1787 in science
- January 11 – William Herschel discovers Titania and Oberon, the first moons of Uranus found.
- February 19 – First light for William Herschel's 40-foot telescope under construction at Observatory House, Slough, England.
- Caroline Herschel is granted an annual salary of £50 by King George III of Great Britain for acting as assistant to her brother William in astronomy.
- William Curtis begins publication of The Botanical Magazine; or Flower-Garden Displayed in London. As Curtis's Botanical Magazine, it will still be published into the 21st century.
- Spanish physician Francisco Xavier Cid publishes Tarantismo Observado en España, a study of tarantulas and the tarantella as a cure for their bite.
- King George III of Great Britain, writing as Ralph Robinson of Windsor, contributes to Arthur Young's Annals of Agriculture.
- Guyton de Morveau, Jean-Henri Hassenfratz, Antoine François, Antoine Lavoisier, Pierre Adet and Claude Berthollet publish Méthode de nomenclature chimique in Paris.
- Jacques Charles proposes Charles's law, a corollary of Boyle's law, describes relationship between temperature and volume of a gas.
- Antoine Lavoisier publishes Méthode de nomenclature chimique.
- Ernst Chladni publishes Entdeckungen über die Theorie des Klanges, demonstrating modes of vibration.
- Jean-Paul Marat publishes the first French translation of Newton's 'Opticks'
- The first great theodolite constructed by Jesse Ramsden for the Anglo-French Survey (1784–1790) linking the observatories of Paris and Greenwich.
- June – William Symington patents improvements to the Watt steam engine.
- c. July – John Wilkinson launches an iron barge in the English Midlands.
- August 27 – Launching a 45-foot (14 m) steam-powered craft on the Delaware River, John Fitch demonstrates the first United States patent for his design.
- December 3 – James Rumsey demonstrates a water-jet propelled boat on the Potomac.
- First production of all-iron edge rail (for underground colliery rail transport), at Plymouth Ironworks, Merthyr Tydfil, South Wales.
- First introduction of a plateway, underground at Sheffield Park Colliery, Yorkshire, England, by John Curr.
- William Chapman designs a segmental skew arch at Finlay Bridge, Naas, on the Kildare Canal in Ireland.
- Levi Hutchins of New Hampshire produces a mechanical alarm clock.
- January 24 – Christophe-Paulin de La Poix de Fréminville (died 1848), French explorer and naturalist.
- March 6 – Joseph von Fraunhofer (died 1826), Bavarian physicist.
- March 8 – Karl Ferdinand von Graefe (died 1840), Polish-born German surgeon.
- March 9 - Josephine Kablick (died 1863), Czech botanist and paleontologist.
- March 16 – Georg Ohm (died 1854), German physicist.
- March 28 – Claudius James Rich (died 1821), British archaeologist and anthropologist.
- March 29 – Carl Philipp Sprengel (died 1859), German botanist.
- April 24 – Mathieu Orfila (died 1853), Spanish-born French physician and chemist.
- May 27 – Benjamin Valz (died 1867), French astronomer.
- June 2 – Nils Gabriel Sefström (died 1845), Swedish chemist and mineralogist.
- June 3 – Auguste Le Prévost (died 1859), French geologist, philologist, archaeologist and historian.
- June 4 – Constant Prévost (died 1856), French geologist.
- June 7 – William Conybeare (died 1857), English geologist.
- June 27 – Thomas Say (died 1834), American naturalist.
- August 16 – Jean Michel Claude Richard (died 1868), French botanist.
- August 24 – James Weddell (died 1834), Flemish-born Anglo-Scots seal hunter and Antarctic explorer.
- September 5 – François Sulpice Beudant (died 1850), French mineralogist et geologist.
- September 15 – Guillaume-Henri Dufour (died 1875), Swiss engineer et topographer.
- November 5 – John Richardson (died 1865), Scottish naturalist, explorer and surgeon.
- November 9 – Johann Natterer (died 1843), Austrian naturalist.
- November 18 – Louis Daguerre (died 1851), French inventor.
- December 17 – John Forbes (died 1861), Scottish physician
- December 17 (or 18) – Jan Evangelista Purkinje (died 1869), Czech anatomist et neurophysiologist.
- February 13 – Ruđer Bošković, Ragusan physicist, mathematician and astronomer (born 1711)
- May 10 – William Watson, English physician, botanist and physicist (born 1715)
- Ogilvie, Marilyn Bailey (1986). Women in Science: Antiquity through the Nineteenth Century. Cambridge, Massachusetts: MIT Press. pp. 97–98. ISBN 0-262-65038-X.
- "Jacques Alexandre César Charles". Centennial of Flight. U.S. Centennial of Flight Commission. 2001. Archived from the original on 2007-02-24. Retrieved 2007-02-23.
- *Roy, William (1790). "An Account of the Trigonometrical Operation, Whereby the Distance between the Meridians of the Royal Observatories of Greenwich and Paris Has Been Determined". Philosophical Transactions of the Royal Society of London. 80: 111–254. doi:10.1098/rstl.1790.0015.
- Harvey, W. S.; Downs-Rose, G. (1980). "The Improved Atmospheric Engine". William Symington, inventor and engine builder. London: Northgate Publishing. pp. 19–32. ISBN 0-85298-443-X.
- "John Wilkinson (1728 – 1808)". History – Historic Figures. BBC. Retrieved 2011-06-29.
- van Laun, John (2001). Early Limestone Railways. London: Newcomen Society. pp. 203–4. ISBN 0-904685-09-8.
- Occasional Paper. Railway and Canal Historical Society, Early Railway Group. 184,192.
- McCutcheon, W. Alan (1984). The Industrial Archaeology of Northern Ireland. Belfast: HMSO. p. 16. ISBN 0-8386-3125-8.