Euler angle

noun

Any one of three angles which together describe the orientation of a rigid body with respect to a fixed three-dimensional coordinate system, according to a formalism introduced by Leonhard Euler.

“Euler angles can also represent the orientation of a mobile frame of reference in physics or the orientation of a basis in 3-dimensional linear algebra.”

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Meanings

nounEuler angle (plural Euler angles)

plural Euler angles

  1. geometryAny one of three angles which together describe the orientation of a rigid body with respect to a fixed three-dimensional coordinate system, according to a formalism introduced by Leonhard Euler.

    Euler angles can also represent the orientation of a mobile frame of reference in physics or the orientation of a basis in 3-dimensional linear algebra.

    3 more examples

    The use of Euler angles or Quaternions to represent entity (i.e., vehicle) orientation in the draft military standard for Distributed Interactive Simulation has drawn fierce debate.

    1991, “AIAA Flight Simulation Technologies Conference: A Collection of Technical Papers”, in AIAA, page 271

    We have not drawn a picture, since Euler angle pictures of three-dimensional rotations are notoriously difficult to comprehend; what is very useful is for the reader to make a set of wire axes with labels to help follow the sequence of rotations.

    2006, Don Koks, Explorations in Mathematical Physics: The Concepts Behind an Elegant Language, Springer, page 171

    Why do we need to know what Euler angles are? Because we use them. Many commercial 3D computer animation packages that are available today use Euler angles to describe and change orientations of objects.

    2008, Midori Kitagawa, Brian Windsor, MoCap for Artists: Workflow and Techniques for Motion Capture, Elsevier (Focal Press), page 188

Origin

Named after Swiss mathematician Leonhard Euler (1707–1783).

Full word history & related roots →

Translations

German eulerscher Winkel, Euler-Winkel
  • eulerscher Winkelany one of three angles that describe orientation in a 3-d coordinate system
  • Euler-Winkelany one of three angles that describe orientation in a 3-d coordinate system
Italian angolo di Eulero
  • angolo di Euleroany one of three angles that describe orientation in a 3-d coordinate system
Romanian unghi Euler
  • unghi Eulerany one of three angles that describe orientation in a 3-d coordinate system
Cite this entry
APA

Euler angle. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/Euler%20angle

MLA

“Euler angle.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Euler%20angle. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “Euler angle,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/Euler%20angle.

Source: Euler angle on Wiktionary, CC BY-SA 4.0.