|Covid-19|January 14 – King Philip V of Spain abdicates the throne in favour of his 16-year-old son Louis I.
January 22 – Bruno Mauricio de Zabala, Spanish Captain general of the Río de la Plata, forces the Portuguese to abandon their fortified settlement at what will become the city of Montevideo in Uruguay.
January 28 – Saint Petersburg State University is established.
February 8 – Catherine I of Russia is officially named czarina by her husband, Peter the Great.
February 20 – The premiere of Giulio Cesare, an Italian opera by George Frideric Handel, takes place in London.
April 7 – Premiere performance of the St John Passion (BWV 245) of Johann Sebastian Bach at St. Nicholas Church, Leipzig.
May 29 – Pope Benedict XIII, born Pierro Orsini, succeeds Pope Innocent XIII as the 245th pope.
June 23 – Treaty of Constantinople is signed, partitioning Persia between the Ottoman Empire and Russia.
July 27 – 'Peter the Wild Boy' is captured near Helpensen in Hanover.
August 31 – Louis I of Spain dies of smallpox aged 17 after a reign of 7 months and his father Philip V resumes the throne.
November 11 – Joseph Blake (alias Blueskin), highwayman, is hanged in London.
Jack Sheppard, highwayman and partner of crime of "Blueskin", is hanged in London.
Willem Mons, lover of Catherine I of Russia, is executed and his head preserved in alcohol.
China expels foreign missionaries.
Blenheim Palace construction is completed in England. It is presented as a gift from the nation to the Duke of Marlborough for his involvement in the Battle of Blenheim in 1704.
The Austrian Netherlands agree to the Pragmatic Sanction.
Shah Mahmud Hotaki of Afghanistan goes insane.
Longman, the oldest surviving publishing house in England, is founded.
January 24 – Frances Brooke, English writer (d. 1789)
February 16 – Christopher Gadsden, American statesman
February 28 – George Townshend, 1st Marquess Townshend, British field marshal (d. 1807)
February 29 – Eva Marie Veigel, ballet dancer known as La Violette (d. 1822)
March 6 – Henry Laurens, political leader during the American Revolutionary War, father of John Laurens (d. 1792)
March 27 – Jane Colden, American botanist (d. 1766)
April 12 – Lyman Hall, American signer of the Declaration of Independence (d. 1790)
April 22 – Immanuel Kant, German philosopher (d. 1804)
April 29 – John Michell, English scientist and geologist (d. 1793)
May 7 – Dagobert Sigmund von Wurmser, Alsatian-born Austrian general (d. 1797)
May 19 – Augustus Hervey, 3rd Earl of Bristol, British admiral and politician (d. 1779)
June 8 – John Smeaton, English civil engineer (d. 1792)
July 2 – Friedrich Gottlieb Klopstock, German poet (d. 1803)
July 10 – Eva Ekeblad, Swedish scientist (d. 1786)
July 31 – Noël François de Wailly, French lexicographer (d. 1801)
August 23 – Abraham Yates, American Continental Congressman (d. 1796)
August 25 – George Stubbs, English painter (d. 1806)
August 27 – John Joachim Zubly, Swiss-born Continental Congressman (d. 1781)
September 3 – Guy Carleton, 1st Baron Dorchester, British soldier and Governor of Quebec (d. 1808)
October 31 – Christopher Anstey, English writer (d. 1805)
December 12 – Samuel Hood, 1st Viscount Hood, British admiral (d. 1816)
December 13 – Franz Aepinus, German scientist (d. 1802)
December 18 – Louise of Great Britain, queen of Frederick V of Denmark (d. 1751)
December 24 – Johann Conrad Ammann, Swiss physician and naturalist (d. 1811)
December 30 – Louis-Jean-François Lagrenée, French painter (d. 1805)
Date unknown– Marie Anne Victoire Pigeon, French mathematician (d. 1767)
February 12 – Elkanah Settle, English writer (b. 1648)
March 7 – Pope Innocent XIII (b. 1655)
March 15 – Marie Jeanne Baptiste of Savoy-Nemours, Regent of Savoy (b. 1644)
March 19 – Lewis Watson, 1st Earl of Rockingham, politician (b. 1655)
May 3 – John Leverett the Younger, American President of Harvard (b. 1662)
May 21 – Robert Harley, 1st Earl of Oxford and Earl Mortimer, English statesman (b. 1661)
June 15 – Henry Sacheverell, English churchman and politician (b. 1674)
August 31 – King Louis I of Spain (b. 1707)
October 2 – François-Timoléon de Choisy, French writer (b. 1644)
October 29 – William Wollaston, English philosophical writer (b. 1659)
November 11 – Joseph "Blueskin" Blake, English highwayman (executed) (b. c. 1700)
November 16 – Jack Sheppard, English criminal (executed) (b. 1702)
November 18 – Bartolomeu de Gusmão, Portuguese naturalist (b. 1685)
November 24 – Ernst Ludwig I, Duke of Saxe-Meiningen (b. 1672)
December 27 – Thomas Guy, English philanthropist (b. 1644)
1724 (MDCCXXIV) was a leap year starting on Saturday (dominical letter BA) of the Gregorian calendar and a leap year starting on Wednesday (dominical letter ED) of the Julian calendar, the 1724th year of the Common Era (CE) and Anno Domini (AD) designations, the 724th year of the 2nd millennium, the 24th year of the 18th century, and the 5th year of the 1720s decade. As of the start of 1724, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.