EuclideanDistance[u,v]
gives the Euclidean distance between vectors u and v.


EuclideanDistance
EuclideanDistance[u,v]
gives the Euclidean distance between vectors u and v.
Details

- EuclideanDistance[u,v] is equivalent to Norm[u-v]. »
- EuclideanDistance can be used with symbolic vectors in GeometricScene.
Examples
open all close allBasic Examples (2)
Scope (2)
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:
Tech Notes
Related Guides
History
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: 08-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: 08-August-2025]}