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title VECTOR_NORMALIZE (Transact-SQL)
description VECTOR_NORMALIZE takes a vector as an input and returns the normalized vector, which is a vector scaled to have a length of 1 in a given norm type.
author WilliamDAssafMSFT
ms.author wiassaf
ms.reviewer damauri, pookam, randolphwest
ms.date 10/03/2025
ms.service sql
ms.subservice t-sql
ms.topic reference
ms.collection
ce-skilling-ai-copilot
ms.update-cycle 180-days
ms.custom
ignite-2025
f1_keywords
VECTOR_NORMALIZE
VECTOR_NORMALIZE_TSQL
helpviewer_keywords
VECTOR_NORMALIZE function
vector, normalize calculation
dev_langs
TSQL
monikerRange =sql-server-ver17 || =sql-server-linux-ver17 || =azuresqldb-current || =azuresqldb-mi-current || =fabric-sqldb

VECTOR_NORMALIZE (Transact-SQL)

[!INCLUDE sqlserver2025-asdb-asmi-fabricsqldb]

Use VECTOR_NORMALIZE to take a vector as an input and return the normalized vector, which is a vector scaled to have a length of 1 in a given norm type.

This standardization is crucial in various artificial intelligence applications where vectors represent different forms of data, such as visual content, textual information, or audio signals. By normalizing vectors, we ensure uniformity in their scale, which is particularly useful for operations that rely on measuring vector distances or for grouping and distinguishing data points.

While Azure OpenAI's models provide normalized vectors, there are other models and frameworks where vectors aren't automatically normalized. For example, in the Gensim library, which is commonly used for natural language processing tasks, vectors aren't always normalized by default.

Users often need to normalize the vectors manually or use specific functions provided by the library to ensure that the vectors are of unit length.

In general, with machine learning models or vector embeddings, it's important to check the documentation or the output of the model to determine whether the vectors are normalized. If normalization is required for your application, you might need to implement it as a separate step if the model doesn't provide normalized vectors by default.

For example, if you want a normalized vector using the Euclidean norm (which is the most common norm type), you can use:

SELECT VECTOR_NORMALIZE ( vector, 'norm2' )
FROM ...

Note

VECTOR_NORMALIZE is available in Azure SQL Managed Instance with the SQL Server 2025 or Always-up-to-date update policy.

Syntax

:::image type="icon" source="../../includes/media/topic-link-icon.svg" border="false"::: Transact-SQL syntax conventions

VECTOR_NORMALIZE ( vector , norm_type )

Arguments

vector

An expression that evaluates to vector data type.

norm_type

A string with the name of the norm type to use to calculate the norm of the given vector. The following norm types are supported:

  • norm1 - The 1-norm, which is the sum of the absolute values of the vector components.
  • norm2 - The 2-norm, also known as the Euclidean Norm, which is the square root of the sum of the squares of the vector components.
  • norminf - The infinity norm, which is the maximum of the absolute values of the vector components.

Return value

The result is a vector with the same direction as the input vector but with a length of 1 according to the given norm.

If the input is NULL, the returned result is also NULL.

An error is returned if norm_type isn't a valid norm type and if the vector isn't of the vector data type.

Examples

Example 1

Normalize a vector:

CREATE TABLE dbo.vectors
(
    ID INT PRIMARY KEY,
    v VECTOR(3) NOT NULL
);

INSERT INTO dbo.vectors (ID, v)
VALUES (1, '[0.1, -2, 42]'),
(2, '[2, 0.1, -42]');

SELECT ID, VECTOR_NORMALIZE(v, 'norm2') AS nv
FROM dbo.vectors;

Example 2

DECLARE @v AS VECTOR(3) = '[1, 2, 3]';
SELECT VECTOR_NORMALIZE(@v, 'norm1'),
       VECTOR_NORMALIZE(@v, 'norminf');

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