Difference Between Relational Algebra and Relational Calculus

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

1. Comparison Chart
2. Definition
3. Key Differences
4. Conclusion

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.

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.