The year 1845 in science and technology involved some significant events, listed below.

• April – Lord Rosse discovers that the nebula M51 has a spiral structure.
• September–October – Cornish mathematician John Couch Adams communicates to James Challis and George Biddell Airy his calculations demonstrating that a body (Neptune) is perturbing the orbit of Uranus.^[1]
• November 10 – Urbain Le Verrier presents to the Académie des sciences in Paris a memoir showing that existing theories fail to account for the motion of Uranus.^[2]
• Construction begins in Ireland of the "Leviathan of Parsonstown", a telescope built by Lord Rosse.

• August–September – Previously unknown Potato blight strikes the potato crop in Ireland: start of the Great Famine.^[3][4]

• March 17 – Stephen Perry patents the rubber band in England.^[5]
• Edmond Frémy discovers the oxidizing agent Frémy's salt.

• August – John Franklin's expedition with HMS Erebus and HMS Terror to find the Northwest Passage is last seen entering Baffin Bay prior to its mysterious disappearance.^[6]

• December 27 – Anesthesia is used in childbirth for the first time, by Dr Crawford Long in Jefferson, Georgia.

• September 13 – Michael Faraday discovers that an intense magnetic field can rotate the plane of polarized light, the Faraday effect.
• C. H. D. Buys Ballot confirms the Doppler effect for sound waves.^[7]
• Kirchhoff's circuit laws are first described by German physicist Gustav Kirchhoff.

• July 26–August 10 – Isambard Kingdom Brunel’s iron steamship Great Britain makes the Transatlantic Crossing from Liverpool to New York, the first screw propelled vessel to make the passage.^[8][9]
• The saxhorn family of valved brass instruments is patented by Adolphe Sax in France.

• January 14 – Physikalische Gesellschaft zu Berlin established and begins publishing Fortschritte der Physik and Verhandlungen.
• August 28 – The journal Scientific American begins publication.
• Alexander von Humboldt's Kosmos: Entwurf einer physischen Weltbeschreibung begins publication.

• Copley Medal: Theodor Schwann^[10]
• Wollaston Medal for Geology: John Phillips

• February 17 (Old Style March 1) – Fyodor Pirotsky (died 1898), Ukrainian-born Russian military and electrical engineer and inventor.
• March 3 – Georg Cantor (died 1918), Russian-born German mathematician.
• March 27 – Wilhelm Röntgen (died 1923), German physicist, discoverer of X-rays, Nobel laureate.
• April 21 – William Healey Dall (died 1927), American malacologist and explorer.
• May 4 – William Kingdon Clifford (died 1879), English geometer.
• May 16 – Élie Metchnikoff (died 1916), Russian-born microbiologist, Nobel laureate.
• June 16 – Heinrich Dressel (died 1920), German archaeologist.
• July 4 – Thomas Barnardo (died 1905), Irish-born physician and philanthropist.
• September 11 – Émile Baudot (died 1903), French telegraph engineer.
• November 14 – Ulisse Dini (died 1918), Italian mathematician.

• January 11 – Etheldred Benett (born 1776), British geologist.
• March 13 – John Frederic Daniell (born 1790), English chemist and physicist.
• March 18 – 'Johnny Appleseed' (John Chapman) (born 1774), American nurseryman.^[11]
• April 10 – Thomas Sewall (born 1786), American anatomist.
• October 18 – Dominique, comte de Cassini (born 1748), French astronomer.
• Jean Henri Jaume Saint-Hilaire (born 1772), French botanist.