> For the complete documentation index, see [llms.txt](https://mariadb.com/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mariadb.com/docs/server/reference/sql-functions/vector-functions/vec_distance_euclidean.md).
# VEC\_DISTANCE\_EUCLIDEAN
WEBINAR
The Next Generation of MariaDB: Powered by Vector Search
{% hint style="info" %}
[Vectors](/docs/server/reference/sql-structure/vectors.md) are available from [MariaDB 11.7](/docs/release-notes/community-server/old-releases/11.7/what-is-mariadb-117.md).
{% endhint %}
## Syntax
```bnf
VEC_DISTANCE_EUCLIDEAN(v, s)
```
## Description
`VEC_Distance_Euclidean` is an SQL function that calculates a Euclidean (L2) distance between two points.
Vectors must be of the same length, a distance between two vectors of different lengths is not defined and `VEC_Distance_Euclidean` returns `NULL` in such cases.
If the vector index was not built for the euclidean function (see [CREATE TABLE with Vectors](/docs/server/reference/sql-structure/vectors/create-table-with-vectors.md)), the index is not used, and a full table scan performed instead. The [VEC\_DISTANCE](/docs/server/reference/sql-functions/vector-functions/vector-functions-vec_distance.md) function is a generic function that behaves either as `VEC_DISTANCE_EUCLIDEAN` or [VEC\_DISTANCE\_COSINE](/docs/server/reference/sql-functions/vector-functions/vec_distance_cosine.md), depending on the underlying index type.
## Example
```sql
INSERT INTO v VALUES
(1, x'e360d63ebe554f3fcdbc523f4522193f5236083d'),
(2, x'f511303f72224a3fdd05fe3eb22a133ffae86a3f'),
(3,x'f09baa3ea172763f123def3e0c7fe53e288bf33e'),
(4,x'b97a523f2a193e3eb4f62e3f2d23583e9dd60d3f'),
(5,x'f7c5df3e984b2b3e65e59d3d7376db3eac63773e'),
(6,x'de01453ffa486d3f10aa4d3fdd66813c71cb163f'),
(7,x'76edfc3e4b57243f10f8423fb158713f020bda3e'),
(8,x'56926c3fdf098d3e2c8c5e3d1ad4953daa9d0b3e'),
(9,x'7b713f3e5258323f80d1113d673b2b3f66e3583f'),
(10,x'6ca1d43e9df91b3fe580da3e1c247d3f147cf33e');
SELECT id FROM v
ORDER BY VEC_Distance_Euclidean(v, x'6ca1d43e9df91b3fe580da3e1c247d3f147cf33e') LIMIT 10;
+----+
| id |
+----+
| 10 |
| 7 |
| 3 |
| 9 |
| 2 |
| 1 |
| 5 |
| 4 |
| 6 |
| 8 |
+----+
```
{% hint style="info" %}
The vector index is only used for nearest-neighbor search when the query combines `ORDER BY VEC_DISTANCE_EUCLIDEAN(...)` with a `LIMIT`. Without `LIMIT`, the distance is computed for every row (a full table scan). See [Vector Overview](/docs/server/reference/sql-structure/vectors/vector-overview.md).
{% endhint %}
## See Also
* [VEC\_DISTANCE](/docs/server/reference/sql-functions/vector-functions/vector-functions-vec_distance.md)
* [VEC\_DISTANCE\_COSINE](/docs/server/reference/sql-functions/vector-functions/vec_distance_cosine.md)
* [Vector Overview](/docs/server/reference/sql-structure/vectors/vector-overview.md)
* [CREATE TABLE with Vectors](/docs/server/reference/sql-structure/vectors/create-table-with-vectors.md)
*This page is licensed: CC BY-SA / Gnu FDL*
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