Truth Table Generator Calculator

Build truth tables from custom logic expressions. Track AND, OR, XOR, NAND, NOR, and implication. Visual summaries make logical behavior easier to verify quickly.

Generate a truth table

Use operator words or symbols such as NOT, AND, OR, XOR, ->, and <->.

NOT or ! AND or & OR or | XOR or ^ NAND NOR -> or IMPLIES <-> or EQUIV

Supported syntax guide

Operation Accepted input Meaning
Negation NOT P, !P, ~P Flips a truth value.
Conjunction P AND Q, P & Q, P && Q True only when both inputs are true.
Disjunction P OR Q, P | Q, P || Q True when at least one input is true.
Exclusive OR P XOR Q, P ^ Q True when inputs differ.
Implication P -> Q, P IMPLIES Q False only when true implies false.
Equivalence P <-> Q, P EQUIV Q, P IFF Q True when both sides match.
NAND / NOR P NAND Q, P NOR Q Negated forms of AND and OR.

Example data table

Sample expression: P -> Q

Row P Q P -> Q
1TTT
2TFF
3FTT
4FFT

Formula used

A truth table lists every possible input pattern for n variables. The total number of rows is:

Rows = 2^n

Each row evaluates the expression with Boolean rules:

The calculator parses the entered expression, evaluates each row, and labels the final output as a tautology, contradiction, or contingency.

How to use this calculator

  1. Enter a logical expression using variables such as P, Q, and R.
  2. Use valid operators like NOT, AND, OR, XOR, ->, or <->.
  3. Set the variable order if you want columns arranged in a specific sequence.
  4. Choose whether intermediate subexpressions should appear in the generated table.
  5. Select either T/F or 1/0 display output.
  6. Press Generate Table to see the results, graph, and summary metrics.
  7. Use the export buttons to save the current table as CSV or PDF.

Frequently asked questions

1. What does this calculator generate?

It creates every possible truth-value combination for the variables in your expression and evaluates the final proposition for each row.

2. How many rows will the table have?

The table uses 2^n rows, where n is the number of distinct variables in the expression.

3. Can I use symbols instead of words?

Yes. You can enter symbols like !, &, |, ^, ->, and <-> instead of operator words.

4. What are intermediate columns?

Intermediate columns show evaluated parts of a longer expression. They help you trace how the final result was built step by step.

5. What does tautology mean?

A tautology is an expression that evaluates to true for every possible row in the truth table.

6. What does contradiction mean?

A contradiction is an expression that evaluates to false for every possible row in the truth table.

7. Why is variable order important?

Variable order controls the column sequence and the row pattern. A consistent order makes comparisons easier across multiple expressions.

8. Can I export the generated table?

Yes. The page includes CSV and PDF export buttons for the current generated truth table.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.