The year 1775 in science and technology involved some significant events.

• The cheetah (Acinonyx jubatus) is described.^[1]

• May 25 – Joseph Priestley's account of his isolation of oxygen in the form of a gas ("dephlogisticated air") is read to the Royal Society of London.^[2]
• Torbern Bergman's De attractionibus electivis ("A Dissertation on Elective Attractions") is published, containing the largest tables of chemical affinity ever published.

• July 30 – 3-year second voyage of James Cook completed, the first eastabout global circumnavigation, during which the Antarctic Circle has been crossed three times, Terra Australis shown to be a myth, and Larcum Kendall's K1 chronometer demonstrated to be a reliable timekeeper for the purpose of calculating longitude.

• Lagrange's Recherches d'Arithmétique develops a general theory of binary quadratic forms.
• First Stanhope Demonstrator, a mechanical device to demonstrate and solve problems in logic, is produced by English aristocrat Charles Stanhope, 3rd Earl Stanhope.^[3]

• English surgeon Percivall Pott finds the first occupational link to cancer, contributing to the science of epidemiology.
• German physician Melchior Adam Weikard anonymously publishes the textbook Der Philosophische Arzt including the earliest description of symptoms resembling attention deficit hyperactivity disorder.

• February 21 – La Specola, Florence's Museum of Zoology and Natural History, opens to the public.
• Johan Christian Fabricius publishes his Systema entomologiæ.
• Peter Forsskål's Descriptiones Animalium: Avium, amphiborum, insectorum, vermium quæ in itinere orientali (containing early observations on bird migration) and Flora Ægyptiaco-Arabica sive descriptiones plantarum quas per Ægyptum Inferiorem et Arabiam felicem detexit are published posthumously, edited by Carsten Niebuhr.^[4]

• May 22 – James Watt's 1769 steam engine patent is extended to June 1800 by Act of Parliament of Great Britain and the first engines are built under it.^[5][6]
• Jacques-Constantin Périer operates a paddle steamer on the Seine, but it proves to be underpowered.^[7]
• Alexander Cumming patents the S-trap in London, laying the foundations for the modern flush toilet.^[8]
• Edinburgh confectioner Charles Spalding devises improvements to the diving bell, adding a system of balance-weights.^[9]
• Pierre-Simon Girard, age 10, invents a water turbine.
• December 30 – John Arnold takes out his first patent for improvements in the construction of marine chronometers in Britain, including the first for a compensation balance.^[10]
• Approximate date – Thomas Mudge invents the detached lever escapement for clocks and watches.
• French Academy of Sciences made the statement that the academy "will no longer accept or deal with proposals concerning perpetual motion."^[11]

• Copley Medal: Nevil Maskelyne^[12]

• January 22 – André-Marie Ampère, French physicist (died 1836)
• February 9 – Farkas Bolyai, Hungarian mathematician (died 1856)
• May 10 – William Phillips, English geologist (died 1828)
• July 23 – Étienne-Louis Malus, French physicist and mathematician] (died 1812)
• September 30 – Robert Adrain, Irish-born mathematician (died 1843)
• November 19 – Johann Karl Wilhelm Illiger, German entomologist and zoologist (died 1813)

• March 3 – Richard Dunthorne, English astronomer (born 1711)
• May 1 – Israel Lyons, English mathematician and botanist (born 1739; died of measles)
• October 25 – Johan Maurits Mohr, Dutch astronomer (born 1716)