Truth Table Calculator

Work out truth table instantly with clear inputs, formula shown and shareable results.

About Truth Table Calculator

A truth table lists every combination of input truth values and the resulting output. With two variables there are four rows; a formula true in all of them is a tautology and one true in none is a contradiction.

Formulas

Implication

P → Q is false only when P is true and Q is false

Biconditional

P ↔ Q is true exactly when P and Q agree

Worked example

With the default values below, Truth Table Calculator returns Result for your P and Q of True. Change any input above and every figure here is recalculated in your browser.

Inputs used

Connective to tabulateone of P AND Q, P OR Q, P XOR Q, P implies Q, P if and only if Q, NAND: P AND Q
Value of P for the highlighted rowaccepts 0–1: 1
Value of Qaccepts 0–1: 1

Results

Result for your P and Q: True
Full truth table (PQ→result): TT→T | TF→F | FT→F | FF→F
Rows that come out true: 1
Classification: Contingent

Step by step

1Values used
2Implication
3Biconditional
4Result for your P and Q= True
5Full truth table (PQ→result)= TT→T | TF→F | FT→F | FF→F
6Rows that come out true= 1
7Classification= Contingent

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is 'false implies true' true?

An implication only promises something when the antecedent holds. With a false antecedent the promise is never tested, so it counts as kept.

How many rows for n variables?

2ⁿ. Three variables need 8 rows, four need 16.