Pronunciation: /ˈprɪn.sə.pəl/ Explain

In mathematics, the word principal has two main meanings:

  1. Principal is the original amount of a loan or deposit on which interest is calculated. If one borrows $1000 at 10% interest, the principal is $1000. For compound interest, the interest is added to the principal. For more information, see Interest.
  2. Principal also means major, largest or most imporant. For example, an ellipse has two axes. The larger of the two axes is called the major axis or the principal axis. Some of the uses of the adjective principal in mathematics are:
    • Principal axis:\ The longer of two axes.
    • Principal diagonal: The diagonal of a square matrix that goes from the upper left to the lower right is called the principal diagonal. This is because it is the diagonal usually used for reference.
    • Principal root: The principal root of a number is the positive square root of that number. The principal root of 25 is 5, not -5.
    • Principal value: The principal value of a inverse trigonometric function is a value that falls in a reference range. For arcsine and arccosine, the range of principal values is -π / 2 to π / 2. For arctangent, the range of principal values is 0 to π.


  1. McAdams, David E.. All Math Words Dictionary, principal. 2nd Classroom edition 20150108-4799968. pg 144. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Principal. 4/28/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

4/28/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
6/7/2010: Initial version. (McAdams, David E.)

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