Euler orbits the Sun at a distance of 2.3–2.6 AU once every 3 years and 9 months (1,373 days). Its orbit has an eccentricity of 0.07 and an inclination of 9° with respect to the ecliptic.
According to the surveys carried out by the Infrared Astronomical Satellite IRAS, the Japanese Akari satellite, and NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Euler measures between 14.49 and 19.773 kilometers in diameter and its surface has an albedo between 0.0416 and 0.0839. The Collaborative Asteroid Lightcurve Link adopts Petr Pravec's revised WISE-data, that is, an albedo of 0.0375 and a diameter of 19.78 kilometers with an absolute magnitude of 12.7.
This minor planet was named after Swiss mathematician, physicist and astronomer Leonhard Euler (1707–1783). His contributions to astronomy included two theories for the motion of the Moon. Euler spent much of his time in St. Petersburg and was associated with the Russian Academy of Sciences. The official naming citation was published by the Minor Planet Center on 15 October 1977 (M.P.C. 4238).