Built and fact-checked by the DocNectar team — see our editorial standards
Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
Mobile Friendly
Fully responsive design. Works on all devices & screen sizes.
Privacy Focused
Your data stays on your device. We don't store any inputs.
100% Free
No hidden costs. This tool is completely free forever.
Prefix (Polish) and postfix (Reverse Polish) notation write operators before or after their operands instead of between them, removing the need for parentheses. This tool converts any infix expression — including ones with nested parentheses and mixed operators — into both forms, using the shunting-yard algorithm.
How it works
The expression is tokenized, then converted to postfix using the shunting-yard algorithm: numbers go straight to the output, while operators are pushed to a stack after popping any stacked operators of equal or higher precedence. Prefix is computed the same way but on the reversed, paren-swapped token list, then the result is reversed back.
- Enter infix expression.
- Click Calculate to see your results.
Examples
A nested-parentheses expression
(3 + 4) * 2 converts to postfix "3 4 + 2 *" and prefix "* + 3 4 2" — both fully remove the need for parentheses while preserving the original meaning.
Who should use it
- Computer science coursework on expression parsing and evaluation.
- Understanding how calculators and compilers internally represent arithmetic expressions.
Industry applications
- Computer science and compiler design
- Programming language theory education
Advantages
- Supports nested parentheses and all four basic operators (+, −, ×, ÷).
- Shows the full token-by-token shunting-yard trace for both conversions.
Limitations
- Does not currently support exponentiation, unary minus, or variables — only numeric literals and +, −, *, /.
Common mistakes to avoid
- Assuming prefix notation is simply the postfix result written backwards for every expression — while reversing figures into the construction, the correct prefix algorithm also requires strict-vs-equal precedence handling to preserve non-commutative operator order (like subtraction and division) correctly.
Best practices
- When manually converting nested expressions, work parentheses from the innermost outward, one operator at a time, rather than trying to convert the whole expression in one pass.
Tips
- If you're building a stack-based expression evaluator, postfix (Reverse Polish) is usually the easier form to evaluate directly, since operators appear right after their operands are ready.