Distance Formula

Pronunciation: /ˈdɪst.əns ˈfɔɹ.mjə.lə/ Explain

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The distance formula is the square root of the square of the difference in x plus the square of the difference in y.
Manipulative 1 - Distance formula Created with GeoGebra.

The distance formula is used to calculate the distance between any two points.[2] For the distance between the origin (0,0) and a point in a plane, the formula is D=square root(x^2+y^2) where the coordinate of the point is (x,y) The formula for the distance between any two points on the Cartesian plane is D=square root((x2-x1)^2+(y2-y1)^2)

The distance formula is derived from the Pythagorean theorem which states for a right triangle with legs of length A and B, and an hypotenuse of length C, then the relationship A2 + B2 = C2 is always true.


  1. McAdams, David E.. All Math Words Dictionary, distance. 2nd Classroom edition 20150108-4799968. pg 63-64. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Barnett Rich, Christopher Thomas. Schaum's Outline of Geometry. 4th edition. pg 206. McGraw-Hill. August 13, 2008. Last Accessed 7/3/2018. Buy the book
  3. John Sparks. The Student's Essential Formula Book. pg 33. AuthorHouse. July 12, 2004. Last Accessed 7/3/2018. Buy the book

Cite this article as:

McAdams, David E. Distance Formula. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/d/distanceformula.html.

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Revision History

4/20/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/23/2010: Added "References". (McAdams, David E.)
12/12/2008: Added manipulative 1. (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
7/12/2008: Changed equations to Hot_Eqn. (McAdams, David E.)
2/4/2008: Fixed spelling error. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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