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Boolean Algebra Simplifier

Reduces a boolean expression to a minimal sum of products, accepting every common notation — AB, A·B, A&B for AND, A+B or A|B for OR, ~A, !A or A' for NOT, plus XOR, NAND and NOR. Shows the prime implicants, not just the final answer.

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Open Boolean Algebra Simplifier and you get an answer straight away, with no account to create. It sits under Algebra & equations in our catalogue, alongside Algebraic Expression Simplifier and Radical Simplifier.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Boolean Algebra Simplifier?

Reduces a boolean expression to a minimal sum of products, accepting every common notation — AB, A·B, A&B for AND, A+B or A|B for OR, ~A, !A or A' for NOT, plus XOR, NAND and NOR. Shows the prime implicants, not just the final answer.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Boolean Algebra Simplifier different from Algebraic Expression Simplifier?

They sit next to each other but answer different questions: Algebraic Expression Simplifier is the one to open when you need it to combines like terms, expands or factors, with implicit multiplication understood (2x is 2·x). When a cancellation removes a factor, the excluded value is stated — (x²−4)/(x−2) is x+2 only for x ≠ 2, and that restriction is part of the answer. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Radical Simplifier is the closest one after this: Simplify square, cube and n-th roots, reduce quotients of radicals and rationalize denominators — e.g. sqrt(50) → 5√2 and 1/sqrt(2) → √2/2 — with the exact form and a decimal value.

What else is worth having open alongside it?

Fraction simplifier and Absolute Value Equation Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Convert a Fraction to a DecimalDivide the top number by the bottom. Here's the rule, why some fractions repeat, how to round them, and how to turn the result into a percentage.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.