Last Updated on February 27, 2023 by Prepbytes

Relational database management systems (DBMS) use relational calculus, a formal language, to express queries. In simple words, relational calculus in DBMS is a non-procedural language, which only focuses on what kind of data is required and it does not care about how to get these data.

## What is Relational Calculus in DBMS?

Relational Calculus in DBMS is a different approach to creating queries. Relational calculus in DBMS is a non-procedural language, in which The user is worried about the specifics of getting the desired outcomes.

The term "relational" in relational calculus refers to the fact that it is based on the relational model of data, which is the foundation of the relational database management system (RDBMS). While the term "calculus" refers to the fact that relational calculus is a formal system of logic used to express queries over relational databases.

**Example of Relational Calculus in DBMS:**

Let’s take an example to understand what is relational calculus in DBMS.

`SELECT the tuples from EMPLOYEE relation with DEPARTMENT= 'NETWORKING'`

In the above example, this is the relational calculus expression to select the tuples from the EMPLOYEE relation with DEPARTMENT=’NETWORKING’.

### Types of Relational Calculus in DBMS

There are mainly two types of relational calculus in DBMS:

- Tuple Relational Calculus (TRC)
- Domain Relational Calculus (DRC)

**1. Tuple Relational Calculus in DBMS:**

Tupe Relational Calculus in DBMS is based on the concept of selecting tuples (rows) from a relation (table) that satisfies certain conditions. Tuple Relational Calculus uses variables to represent tuples and logical predicates to specify the conditions that must be met for the tuples to be selected. The resulting expression is a formula that describes a set of tuples that meet the specified conditions.

The general syntax for Tuple Relational Calculus is:

`{ t | P (t) } or { t | Condition (t) }`

In the above syntax, t is the resulting tuples, and P(t) is the condition used to get t. Let’s take an example to understand the tuple relational calculus in dbms.

**Example of Tuple Relational Calculus in DBMS:**

Now, we will take the database table Employee and try to apply the Tuple Relational Calculus expression on that table.

Employee_id | Employee_name | Department |
---|---|---|

101 | Naimish | Computer |

102 | Sahil | Finance |

103 | Divyesh | Computer |

104 | Nikunj | Account |

105 | Gautam | Computer |

106 | Vishal | HR |

107 | Meet | Business |

108 | Milan | Business |

**Query:**

`{t \| t ∈ Employee ∧ t.Department = ’Computer’} or TRC Query: {t \| Employee(t) ∧ t[Department] = ‘Computer’}`

**Output:**

Employee_id | Employee_name | Department |
---|---|---|

101 | Naimish | Computer |

103 | Divyesh | Computer |

105 | Gautam | Computer |

The above query will select the tuples from the table Employee, where Department of the tuple will be ‘Computer’. In the output, we can see that we get three tuples from the table Employee, in which department of the employee is the computer.

**2. Domain Relational Calculus in DBMS:**

Domain Relational Calculus in DBMS is based on the concept of selecting values from a relation (table) that satisfy certain conditions. Domain Relational Calculus uses variables to represent individual values, and logical predicates to specify the conditions that must be met for the values to be selected. The resulting expression is a formula that describes a set of values that meet the specified conditions.

The **General Syntax** for Domain Relational Calculus is:

`{ ` | P(x1,x2,x3,x4,...,xn) }

In the above syntax, < x1,x2,x3,x4,…,xn> are called the domain variables and these variables are used to fetch required column values. P(x1,x2,x3,x4,…,xn) is called a predicate condition or predicate expression. Let’s take an example to understand the tuple relational calculus in dbms.

**Example of Domain Relational Calculus in DBMS:**

Now, we will take the database table Employee and try to apply the Domain Relational Calculus expression on that table.

Employee_id | Employee_name | Department |
---|---|---|

101 | Naimish | Computer |

102 | Sahil | Finance |

103 | Divyesh | Computer |

104 | Nikunj | Account |

105 | Gautam | Computer |

106 | Vishal | HR |

107 | Meet | Business |

108 | Milan | Business |

**Query:**

`{` \| ∈ Employee∧ x3 = ‘Computer’}

**Output:**

Employee_id | Employee_name | Department |
---|---|---|

101 | Naimish | Computer |

103 | Divyesh | Computer |

105 | Gautam | Computer |

The predicate condition is that the first two domain variables, x1, and x2, should be present while matching the condition for each row and the third domain variable, x3, should be equal to "Computer" in the query above. x1, x2, and x3 (ordered) refer to the attribute or column that we need in the result.

**Conclusion**

In conclusion, this article will help you to understand what is relational calculus in DBMS. In addition, you will also learn the types of relational calculus in DBMS with appropriate examples.

## FAQs Related to Relational Calculus

**1. What is the difference between Tuple Relational Calculus and Domain Relational Calculus?**

Tuple Relational Calculus is used to select tuples (rows) from a relation (table), whereas Domain Relational Calculus is used to select individual values from a relation. Tuple Relational Calculus uses tuple variables to represent tuples, while Domain Relational Calculus uses individual value variables.

**2. Is Relational Calculus a procedural or non-procedural query language?**

Relational Calculus is a non-procedural query language. It specifies what data is needed, rather than how to get it. The actual implementation of the query is left to the DBMS system.

**3. What are the limitations of Relational Calculus?**

Relational Calculus can be more difficult to understand than Relational Algebra, especially for users who are not familiar with formal logic. It can also be less efficient than Relational Algebra, especially for complex queries, as the DBMS needs to translate the calculus expressions into equivalent algebraic expressions before executing them.

**4. Can Relational Calculus be used to modify data in a database?**

No, Relational Calculus is a read-only language that can only be used to select data from a database. To modify data, users need to use Data Manipulation Language (DML) statements, such as SQL INSERT, UPDATE and DELETE statements.

**5. Can Relational Calculus be used to express complex queries?**

Yes, Relational Calculus can be used to express complex queries that cannot be easily expressed using Relational Algebra. It allows users to specify complex conditions and queries using logical predicates.

**6. Can Relational Calculus be used in NoSQL databases?**

No, Relational Calculus is specific to relational databases and cannot be used in NoSQL databases. NoSQL databases use different query languages and data models that are designed to handle non-tabular and unstructured data.