The year 1813 in science and technology involved some significant events, listed below.

• April – William Charles Wells reads a paper to the Royal Society of London making the first clear statement about natural selection.^[1][2][3][4]
• Charles Waterton begins the process of turning his estate at Walton Hall, West Yorkshire, England, into what is, in effect, the world's first nature reserve.^[5]

• Mathieu Orfila publishes his groundbreaking Traité des poisons, formalizing the field of toxicology.^[6]
• Louis Jacques Thénard commences publication of his textbook Traité de chimie élémentaire, théorique et pratique in Paris.
• Edward Howard invents the enclosed vacuum pan for refining sugar.

• May 11 – Gregory Blaxland, William Lawson and William Wentworth leave on an expedition to cross the Blue Mountains (New South Wales).

• S. D. Poisson publishes Poisson's equation, his correction of Laplace's second order partial differential equation for potential.^[7]

• British engineer Peter Ewart supports the idea of the conservation of energy in his paper "On the measure of moving force".

• Henri de Saint-Simon publishes Physiologie sociale.

• Probable date – George E. Clymer invents the Columbian press.

• March 1 – Sir Humphry Davy employs Michael Faraday as "chemical assistant" at the Royal Institution of Great Britain in London.

• Copley Medal: William Thomas Brande^[8]

• January 19 – Henry Bessemer, English inventor (died 1898)
• February 18 – Karl Weltzien, Russian-born German inorganic chemist, an organizer of the Karlsruhe Congress (died 1870)
• March 19 – David Livingstone, Scottish missionary and explorer (died 1873)
• April 16 - Justin Benoît, French surgeon and anatomist (died 1893)^[9]
• July 12 – Claude Bernard, French physiologist (died 1878)
• October 17 – Georg Büchner, Hessian-born writer and anatomist (died 1837)
• December 19 – Thomas Andrews, Irish chemist (died 1885)
• December 29 – Alexander Parkes, English chemist (died 1890)

• April 10 – Joseph Louis Lagrange, Piedmont-born mathematician (born 1736)
• April 19 – Benjamin Rush, Founding Father of the United States, chemist and physician (born 1746)
• April 27 – General Zebulon Pike, American explorer (born 1779)
• May – Johann Karl Wilhelm Illiger, German zoologist (born 1775)
• July 22 – George Shaw, English naturalist (born 1751)
• August 23 – Alexander Wilson, Scottish American ornithologist (born 1766)