Logic Calculator
Free truth table generator for propositional logic and Boolean algebra. Enter an expression to get its truth table, properties, equivalent forms and circuit diagram, instantly in your browser.
Input a logical expression to analyze it (supports propositional logic, Boolean algebra)
Guide
Click an operator to try its example in the calculator. Each one shows every way you can type it.
Learn logic, step by step
A guided path from your first proposition through truth tables and Boolean algebra to how logic is used in programming, mathematics and philosophy.
Practice Exercises
Work through exercises on truth tables, Boolean algebra, logical equivalences and proofs. Track your progress and run adaptive training sessions.
Truth Table to Expression
Convert any truth table into a logical expression. Generate Boolean formulas in Disjunctive Normal Form (DNF) or Conjunctive Normal Form (CNF) from your custom truth table.
About Logic Calculator
A comprehensive logic calculator, propositional calculator, and Boolean calculator tool. Perfect for students and professionals working with propositional logic, Boolean algebra, predicate logic, truth tables, and logical expressions.
Contact & Report Issues
Found a bug or have feedback? We'd love to hear from you. Email us at [email protected]. Enquiries are preferred in English.
Frequently Asked Questions
Find answers to common questions about using the Logic Calculator
What logical operators does the calculator support?
The calculator supports all standard logical operators: NOT (¬, !), AND (&, ∧), OR (|, ∨), IMPLIES (→, ->), and BICONDITIONAL (↔, <->). You can use these operators to build complex logical expressions.
How do I type symbols like ∧ and → on an ordinary keyboard?
You do not have to. Every symbol has an ASCII spelling the calculator understands: & for ∧, | for ∨, ! or ~ for ¬, -> for →, and <-> for ↔. The constants ⊤ and ⊥ can be written as true and false, or T and F. If you prefer the symbols themselves, the operator keyboard under the input inserts them for you.
Can I check if two logical expressions are equivalent?
Yes! Use the equivalence check feature by separating two expressions with '==' to determine if they are logically equivalent. The calculator will compare their truth tables to verify equivalence.
Can the calculator check whether an argument is valid?
Yes. Write the premises separated by commas, then a turnstile, then the conclusion, as in 'p, p -> q ⊨ q'. The turnstile can be typed as |= or |- instead. The calculator reports whether the conclusion follows, which premises are actually needed, whether the premises can all be true at once, and, when the argument fails, countermodels that make every premise true while the conclusion is false.
What does 'satisfiable' and 'valid' mean?
A satisfiable expression can be made true under at least one assignment of truth values. A valid expression (tautology) is true under all possible assignments. The calculator automatically checks both properties for your expressions.
Data
We use local storage to store your history. If you want to clear that data use the button below to do so.