(definition)

**Definition:**
The straight line distance between two points. In a plane with p_{1} at (x_{1}, y_{1}) and p_{2} at (x_{2}, y_{2}), it is √((x_{1} - x_{2})² + (y_{1} - y_{2})²).

**See also**
*rectilinear*, *Manhattan distance*, *L _{m} distance*.

*Note:
In N dimensions, the Euclidean distance between two points p and q is √(∑ _{i=1}^{N} (p_{i}-q_{i})²) where p_{i} (or q_{i}) is the coordinate of p (or q) in dimension i.*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Tue Jan 16 10:34:44 2018.

Cite this as:

Paul E. Black, "Euclidean distance", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/euclidndstnc.html