Math & Conversions

Boolean Algebra Calculator

Evaluate the basic logic gates for two boolean inputs. Choose True or False for A and B and the tool returns A AND B, A OR B, A XOR B, and A NAND B as 1 or 0. Free, runs in the browser, no sign-up.

What this calculator does

The Boolean Algebra Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Evaluate the basic logic gates for two boolean inputs. Choose True or False for A and B and the tool returns A AND B, A OR B, A XOR B, and A NAND B as 1 or 0. Free, runs in the browser, no sign-up. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Boolean Algebra Calculator

Result

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A AND B
—
A OR B
—
A XOR B
—
A NAND B

About Boolean Algebra Calculator

The Boolean Algebra Calculator takes two inputs, A and B, each set to True (1) or False (0), and evaluates four logic operations at once: AND, OR, XOR, and NAND. Each result is shown as 1 for true or 0 for false.

AND is true only when both inputs are true, OR is true when at least one is, XOR is true when the inputs differ, and NAND is the negation of AND.

Formula & Mathematical Calculation

A AND B = f(Input A, Input B)

Calculated according to standard math formulas implemented in the calculator core.

Calculation Example

Set A to True (1) and B to False (0). AND is 0 because the inputs are not both true, OR is 1 because one input is true, XOR is 1 because the inputs differ, and NAND is 1 because it inverts the AND result. The tool shows AND = 0, OR = 1, XOR = 1, NAND = 1.

Key Benefits

  • Evaluates AND, OR, XOR, and NAND together from a single pair of inputs.
  • Uses simple True/False dropdowns, so no expression syntax is needed.
  • Displays each result as a clear 1 or 0.
  • Free and runs in the browser with no sign-up.

How to Use this Calculator

  1. Set Input A
    Choose True (1) or False (0) in the Input A dropdown.
  2. Set Input B
    Choose True (1) or False (0) in the Input B dropdown.
  3. Calculate
    Press Calculate to see the AND, OR, XOR, and NAND results.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Boolean Algebra Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

It computes A AND B, A OR B, A XOR B, and A NAND B for the two inputs you select.

OR returns 1 when at least one input is true, while XOR returns 1 only when the two inputs differ, so True with True gives OR = 1 but XOR = 0.

NAND stands for NOT-AND, so it returns 0 exactly when AND returns 1 and returns 1 otherwise.

No. Both inputs are dropdowns limited to True (1) and False (0), so only valid boolean values can be selected.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.