or·​thog·​o·​nal ȯr-ˈthä-gə-nᵊl How to pronounce orthogonal (audio)
: intersecting or lying at right angles
In orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel.
: having perpendicular slopes or tangents at the point of intersection
orthogonal curves
: having a sum of products or an integral (see integral entry 1 sense 1b) that is zero or sometimes one under specified conditions: such as
of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero
of vectors : having the scalar product equal to zero
of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to one if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix
of a linear transformation : having a matrix (see matrix sense 5a) that is orthogonal : preserving length and distance
: composed of mutually orthogonal elements
an orthogonal basis of a vector space
: statistically independent
mental ability may be classified into several orthogonal … factorsO. D. Duncan
: orthographic sense 1
orthogonal projection
orthogonality noun
orthogonally adverb

Examples of orthogonal in a Sentence

Recent Examples on the Web In a 10,000-dimensional space there are millions of nearly orthogonal vectors. Anil Ananthaswamy, Quanta Magazine, 13 Apr. 2023 North African Jewish and non-Jewish populations form distinctive, orthogonal clusters. Razib Khan, Discover Magazine, 13 Aug. 2012 In 10,000-dimensional space, there are 10,000 such mutually orthogonal vectors. Anil Ananthaswamy, Quanta Magazine, 13 Apr. 2023 This duality is orthogonal at best. Neil Senturia, San Diego Union-Tribune, 1 Nov. 2021 Next, ceramic spheres and compressed aluminum powder rods are stacked in an orthogonal, grillage pattern and enclosed in a steel box using spot welds. Caroline Delbert, Popular Mechanics, 20 July 2020 The distance between the two towns can be measured on three (orthogonal) dimensions: longitude, latitude, and altitude. Neuroskeptic, Discover Magazine, 9 Jan. 2012 This direction favors subsequent hydraulic fractures being orthogonal to the well. Ian Palmer, Forbes, 19 May 2022 But anything that conducts an electric field also conducts a magnetic field in the orthogonal direction. James Conca, Forbes, 27 Sep. 2021 See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'orthogonal.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History


Middle French, from Latin orthogonius, from Greek orthogōnios, from orth- + gōnia angle — more at -gon

First Known Use

circa 1560, in the meaning defined at sense 1a

Time Traveler
The first known use of orthogonal was circa 1560

Dictionary Entries Near orthogonal

Cite this Entry

“Orthogonal.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/orthogonal. Accessed 29 Sep. 2023.

Medical Definition


or·​thog·​o·​nal ȯr-ˈthäg-ən-ᵊl How to pronounce orthogonal (audio)
: lying or intersecting at right angles
: being, using, or made with three ECG leads whose axes are perpendicular to each other and to the frontal, horizontal, and sagittal axes of the body
the three orthogonal leads were recorded simultaneously on magnetic tapeMassoud Nemati et al.
: statistically independent
mental ability may be classified into several orthogonal … factorsO. D. Duncan

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