Relational Algebra and Relational Calculus are the formal query languages for a relational model. Both form the base for the SQL language which is used in most of the relational DBMSs. **Relational Algebra** is a procedural language.

On the other hands, **Relational Calculus** is a declarative language. Relational Algebra and Relational Calculus can be further differentiated on many aspects, which I have discussed below with the help of comparison chart.

### Content: Relational Algebra Vs Relational Calculus

### Comparison Chart

Basis for Comparison | Relational Algebra | Relational Calculus |
---|---|---|

Basic | Relational Algebra is a Procedural language. | Relational Claculus is Declarative language. |

States | Relational Algebra states how to obtain the result. | Relational Calculus states what result we have to obtain. |

Order | Relational Algebra describes the order in which operations have to be performed. | Relational Calculus does not specify the order of operations. |

Domain | Relational Algebra is not domain dependent. | Relation Claculus can be domain dependent. |

Related | It is close to a programming language. | It is close to the natural language. |

### Definition of Relational Algebra

Relational algebra presents the basic set of operations for relational model. It is a **procedural** language, which describes the procedure to obtain the result. Relational algebra is prescriptive because it describes the **order of operations** in the query that specifies * how *to retrieve the result of a query.

The sequence of operations in a relation algebra is called **relational algebra expression. **The Relational Algebra Expression either takes one relation or two relations as an input to the expression and produces a new relation as a result. The resultant relation obtained from the relational algebra expressions can be further composed to the other relational algebra expression whose result will again be a new relation.

The Relation Algebra forms the framework for implementing and optimizing queries while query processing. Relational algebra is an integral part of relational DBMS. The fundamental operation included in relational algebra are { **Select (σ), Project (π), Union (∪ ), Set Difference (-), Cartesian product (×) and Rename (ρ)**}.

### Definition of Relational Calculus

Unlike Relational Algebra, Relational Calculus is a higher level **Declarative** language. In converse to the relational algebra, relational calculus defines ** what** result is to be obtained. Like Relational Algebra, Relational Calculus

**does not specify the sequence of operations**in which query will be evaluated.

The sequence of relational calculus operations is called **relational calculus expression** that also produces a new relation as a result. The Relational Calculus has two variations namely **Tuple Relational Calculus** and **Domain Relational Calculus**.

The Tuple Relational Calculus** list the tuples** to selected from a relation, based on a certain **condition** provided. It is formally denoted as:

**{ t | P(t) }**

Where **t** is the set of tuples fro which the condition **P** is true.

The next variation is Domain Relational Calculus, which in contrast to Tuple Relational Calculus **list the attributes** to be selected from a relation, based on certain **condition**. The formal definition of Domain Relational Calculus is as follow:

**{<X1, X2, X3, . . . Xn> | P(X1, X2, X3, . . . Xn)}**

Where **X1, X2, X3, . . . Xn** are the attributes and **P** is the certain condition.

## Key Differences Between Relational Algebra and Relational Calculus

- The basic difference between Relational Algebra and Relational Calculus is that Relational Algebra is a Procedural language whereas, the Relational Calculus is a Non-Procedural, instead it is a Declarative language.
- The Relational Algebra defines how to obtain the result whereas, the Relational Calculus define what information the result must contain.
- Relational Algebra specifies the sequence in which operations have to be performed in the query. On the other hands, Relational calculus does not specify the sequence of operations to performed in the query.
- The Relational Algebra is not domain dependent whereas, the Relational Calculus can be domain dependent as we have Domain Relational Calculus.
- The Relational Algebra query language is closely related to programming language whereas, the Relational Calculus is closely related to the Natural Language.

### Conclusion

Relational Algebra and Relational Calculus both have equivalent expressive power. The main difference between them is just that Relational Algebra specify how to retrieve data and Relational Calculus defines what data is to be retrieved.

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