The year 1513 in science and technology included a number of events, some of which are listed here.

• March 27 – Juan Ponce de León becomes the first European definitely known to sight the modern-day territory of the United States, specifically Florida, mistaking it for another island. His expedition lands on April 2.^[1]
• May – Portuguese explorer Jorge Álvares lands on Lintin Island in the Pearl River estuary.^[1]
• September 26 – Vasco Núñez de Balboa, "silent upon a peak in Darién", first sees what will become known as the Pacific Ocean.^[1]
• Portuguese land on Ambon Island.
• Piri Reis map compiled.
• Publication in Oppenheim of Johannes Stöffler's treatise on the construction and use of astrolabes, Elucidatio fabricae ususque astrolabii.

• Eucharius Rösslin publishes Der Rosengarten, an obstetrics manual primarily for midwives written in German which will be widely translated and circulated in Europe.

• Jacques Daléchamps, French physician and botanist (died 1588)

• Ibn Ghazi al-Miknasi, Moroccan scholar and mathematician (born 1437)
• Hua Sui, Chinese pioneer of metal movable type printing (born 1439)