Polish Notation Converter

Name: Polish Notation Converter
Author: Jitendra Kumar

Convert expressions between infix, prefix Polish notation, and postfix Reverse Polish notation with parse steps and expression-tree traversal.

Last Updated: May 2026

Prefix Polish

* + A B - C D

Postfix RPN

A B + C D - *

Fully Parenthesized Infix

((A + B) * (C - D))

Tree Depth

Notation Converter Inputs

Convert binary arithmetic expressions between infix, prefix Polish notation, and postfix Reverse Polish notation.

Input notation

Prefix and postfix examples should be space-separated.

Expression

Supports values, variables, parentheses in infix mode, and binary + - * / ^ operators.

Conversion Results

Output	Rule	Value
Original tokens	( A + B ) * ( C - D )	11 tokens
Prefix Polish	preorder: operator, left, right	* + A B - C D
Infix	left, operator, right	((A + B) * (C - D))
Postfix RPN	postorder: left, right, operator	A B + C D - *
Expression tree nodes	operators plus operands	7

Parse Steps

Step	Action	Result
1	Tokenize the input	( A + B ) * ( C - D )
2	Use shunting-yard precedence to build postfix	A B + C D - *
3	Build a binary expression tree	7 nodes
4	Traverse tree as prefix, infix, and postfix	All notation outputs are generated from the same tree.

Expression Parsing Notice

This converter is for notation practice and expression-structure checks. It supports binary arithmetic operators only and does not evaluate expressions, simplify algebra, or parse functions.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, reviews methodology, labels, assumptions, and trust-sensitive publishing decisions for this topic area.

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Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

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Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

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How to Use the Polish Notation Converter

Choose the notation of your input expression. Infix expressions can use parentheses, while prefix and postfix expressions should use space-separated operators and operands.

Enter an expression with variables, numbers, and binary +, -, *, /, or ^ operators. The converter returns prefix Polish, fully parenthesized infix, and postfix RPN forms.

Step 1: Choose input notation
Select infix, prefix Polish, or postfix Reverse Polish notation.
Step 2: Enter the expression
Use values or variables with binary arithmetic operators.
Step 3: Review converted forms
Compare prefix, infix, and postfix outputs built from the same expression tree.
Step 4: Check parse steps
Use the token and parse-step tables to verify the conversion logic.

How This Polish Notation Converter Works

The converter tokenizes the input, then builds a binary expression tree. Infix input is first converted with operator precedence rules similar to the shunting-yard algorithm.

Prefix input is read from right to left with a stack. Postfix input is read from left to right with a stack. Each binary operator combines two operands into a new tree node.

Once the tree exists, prefix notation is a preorder traversal, infix notation is an inorder traversal, and postfix notation is a postorder traversal.

Polish Notation Guide

Notation Types

Notation	Example	Meaning
Infix	(A + B) * C	Operators are written between operands.
Prefix Polish	* + A B C	Operators are written before their operands.
Postfix RPN	A B + C *	Operators are written after their operands.
Expression tree	operator with left and right children	A shared structure used to generate all three forms.

Infix Operator Rules

Operator	Precedence	Rule
^	Highest	Right associative in infix mode.
* and /	Middle	Evaluated before addition and subtraction.
+ and -	Lowest	Evaluated left to right.
Parentheses	Override precedence	Supported in infix input only.

Examples

Input type	Input	Prefix output	Postfix output
Infix	(A + B) * (C - D)	* + A B - C D	A B + C D - *
Prefix	* + A B - C D	* + A B - C D	A B + C D - *
Postfix	A B + C D - *	* + A B - C D	A B + C D - *
Power	a + b * c ^ d	+ a * b ^ c d	a b c d ^ * +