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1758 (MDCCLVIII) was a common year starting on Sunday of the Gregorian calendar and a common year starting on Thursday of the Julian calendar, the 1758th year of the Common Era (CE) and Anno Domini (AD) designations, the 758th year of the 2nd millennium, the 58th year of the 18th century, and the 9th year of the 1750s decade. As of the start of 1758, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.

• Rudjer Boscovich makes his atomic theory, in Theoria philosophiae naturalis redacta ad unicam legem virium in nalura existentium.
• A fire destroys a bit of Christiania, Norway.

• J. R. Geigy(later named to Novartis), a global pharmaceutical brand was founded in Basel, Switzerland.

• January 6 – Charles Ganilh, French economist, politician (d. 1836)
• January 9 – George Leveson-Gower, 1st Duke of Sutherland (d. 1833)
• January 11 – François Louis Bourdon, French Revolutionary politician (d. 1797)
• January 17 – Marie Anne Simonis, Belgian textile industrialist (d. 1831)
• January 20 – Marie-Anne Pierrette Paulze, French chemist (d. 1836)
• January 24 – Frederick Ponsonby, 3rd Earl of Bessborough (d. 1844)
• February 1
  • Jacques Antoine Marie de Cazalès, French orator, politician (d. 1805)
  • David Ochterlony, Massachusetts-born general with the East India Company (d. 1825)
• February 2 – George Thicknesse, 19th Baron Audley (d. 1818)
• February 3
  • Francis Napier, 8th Lord Napier of Great Britain (d. 1823)
  • Vasily Kapnist, Ukrainian poet, playwright (d. 1823)
• February 10 – Amalia Holst, German writer, intellectual, and feminist (d. 1829)
• February 17 – John Pinkerton, British antiquarian (d. 1826)
• February 25 – Joseph McDowell, U.S. Representative for North Carolina (d. 1799)
• February 28 – Nicolas François, Count Mollien, French financier (d. 1850)
• March 6 – William Russell, U.S. soldier (d. 1825)
• March 9 – Franz Joseph Gall, German pioneering neuroanatomist (d. 1828)
• March 12 – Leopold Karel, Count of Limburg Stirum (d. 1840)
• March 15 – Magdalene Sophie Buchholm, Norwegian poet (d. 1826)
• March 25 – Richard Dobbs Spaight, Governor of North Carolina (d. 1802)
• April 1 – Benjamin Mooers, American soldier (d. 1838)
• April 4
  • John Hoppner, English portrait-painter (d. 1810)
  • Pierre-Paul Prud'hon, French painter (d. 1823)
• April 16 – Christian Karl August Ludwig von Massenbach, Prussian soldier (d. 1827)
• April 19 – Fisher Ames, U.S. Congressman for Massachusetts (d. 1808)
• April 22 – Francisco Javier Castaños, 1st Duke of Bailén, Spanish general (d. 1852)
• April 23
  • Alexander Hood, British Royal Navy officer (k. 1798)
  • Alexander Cochrane, British Royal Navy officer (d. 1832)
  • Philip Gidley King, British Royal Navy officer, colonial administrator (d. 1808)
• April 27 – Charles Dumont de Sainte-Croix, French zoologist (d. 1830)

• April 28 – James Monroe, 5th President of the United States (d. 1831)
• April 29 – Georg Carl von Döbeln, Swedish officer, general and war hero (d. 1820)
• April 30
  • Emmanuel Vitale, Maltese military leader (d. 1802)
  • Jane West, English writer (d. 1852)

• May 6
  • Maximilien de Robespierre, French revolutionary (d. 1794)
  • André Masséna, Napoleonic general, Marshal of France (d. 1817)
• May 8 – John Heath, U.S. Representative for Virginia (d. 1810)
• May 15 – Thomas Taylor, English neoplatonist translator (d. 1835)
• May 17
  • Sir John St Aubyn, 5th Baronet, English fossil collector (d. 1839)
  • Honoré IV, Prince of Monaco (d. 1819)
• June 19 – Raffaello Sanzio Morghen, Italian engraver (d. 1833)
• June 22 – Joseph McMinn, governor of Tennessee (d. 1824)
• June 29 – Clotilde Tambroni, Italian philologist, linguist (d. 1817)
• June 30 – James Stephen, British lawyer (d. 1832)
• July 4 – Charles d'Abancour, French statesman (d. 1792)
• July 25 – Elizabeth Hamilton, English writer (d. 1816)
• July 31 – Rosalie de Constant, Swiss naturalist (d. 1834)
• July 31 – Jeremiah Colegrove, U.S. farmer, manufacturer and soldier (d. 1836)
• August 2 – William Campbell, Chief Justice of the Supreme Court of Upper Canada, resident of Toronto (d. 1834)
• August 5 – Emperor Go-Momozono of Japan (d. 1779)
• August 10 – Armand Gensonné, French politician (d. 1793)
• August 14 – Carle Vernet, French painter (d. 1835)

• August 24
  • Edward James Eliot, English politician (d. 1797)
  • Thomas Picton, British soldier, colonial governor (k. 1815)
  • Duchess Sophia Frederica of Mecklenburg-Schwerin (d. 1794)
• August 25 – Israel Pellew, English naval officer (d. 1832)
• September 1 – George Spencer, 2nd Earl Spencer, English Whig politician (d. 1834)
• September 9 – Alexander Nasmyth, Scottish portrait and landscape painter (d. 1840)
• September 10 – Hannah Webster Foster, U.S. novelist (d. 1840)
• September 18 – Louis Friant, French Napoleonic soldier (d. 1829)
• September 20 – Jean-Jacques Dessalines, leader of the Haitian Revolution (d. 1806)

• September 21
  • Antoine Isaac Silvestre de Sacy, French linguist, orientalist (d. 1838)
  • Christopher Gore, U.S. lawyer, politician (d. 1827)
• September 25 – Maria Anna Thekla Mozart called Marianne, known as Bäsle ("little cousin"), cousin of Wolfgang Amadeus Mozart (d. 1841)
• September 26 – Cosme Argerich, Argentine Surgeon General (d. 1820)

• September 29
  • Horatio Nelson, 1st Viscount Nelson, British admiral (d. 1805)
  • Fanny von Arnstein, Austrian salonnière (d. 1802)
• October 5 – Seymour Fleming, British noblewoman (d. 1818)
• October 6 – Watkin Tench, British Marine officer (d. 1833)
• October 7 – Joshua Coit, U.S. lawyer, politician (d. 1798)
• October 11 – Heinrich Wilhelm Matthias Olbers, German astronomer (d. 1840)
• October 12
  • James Davenport, U.S. Representative for Connecticut (d. 1797)
  • Theodorus Bailey, U.S. Representative for New York (d. 1828)
• October 15 – Johann Heinrich von Dannecker, German sculptor (d. 1841)

• October 16
  • John Paulding, U.S. soldier (d. 1818)
  • Noah Webster, U.S. lexicographer (d. 1843)
• October 22/6 – Vincenzo Dandolo, Italian chemist, agriculturist (d. 1819)
• October 28 – John Sibthorp, English botanist (d. 1796)
• October 28 – Joseph-François-Louis-Charles de Damas, French general (d. 1829)
• October 31 – Thomas Gisborne, Anglican priest, abolitionist (d. 1846)
• November 5 – Louis-Marie Aubert du Petit-Thouars, French botanist (d. 1831)
• November 11
  • Carl Friedrich Zelter, German composer (d. 1832)
  • Caleb P. Bennett, U.S. soldier, politician (d. 1836)
• November 12 – Jean Joseph Mounier, French politician (d. 1806)
• November 16 – Peter Andreas Heiberg, Danish author, philologist (d. 1841)
• November 20 – Abraham B. Venable, U.S. Representative for Virginia (d. 1811)
• November 25 – John Armstrong, Jr., U.S. soldier, statesman (d. 1843)
• December 5 – George Beauclerk, 4th Duke of St Albans (d. 1787)
• December 9 – Richard Colt Hoare, English antiquarian, archaeologist (d. 1838)
• December 21 – Jean Baptiste Eblé, French general (d. 1812)
• December 23 – John M. Vining, U.S. Representative for Delaware (d. 1802)

• Georges Antoine Chabot, French jurist, statesman (d. 1819)
• Nicholas Fish, U.S. Revolutionary soldier (d. 1833)
• Anthimos Gazis, Greek scholar, philosopher (d. 1828)
• Samuel Hardy, U.S. lawyer and statesman from Virginia (d. 1785)
• Jamphel Gyatso, 8th Dalai Lama of Tibet (d. 1804)
• Charles Lee, U.S. Attorney General (d. 1815)
• Samuel Sterett, American politician, U.S. Representative for Maryland (d. 1833)
• Marie-Claire Heureuse Félicité, Empress of Haiti (d. 1858)

• Kamehameha I, King of Hawaii (d. c. 1819)

• January 7 – Allan Ramsay, Scottish poet (b. 1686)
• January 17 – James Hamilton, 6th Duke of Hamilton, Scottish peer (b. 1724)
• January 18 – François Nicole, French mathematician (b. 1683)
• February 10 – Thomas Ripley, English architect (b. 1683)
• March 2 – Pierre Guérin de Tencin, French cardinal (b. 1679)
• March 6 – Henry Vane, 1st Earl of Darlington, English politician (b. c. 1705)
• March 18
  • Matthew Hutton, Archbishop of Canterbury (b. 1693)
  • Thomas Zebrowski, Lithuanian Jesuit scientist (b. 1714)

• March 22
  • Jonathan Edwards, U.S. minister (b. 1703)
  • Richard Leveridge, English bass and composer (b. 1670)
• April 7 – Joseph Blanchard, American soldier (b. 1704)
• April 21 – Francesco Zerafa, Maltese architect (b. 1679)
• April 22 – Antoine de Jussieu, French naturalist (b. 1686)
• April 30 – François d'Agincourt, French composer (b. 1684)
• May 3 – Pope Benedict XIV (b. 1675)
• May 28 – Ernst August II, Duke of Saxe-Weimar and Eisenach (b. 1737)
• June 3 – Charles Butler, 1st Earl of Arran (b. 1671)
• June 9 – Antonio de los Reyes Correa, Puerto Rican soldier
• June 12 – Prince Augustus William of Prussia (b. 1722)
• July 6 – George Howe, 3rd Viscount Howe, British general (in battle) (b. c. 1725)

• July 7 – Marthanda Varma, Rani of Attingal (b. 1706)
• July 15 – Ambrosius Stub, Danish poet (b. 1705)
• July 18 – Duncan Campbell, Scottish soldier
• August 2 – George Booth, 2nd Earl of Warrington (b. 1675)
• August 15 – Pierre Bouguer, French mathematician (b. 1698)
• August 17 – Stepan Fyodorovich Apraksin, Russian soldier (b. 1702)
• August 23 – Ulrika Eleonora von Düben, Swedish lady in waiting (b. 1722)
• August 27 – Barbara of Portugal, Princess of Portugal and Queen of Spain (b. 1711)
• September 5 – Dmitry Ivanovich Vinogradov, Russian chemist (b. c. 1720)
• September 23 – John FitzPatrick, 1st Earl of Upper Ossory (b. 1719)
• October 2 (bur.) – Philip Southcote, English landscape gardener (b. 1698)
• October 12 – Richard Molesworth, 3rd Viscount Molesworth, British field marshal (b. 1680)

• October 14
  • Wilhelmine of Prussia, Margravine of Brandenburg-Bayreuth, daughter of Friedrich Wilhelm I of Prussia (b. 1709)
  • James Francis Edward Keith, Scottish soldier and Prussian field marshal (b. 1696)
• October 20 – Charles Spencer, 3rd Duke of Marlborough, British politician (b. 1706)
• October 25/8 – Theophilus Cibber, English actor (b. 1703)
• November 5 – Hans Egede, Norwegian Lutheran missionary (b. 1686)
• November 12 – John Cockburn, Scottish politician
• November 20 – Johan Helmich Roman, Swedish composer (b. 1694)
• November 22 – Richard Edgcumbe, 1st Baron Edgcumbe, English politician (b. 1680)
• November 27 – Senesino, Italian singer (b. 1686)
• December 5 – Johann Friedrich Fasch, German composer (b. 1688)

• December 12 – Françoise de Graffigny, French lettrist (b. 1695)
• December 16 – Andrzej Stanisław Załuski, Polish-Lithuanian bishop (b. 1695)
• December 25 – James Hervey, English clergyman, writer (b. 1714)
• December 26 – François Joseph Lagrange-Chancel, French dramatist, satirist (b. 1677)

• François Mackandal, Haitian revolutionary leader, burned at the stake
• Nathaniel Meserve, American shipwright (b. 1704)
• Hyder Ali and his Sepoy capture Bangalore from "Khande Rao of the Maratha Confederacy". (Part of the Seven Years' War).
• Verónica II Guterres, African monarch