Euler's Formula

Pronunciation: /ˈɔɪ.lərz ˈfɔɹ.mjə.lə/ Explain

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Euler's formula is e^i*theta}=cos(theta)+i*sin(theta).[1] It is remarkable in that it relates trigonometric function functions with complex numbers. Euler's formula maps the natural constant e raised to the complex exponent i^theta to the complex plane using the trigonometric expression cos(theta)+i*sin(theta). This equation is true only if the angle θ is measured in radians.

Euler's formula is named after Leonhard Euler who published it in its present form in 1748.

Leonard Euler was a very prolific mathematician. Note that the phrase Euler's Formula is used to indicate different formulas in different disciplines.


  1. McAdams, David E.. All Math Words Dictionary, euler's formula. 2nd Classroom edition 20150108-4799968. pg 73. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Paul J. Nahin. Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills. Princeton University Press. April 10, 2006. Last Accessed 7/9/2018. Buy the book
  3. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pg 30. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 7/9/2018. Buy the book

Cite this article as:

McAdams, David E. Euler's Formula. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/29/2010: Added "References". (McAdams, David E.)
12/23/2008: Initial version. (McAdams, David E.)

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