Math July 13, 2026 · 8 Min Read

Polish Notation Converter – Guide & Formulas

Convert between Polish (prefix), Reverse Polish (postfix), and standard infix notation. Supports fully parenthesized expressions with step-by-step solutions.

Convert mathematical expressions between Polish (prefix), Reverse Polish (postfix), and standard infix notation with our free online converter. See step-by-step conversions using the Shunting Yard algorithm.

Key Takeaway

Use the free Polish Notation Converter to convert between polish (prefix), reverse polish (postfix), and standard infix notation. supports fully parenthesized expressions with step-by-step solutions. Get instant results with step-by-step explanations.

How to Use the Polish Notation Converter

  1. Step 1: Enter a mathematical expression in any notation (infix, prefix, or postfix)
  2. Step 2: Select the output notation you want to convert to
  3. Step 3: Click Convert to see the result and step-by-step conversion process
  4. Step 4: Review the tokenized expression and operator stack at each step

The Formula

Infix notation places operators between operands (A + B). Prefix (Polish) notation places operators before operands (+AB). Postfix (Reverse Polish) notation places operators after operands (AB+). The Shunting Yard algorithm uses a stack to convert between notations.

Variable Definitions

  • Infix: Standard notation with operators between operands (e.g., 3 + 4)
  • Prefix: Polish notation with operators before operands (e.g., + 3 4)
  • Postfix: Reverse Polish notation with operators after operands (e.g., 3 4 +)
  • Shunting Yard: Dijkstra's algorithm for converting infix to postfix using a stack
  • Operand: A number or variable in an expression
  • Operator: A mathematical symbol that performs an operation (+, -, *, /, ^)

Converting 3 + 4 × 2 to Postfix

Convert the infix expression to Reverse Polish (postfix) notation.

  1. Step 1: Tokenize the expression: [3, +, 4, ×, 2]
  2. Step 2: Read 3 (operand) → output: 3
  3. Step 3: Read + (operator) → push to stack: [+]
  4. Step 4: Read 4 (operand) → output: 3 4
  5. Step 5: Read × (higher precedence than +) → push to stack: [+, ×]
  6. Step 6: Read 2 (operand) → output: 3 4 2
  7. Step 7: End of input → pop all operators → output: 3 4 2 × +

Frequently Asked Questions

Why is Polish notation useful in computer science?

Polish and Reverse Polish notations eliminate the need for parentheses and operator precedence rules, making expression parsing and evaluation much simpler for compilers and calculators.

What is the Shunting Yard algorithm?

Developed by Edsger Dijkstra, it uses a stack to convert infix expressions to postfix by respecting operator precedence and associativity rules.

Do all calculators use RPN?

Many scientific and programmable calculators (like HP calculators) support RPN because it requires fewer keystrokes and no parentheses for complex expressions.

Can this converter handle parentheses?

Yes, the converter handles fully parenthesized and partially parenthesized expressions, correctly converting them while respecting grouping and precedence.

What operators are supported?

The converter supports addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and parentheses for grouping.