Database normalization is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by Edgar F. Codd as part of his relational model.

Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of synthesis (creating a new database design) or decomposition (improving an existing database design).

Informally, a relational database relation is often described as "normalized" if it meets third normal form. Most 3NF relations are free of insertion, update, and deletion anomalies.

The normal forms (from least normalized to most normalized) are:

• UNF: Unnormalized form
• 1NF: First normal form
• 2NF: Second normal form
• 3NF: Third normal form
• EKNF: Elementary key normal form
• BCNF: Boyce–Codd normal form
• 4NF: Fourth normal form
• ETNF: Essential tuple normal form
• 5NF: Fifth normal form
• DKNF: Domain-key normal form
• 6NF: Sixth normal form

	UNF	1NF	2NF	3NF	EKNF	BCNF	4NF	ETNF	5NF	DKNF	6NF
Primary key (no duplicate tuples)
No repeating groups
Atomic columns (cells have single value)
No partial dependencies (values depend on the whole of every Candidate key)
No transitive dependencies (values depend only on Candidate keys)
Every non-trivial functional dependency involves either a superkey or an elementary key's subkey											N/A
No redundancy from any functional dependency											N/A
Every non-trivial, multi-value dependency has a superkey											N/A
A component of every explicit join dependency is a superkey											N/A
Every non-trivial join dependency is implied by a candidate key											N/A
Every constraint is a consequence of domain constraints and key constraints											N/A
Every join dependency is trivial

Example of a step by step normalization

Normalization is a database design technique, which is used to design a relational database table up to higher normal form. The process is progressive, and a higher level of database normalization cannot be achieved unless the previous levels have been satisfied.

That means that, having data in unnormalized form (the least normalized) and aiming to achieve the highest level of normalization, the first step would be to ensure compliance to first normal form, the second step would be to ensure second normal form is satisfied, and so forth in order mentioned above, until the data conform to sixth normal form.

However, it is worth noting that normal forms beyond 4NF are mainly of academic interest, as the problems they exist to solve rarely appear in practice.

Please note that the data in the following example were intentionally designed to contradict most of the normal forms. In real life, it's quite possible to be able to skip some of the normalization steps because the table doesn't contain anything contradicting the given normal form. It also commonly occurs that fixing a violation of one normal form also fixes a violation of a higher normal form in the process. Also one table has been chosen for normalization at each step, meaning that at the end of this example process, there might still be some tables not satisfying the highest normal form.

Initial data

Let a database table with the following structure:

We assume in this example that each book has only one author.

Satisfying 1NF

To satisfy 1NF, the values in each column of a table must be atomic. In the initial table, Subject contains a set of subject values, meaning it does not comply.

One way to achieve the 1NF would be to separate the duplicities into multiple columns using repeating groups 'subject':

Although now the table formally complies to the 1NF (is atomic), the problem with this solution is obvious - if a book has more than three subjects, it cannot be added to the database without altering its structure.

To solve the problem in a more elegant way, it is necessary to identify entities represented in the table and separate them into their own respective tables. In this case, it would result in Book, Subject and Publisher tables:

Simply separating the initial data into multiple tables would break the connection between the data. That means the relationships between the newly introduced tables need to be determined. Notice that the Publisher ID column in the Book's table is a foreign key realizing many-to-one relation between a book and a publisher.

A book can fit many subjects, as well as a subject may correspond to many books. That means also a many-to-many relationship needs to be defined, achieved by creating a link table:

Instead of one table in unnormalized form, there are now 4 tables conforming to the 1NF.

Satisfying 2NF

The Book table has one candidate key, the compound key {Title , Format}. Consider the following table fragment:

All of the attributes that are not part of the key depend on Title, but only Price also depends on Format. To conform to 2NF and remove duplicities, every non-key attribute must depend on the whole key, not just part of it.

To normalize this table, make {Title} the (simple) key so that every non-key attribute depends upon the whole key, and remove Price into a separate table so that its dependency on Format can be preserved:

Now, the book table conforms to 2NF.

Satisfying 3NF

A table in third normal form (3NF) is a table in 2NF that has no transitive dependencies. Note the book table with more rows (previously omitted for brevity):

Genre ID and Genre Name both depend upon the primary key {Title}, but they are not independent of one another. The dependency of, say, Genre Name on the primary key can be deduced from the dependency of Genre Name on Genre ID and of Genre ID on the primary key. Since there are more titles than genres, that dependency introduces redundant data into the Book table which can be eliminated by abstracting the dependency of Genre Name on Genre ID into its own table:

The Book table is now in third normal form. Although tables in 1NF are by definition normalized, "normalized" is commonly used to mean 3NF.

Satisfying EKNF

The elementary key normal form (EKNF) falls strictly between 3NF and BCNF and is not much discussed in the literature. It is intended “to capture the salient qualities of both 3NF and BCNF” while avoiding the problems of both (namely, that 3NF is “too forgiving” and BCNF is “prone to computational complexity”). Since it is rarely mentioned in literature, it is not included in this example.

Satisfying BCNF

Consider the table in 3NF from the previous step:

There is a non-trivial dependency violating BCNF - {Author} → {Author Nationality}. Therefore, the table should be decomposed:

Now, each attribute represents a fact about the key, the whole key, and nothing but the key. Therefore BCNF has been achieved.

Satisfying 4NF

Assume the database is owned by a book retailer franchise that has several franchisees that own shops in different locations. And therefore the retailer decided to add a table that contains data about availability of the books at different locations:

As this table structure consists of a compound primary key, it doesn't contain any non-key attributes and it's already in BCNF (and therefore also satisfies all the previous normal forms). However, if we assume that all available books are offered in each area, we might notice that the Title is not unambiguously bound to a certain Location and therefore the table doesn't satisfy 4NF.

That means that, to satisfy the fourth normal form, this table needs to be decomposed as well:

Now, every record is unambiguously identified by a superkey, therefore 4NF is satisfied.

Satisfying ETNF

Suppose the franchisees can also order books from different suppliers. Let the relation also be subject to the following constraint:

• If a certain supplier supplies a certain title
• and the title is supplied to the franchisee
• and the franchisee is being supplied by the supplier,
• then the supplier supplies the title to the franchisee.

This table is in 4NF, but the Supplier ID is equal to the join of its projections: { { Supplier ID , Book } , { Book, Franchisee ID } , { Franchisee ID , Supplier ID } }. No component of that join dependency is a superkey (the sole superkey being the entire heading), so the table does not satisfy the ETNF and can be further decomposed:

The decomposition produces ETNF compliance.

Satisfying 5NF

To spot a table not satisfying the 5NF, it is usually necessary to examine the data thoroughly. Suppose the table from 4NF example with a little modification in data and let's examine if it satisfies 5NF:

If we decompose this table, we lower redundancies and get the following two tables:

What happens if we try to join these tables? The query would return the following data:

Apparently, the JOIN returns three more rows than it should - let's try to add another table to clarify the relation. We end up with three separate tables:

What will the JOIN return now? It actually is not possible to join these three tables. That means it wasn't possible to decompose the Franchisee - Book Location without data loss, therefore the table already satisfies 5NF.

Satisfying DKNF

Let's have a look at the Book table from previous examples and see if it satisfies the Domain Key Normal Form:

Logically, Thickness is determined by number of pages. That means it depends on Pages which is not a key. Let's set an example convention saying a book up to 350 pages is considered "slim" and a book over 350 pages is considered "thick".

This convention is technically a constraint but it is neither a domain constraint nor a key constraint; therefore we cannot rely on domain constraints and key constraints to keep the data integrity.

In other words - nothing prevents us from putting, for example, "Thick" for a book with only 50 pages - and this makes the table violate DKNF.

To solve this, we can create a table holding enumeration that defines the Thickness and remove that column from the original table:

That way, the domain integrity violation has been eliminated, and the table is in DKNF.

Satisfying 6NF

A simple and intuitive definition of the sixth normal form is that "a table is in 6NF when the row contains the Primary Key, and at most one other attribute".

That means, for example, the Publishers table designed while creating the 1NF

needs to be further decomposed into two tables:

The obvious drawback of 6NF is the proliferation of tables required to represent the information on a single entity. If a table in 5NF has one primary key column and N attributes, representing the same information in 6NF will require N tables; multi-field updates to a single conceptual record will require updates to multiple tables; and inserts and deletes will similarly require operations across multiple tables. For this reason, in databases intended to serve Online Transaction Processing needs, 6NF should not be used.

However, in data warehouses, which do not permit interactive updates and which are specialized for fast query on large data volumes, certain DBMSs use an internal 6NF representation - known as a Columnar data store. In situations where the number of unique values of a column is far less than the number of rows in the table, column-oriented storage allow significant savings in space through data compression. Columnar storage also allows fast execution of range queries (e.g., show all records where a particular column is between X and Y, or less than X).

In all these cases, however, the database designer does not have to perform 6NF normalization manually by creating separate tables.