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The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization of query optimization, which is finding more efficient manners to execute the same query in a database.
The relational calculus is similar to the relational algebra, which is also part of the relational model: While the relational calculus is meant as a declarative language that prescribes no execution order on the subexpressions of a relational calculus expression, the relational algebra is meant as an imperative language: the sub-expressions of a relational algebraic expression are meant to be executed from left-to-right and inside-out following their nesting.
Per Codd's theorem, the relational algebra and the domain-independent relational calculus are logically equivalent.