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EuclideanDistance[u,v]

gives the Euclidean distance between vectors u and v.

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Applications  
Properties & Relations  
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EuclideanDistance

EuclideanDistance[u,v]

gives the Euclidean distance between vectors u and v.

Details

Examples

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Basic Examples  (2)

Euclidean distance between two vectors:

Euclidean distance between numeric vectors:

Scope  (2)

Compute distance between any vectors of equal length:

Compute distance between vectors of any precision:

Applications  (2)

Cluster data using Euclidean distance:

Demonstrate the triangle inequality:

Properties & Relations  (7)

EuclideanDistance is equivalent to Norm of a difference:

The square of EuclideanDistance is SquaredEuclideanDistance:

EuclideanDistance is greater than or equal to ChessboardDistance:

CosineDistance includes a dot product scaled by Euclidean distances from the origin:

CorrelationDistance includes a dot product scaled by Euclidean distances from means:

StandardDeviation as a EuclideanDistance from the Mean:

EuclideanDistance computed from RootMeanSquare of a difference:

Wolfram Research (2007), EuclideanDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/EuclideanDistance.html.

Text

Wolfram Research (2007), EuclideanDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/EuclideanDistance.html.

CMS

Wolfram Language. 2007. "EuclideanDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EuclideanDistance.html.

APA

Wolfram Language. (2007). EuclideanDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EuclideanDistance.html

BibTeX

@misc{reference.wolfram_2025_euclideandistance, author="Wolfram Research", title="{EuclideanDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/EuclideanDistance.html}", note=[Accessed: 29-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_euclideandistance, organization={Wolfram Research}, title={EuclideanDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/EuclideanDistance.html}, note=[Accessed: 29-August-2025]}