1736 (MDCCXXXVI) was a leap year starting on Sunday of the Gregorian calendar and a leap year starting on Thursday of the Julian calendar, the 1736th year of the Common Era (CE) and Anno Domini (AD) designations, the 736th year of the 2nd millennium, the 36th year of the 18th century, and the 7th year of the 1730s decade. As of the start of 1736, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
|Ab urbe condita||2489|
|Balinese saka calendar||1657–1658|
|British Regnal year||9 Geo. 2 – 10 Geo. 2|
|Chinese calendar||乙卯年 (Wood Rabbit)|
4432 or 4372
— to —
丙辰年 (Fire Dragon)
4433 or 4373
|- Vikram Samvat||1792–1793|
|- Shaka Samvat||1657–1658|
|- Kali Yuga||4836–4837|
|Japanese calendar||Kyōhō 21 / Genbun 1|
|Julian calendar||Gregorian minus 11 days|
|Minguo calendar||176 before ROC|
|Thai solar calendar||2278–2279|
1862 or 1481 or 709
— to —
1863 or 1482 or 710
|Wikimedia Commons has media related to 1736.|
- January 23 – The Civil Code of 1734 is passed in Sweden.
- January 26 – Stanislaus I of Poland abdicates his throne.
- February 12 – Francis I, Holy Roman Emperor marries Maria Theresa of Austria, ruler of the Habsburg Empire.
- April – The Genbun era begins in Japan. The era of Kyōhō Reforms ends.
- March 8 – Nader Shah, founder of the Afsharid Dynasty, is crowned Shah of Iran.
- March 31 – Bellevue Hospital was founded.
- April 14 – The Porteous Riots erupt in Edinburgh, after the execution of smuggler Andrew Wilson, when town guard Captain John Porteous orders his men to fire at the crowd. Porteous is arrested later.
- April 25 – Easter occurs on the latest possible date (the next time is in 1886).
- May 8 – Frederick, Prince of Wales, marries Princess Augusta of Saxe-Gotha.
- May 26 – Battle of Ackia: British and Chickasaw Native Americans defeat French troops.
- June 8 – Leonhard Euler writes to James Stirling, describing the Euler–Maclaurin formula, providing a connection between integrals and sums.
- June 19 – A French Academy of Sciences expedition, led by Pierre Louis Maupertuis, with Anders Celsius, begins work on measuring a meridian arc in Meänmaa, Finland.
- July – Russo-Turkish War (1735–39): Russian forces under Peter Lacy storm the Ottoman fortress of Azov.
- August 12 – A fire in St. Petersburg, capital of the Russian Empire, destroys 2,000 buildings, the city's post office, and several palaces.
- September 7 – An Edinburgh crowd drags John Porteous out of his cell in Tolbooth Prison, and lynches him.
- December 7 – Benjamin Franklin builds the first volunteer fire company in Philadelphia.
- December 26 – Andrew Michael Ramsay gives an oration, in which he relates the heritage and internationalism of Freemasonry to that of the Crusades.
- Neustrelitz becomes the capital of Mecklenburg-Strelitz.
- Bushehr is founded in Persia.
- The Belgrade Fortress is completed.
- George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain.
- A fire in the Russian city of Saint Petersburg burns 2,000 houses.
- A fire in Stony Stratford, England consumes 53 houses.
- One of the earliest records of use of a bathing machine is made at Scarborough, England.
- Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador.
- Leonhard Euler produces the first published proof of Fermat's "little theorem." 
- Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations (anonymously).
- Muhammad ibn Abd al-Wahhab writes the Kitab at-tawhidt, marking the beginning of Wahhabism.
- The Haidamakas raid the shtetl of Pavoloch, killing 35.
- January 19 – James Watt, Scottish inventor (d. 1819)
- January 25 – Joseph-Louis Lagrange, Italian-born mathematician (d. 1813)
- February 3 – Johann Georg Albrechtsberger, Austrian musician (d. 1809)
- February 29 – Ann Lee, English-born American religious leader (d. 1784)
- March 20 - Rama I, First King of Siam (d. 1809)
- May 8 – Caterina Dolfin, Italian (Venetian) poet (d. 1793)
- May 10 – George Steevens, English literary critic (d. 1800)
- May 29 – Patrick Henry, American patriot (d. 1799)
- June 3 – Sir John Acton, 6th Baronet, Prime Minister of Naples (d. 1811)
- June 7 – Fermín Lasuén, Spanish missionary (d. 1803)
- June 14 – Charles-Augustin de Coulomb, French physicist (d. 1806)
- June 21 – Enoch Poor, American general (d. 1780)
- June 25 – John Horne Tooke, English politician, philologist (d. 1812)
- July – Juan Bautista de Anza, Governor of the Spanish Province of New Mexico (d. 1788)
- July 6 – Daniel Morgan, American pioneer, Congressman from Virginia, and general (d. 1802)
- August 9 – Louis Joseph, Prince of Condé (d. 1818)
- August 15 – Alexander Runciman, Scottish painter (d. 1785)
- August 26 – Jean-Baptiste L. Romé de l'Isle, French geologist (d. 1790)
- September 15 – Jean Sylvain Bailly, French astronomer (d. 1793)
- September 16 – Carter Braxton, signer of the American Declaration of Independence (d. 1797)
- October 27 – James Macpherson, Scottish poet (d. 1796)
- date unknown
- January 8 – Jean Leclerc (theologian), Swiss theologian and biblical scholar (b. 1657)
- January 17 – Matthäus Daniel Pöppelmann, German architect (b. 1662)
- January 31 – Filippo Juvarra, Italian architect (b. 1678)
- February 1 – James Stanley, 10th Earl of Derby, English politician (b. 1664)
- February 7 – Stephen Gray, English dyer, astronomer, and scientist (b. 1666)
- March 16 – Giovanni Battista Pergolesi, Italian composer (b. 1710)
- March 25 – Nicholas Hawksmoor, British architect (b. c. 1661)
- April 21 – Prince Eugene of Savoy, French-born Austrian general (b. 1663)
- April 30 – Johann Albert Fabricius, German scholar and bibliographer (b. 1668)
- May 9 – Diogo de Mendonça Corte-Real, Portuguese politician (b. 1658)
- June 6 – Jean Baptiste de La Vérendrye, eldest son of Pierre Gaultier de Varennes et de La Vérendrye (b. 1713)
- July 7 – William Hardres, British politician (b. 1686)
- August 14 – Victor Honoré Janssens, Flemish painter (b. 1658)
- September 16 – Daniel Gabriel Fahrenheit, German physicist and inventor (b. 1686)
- September 26 – Louise Diane d'Orléans, last child of Philippe II, Duke of Orleans (b. 1716)
- October 22 – George Clarke, English politician, architect (b. 1661)
- November 2 – Louis Antoine de Pardaillan de Gondrin, French duke (b. 1664)
- December 10 – António Manoel de Vilhena, Portuguese 66th Grandmaster of the Knights Hospitaller (b. 1663)
- December 12 (burial) – Antonina Houbraken, Dutch draughtswoman (b. 1686)
- December 22 – Sir William Robinson, 1st Baronet, British politician (b. 1655)
- December 26 – Antonio Caldara, Italian composer (b. 1670)
- date unknown
- Piippola, Takalo. "Degree measurements by de Maupertuis in the Tornionlaakso Valley 1736-1737". Retrieved May 6, 2012.
- "Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, Cornelius Walford, ed. (C. and E. Layton, 1876) p50
- Journal du voyage fait par ordre du roi à l'équateur. Paris. 1751.
- Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio.
- An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst.