of the counts of Stolberg and Wernigerode is founded in Germany.
- The Solar cycle enters the 70-year Maunder Minimum during which sunspots will be rare.
- Wallpaper begins to replace tapestries as a wall decoration.
- January 9 – Sir William Villiers, 3rd Baronet, English politician (d. 1712)
- January 28 – Gottfried Vopelius, German academic (d. 1715)
- February 9 – Johann Aegidius Bach, German organist, father of Johann Bernhard Bach (d. 1716)
- February 13 – Vere Fane, 4th Earl of Westmorland, English Earl (d. 1693)
- February 22 – Johann Christoph Bach, German composer (d. 1693)
- February 24 – Francis I Rákóczi, Hungarian prince of Transylvania (d. 1676)
- March 17 – Peter Du Cane, the elder, English alderman (d. 1714)
- March 25 – Marco Battaglini, Catholic bishop (d. 1717)
- April 3 – François Vachon de Belmont, Catholic bishop (d. 1732)
- April 11 – Juan del Valle y Caviedes, Spanish-born Peruvian poet (d. 1697)
- April 22 – Christine of Baden-Durlach, German noblewoman (d. 1705)
- May 4 – Thomas Alvey, Physician (d. 1704)
- May 15 – George Jeffreys, 1st Baron Jeffreys, British judge (d. 1689)
- June 13 – Giacomo Cantelmo, Roman Catholic cardinal (d. 1702)
- June 14 – Haquin Spegel, Swedish bishop (d. 1714)
- June 15 – Sidney Godolphin, 1st Earl of Godolphin, English politician (d. 1712)
- July 27 – Frederik Johan van Baer, Dutch army commander (d. 1713)
- July 28 – Marguerite Louise d'Orléans (d. 1721)
- August 3 – August Kühnel, German composer and violist (d. 1700)
- August 5 – Charles Schomberg, 2nd Duke of Schomberg, English general (d. 1693)
- August 6 – Joseph Herrick, principal law enforcement officer in Salem (d. 1710)
- August 10 – Eusebio Kino, Italian Catholic missionary (d. 1711)
- August 14 – Carlos de Sigüenza y Góngora, Mexican academic (d. 1700)
- August 16 – Jean de La Bruyère, French writer (d. 1696)
- August 25 – Jacob van Wassenaer Obdam (younger), Dutch general (d. 1714)
- August 30 – Giuseppe Avanzi, Italian painter (d. 1718)
- September 4 – John North (Trinity), fifth of fourteen children of Sir Dudley North (d. 1683)
- September 4 – Johannes Jakob Buxtorf (d. 1705)
- September 10 – Romeyn de Hooghe, Dutch Golden Age painter, engraver, and sculptor (d. 1708)
- September 21 – Louis Jolliet, Canadian explorer (d. 1700)
- September 22 – Chikka Devaraja, Ruler of Mysore (d. 1704)
- September 28 – Sir Edward Hales, 3rd Baronet, English politician (d. 1695)
- October 1 – John Alford (died 1691), English politician (d. 1691)
- October 7 – Bernard Desjean, Baron de Pointis, French admiral and privateer (d. 1707)
- October 10 – Jakob Gronovius, Dutch classical scholar (d. 1716)
- October 21 – Christine Charlotte of Württemberg, Regent of East Frisia (d. 1699)
- October 26 – Aert de Gelder, Dutch painter (d. 1727)
- October 28 – John Philip II, Wild- and Rhinegrave of Salm-Dhaun, German noble (d. 1693)
- November 1 – Thomas Pereira (d. 1708)
- November 6 – Johann Gottfried von Guttenberg, Prince-Bishop of Würzburg (d. 1698)
- November 11 – Govert van der Leeuw, Dutch painter (d. 1688)
- November 12 – Georg Wolfgang Wedel, Physician, surgeon, botanist, chemist, philosopher (d. 1721)
- November 17 – Nicolas Lemery (d. 1715)
- November 30 – Andreas Werckmeister, German organist, music theorist, and composer (d. 1706)
- December 3 – Michał Stefan Radziejowski, Catholic cardinal (d. 1705)
- December 14 – Jacob de Wilde, Dutch civil servant, art collector (d. 1721)
- December 24 – Hans Carl von Carlowitz (d. 1714)
- December 27 – Giovanni Antonio Viscardi, Swiss architect (d. 1713)
- September 25 – Naitō Kiyokazu, Daimyo who ruled the Takatō Domain (d. 1714)
- unknown date – Gian Antonio Fumiani, Italian painter of the Baroque period (d. 1710)
- probable – Captain William Kidd, Scottish pirate (d. 1701)
- January 10 – William Laud, Archbishop of Canterbury (b. 1573)
- April 16 – Tobias Hume, English composer (b. c. 1559)
- June 13 – Miyamoto Musashi, Japanese swordsman (b. c. 1584)
- July 15 – Michael I of Russia (b. 1596)
- July 17 – Robert Carr, 1st Earl of Somerset, Scottish politician (b. c. 1590)
- July 22 – Gaspar de Guzmán, Count-Duke of Olivares, Spanish statesman (b. 1587)
- August 6 – Lionel Cranfield, 1st Earl of Middlesex, English merchant (b. 1575)
- August 18 – Eudoxia Streshneva, tsaritsa, wife of Mikhail I of Russia (b. 1608)
- August 28 – Hugo Grotius, Dutch philosopher and writer (b. 1583)
- September 8 – Francisco de Quevedo, Spanish writer (b. 1580)
- December 12 – Giovanni Bernardino Azzolini or Mazzolini or Asoleni, Italian painter (b. c. 1572)