About This Site
A free infix to postfix converter that shows its working — and a short account of how the results are checked before they are published.
What this site is
infixtopostfixconverter.com is a free tool for converting infix expressions to postfix (Reverse Polish Notation) and prefix, together with a small set of reference pages explaining how the conversion actually works.
There is no sign-up, no paywall and no limit on how many expressions you convert.
Why it exists
Plenty of pages will give you the postfix form of an expression. Very few show you the working — which operator was popped at which point, and why. That working is the part exams ask for and the part that tells you where your own implementation went wrong.
So every tool here shows its reasoning. The converter prints a trace table with one row per token and a sentence explaining each decision. The stack visualiser animates the same thing, one push and pop at a time.
How the conversion works
Everything runs on Dijkstra's shunting-yard algorithm, written in plain JavaScript and executed entirely in your browser. Nothing you type is sent anywhere — there is no server-side conversion, which is also why the site keeps working if you lose your connection after the page has loaded.
The full algorithm, with pseudocode and complexity analysis, is documented on the conversion algorithm page.
How the results are checked
Correctness matters more than anything else on a site like this, so the output is verified rather than assumed:
- The conversion engine is tested against a fixed set of expressions covering precedence, nested brackets, right associativity, unbalanced input and every malformed-expression case the validator claims to catch.
-
Every C program published on this site is compiled with
-Wall -Wextra -std=c99and run before it is posted. The code you copy is the code that was tested. - The C programs and the browser engine are cross-checked against each other on the same expressions. If the two ever disagreed, one of them would be wrong.
That does not make mistakes impossible. If you find one, please tell us — include the exact expression and it will get looked at.
What the converter does and does not handle
| Supported | Not supported |
|---|---|
Single-letter operands (A) |
Function calls such as sin(x) or max(a, b) |
Multi-character names (rate, x1) |
Comparison and logical operators (<, &&) |
Integers and decimals (250, 3.5) |
Assignment (x = a + b) — convert the right-hand side only |
Operators + - * / % ^ |
Unary minus before a variable or bracket — rewrite -x as (0 - x) |
| Round, square and curly brackets, nested to any depth | Implied multiplication — write 2 * (3 + 4), not 2(3 + 4) |
| Evaluating the result when every operand is numeric | Symbolic algebra or simplification |
These limits are deliberate. The site teaches the classical data-structures algorithm, and that algorithm is defined over binary operators and brackets. Adding function calls and unary operators would make the traces harder to follow without teaching anything extra.
Who it is for
Mostly students taking a data structures or compilers course, where infix to postfix conversion is a standard topic and usually the first real use of a stack. It is also useful to anyone writing an expression parser who wants a reference implementation to compare against.
Corrections and suggestions
Wrong results, unclear explanations, broken code samples and requests for new converters are all welcome. The contact page has a form that prefills the details worth including.