| 1799–1825 | [maths] | The French mathematician and physicist Pierre-Simon Laplace publishes the five-volume Traité de mécanique céleste/Celestial Mechanics, which applies calculus to the motions of celestial bodies and Isaac Newton's theories of the Solar System to show how its stability is implicit in the law of gravitation. |
| 1800–1850 | USA [consumer products] | A revolution in retail and wholesale trade occurs: specialization transforms the urban retail market, replacing the general store with individual stores for hardware, groceries, dry goods, furnishing, books, tobacco, and so on. Cash-only sales policies are instituted around 1806. |
| 1810–1859 | USA [agriculture] | US cotton production, the vast majority of which is grown in the southern states, rises from 171,000 bales in 1810 to just under 5.4 million in 1859. |
| 1819–1826 | UK [other structures] | Scottish engineer Thomas Telford constructs the 177 m/580 ft Menai suspension bridge over the Menai Straits between Bangor, Wales and the island of Anglesey. The first modern suspension bridge, it uses chains of wrought-iron links suspended from masonry towers at either end. Lacking stiffening girders it is vulnerable to high winds. |
| c. 1820 | [maths] | The German mathematician Carl Friedrich Gauss reintroduces the normal distribution curve (‘Gausian distribution’) – a basic statistical tool. |
| c. 1820 | UK [sports] | Squash rackets, a version of rackets with a softer ball, is invented and developed at Harrow School, London, England. |
| 1820 | USA [football] | The first football games are played in US colleges. The game is a form of hazing by sophomores inflicted on freshmen by kicking the freshmen instead of the ball. The game is banned in the 1830s because of the high number of injuries. |
| 1820 | Spain [painting] | The Spanish artist Francisco José de Goya y Lucientes paints Saturn Devouring One of His Children. This is one of the ‘Black Pictures’ he paints on the walls of his own house, private works that are dark, savage, and violent. |
| 1820 | France [painting] | The French artist Théodore Géricault completes his painting The Raft of the Medusa, a grim depiction of a recent shipwreck. It becomes one of the major works of Romanticism. |
| c. 1820 | France [physics] | French physicist André Ampère develops an instrument that uses a needle to measure the flow of electricity. It is the first measurement of electricity. |
| 1820 | Germany [physics] | German inventor Johann Schweigger develops the first galvanometer for measuring the intensity and direction of an electric current. |
| 1820 | England [poetry] | The English poet John Keats publishes the first version of his epic poem Hyperion. A second version appears posthumously in 1856. He also publishes the poems The Eve of Saint Agnes and Ode to a Nightingale. |
| 1820 | England [poetry] | The English poet Percy Bysshe Shelley publishes the poems Prometheus Unbound and Ode to the West Wind. |
| 1 January 1820 | Spain [revolution] | A revolution begins in Spain due to King Ferdinand VII's failure to adhere to the constitution of 1812 and his sending of troops to South America to put down risings in the Spanish colonies that have attracted much popular support in Spain itself. |
| 14 January 1820 | Antarctica [exploration] | English naval officer Edward Bransfield lands on Deception Island in Antarctica, and plants the Union Jack and buries a bottle containing coins there. He sights high, snow-covered mountains to the south on 20 January – the first sighting of mainland Antarctica. |
| 29 January 1820 | England [births and deaths] | George III, king of Great Britain and Ireland 1760–1820, dies in Windsor Castle, England (81). |
| 29 January 1820 | Britain [political events] | Following the death of King George III of Britain, he is succeeded by the prince regent as George IV. |
| 15 February 1820 | USA [births and deaths] | Susan B(rownell) Anthony, US suffragette whose work eventually leads to women's suffrage in the USA (1920), born in Adams, Massachusetts (–1906). |
| 20 February 1820 | France [administration] | Elie, duc de Decazes, is dismissed as prime minister of France after the assassination of Charles-Ferdinand d'Artois, duc de Berry, and is succeeded by his predecessor, the more right-wing Armand du Plessis, duc de Richelieu. |
| 6 March 1820 | USA [law and government] | The ‘Missouri Compromise’ is decided by the US Congress, allowing Missouri to enter the Union as a slave state and Maine as a nonslave state, and banning slavery in all Louisiana Purchase territories north of Missouri's southern border. |
| 7 March 1820 | Spain [political events] | King Ferdinand VII of Spain is forced by popular pressure to restore the constitution of 1812 and to abolish the Inquisition, the body responsible for upholding Catholicism in Spain. |
| 12 May 1820 | England, Florence [births and deaths] | Florence Nightingale, ‘Lady of the Lamp’, English nurse who is in charge of nursing the British troops during the Crimean War and who establishes nursing as a profession for women, born in Florence, Italy (–1910). |
| 6 June 1820 | UK [political events] | Caroline, Princess of Wales, whom King George IV of Britain wishes to divorce, triumphantly enters London, England, demanding her recognition as queen. |
| 28 November 1820 | Prussia [births and deaths] | Friedrich Engels, German socialist philosopher who, with Karl Marx, writes The Communist Manifesto (1848) which lays the foundations of modern communism, born in Barmen, Prussia (now Germany) (–1895). |
| December 1820 | USA [elections] | James Monroe and Daniel D Tompkins are re-elected as US president and vice-president respectively. |