Polish Notation Calculator (Prefix & Postfix)
Evaluate expressions written in Polish notation (prefix) or Reverse Polish notation (postfix). Use spaces between tokens.
+, -, *, /, ^, %, neg, sqrt, abs, sin, cos, tan, ln, log. Constants: pi, e.Evaluation Steps
- No steps yet.
What Is a Polish Calculator?
A polish calculator evaluates math expressions written in Polish notation. In this format, the operator appears before its operands. For example, the infix expression (3 + 4) becomes + 3 4. A related style, Reverse Polish Notation (RPN), places the operator after operands, such as 3 4 +.
These notations are popular in computer science, compilers, stack-based languages, and classic scientific calculators because they remove ambiguity and reduce the need for parentheses.
Prefix vs Postfix: Quick Comparison
Prefix (Polish)
- Operator comes first:
* + 2 3 4 - Represents
(2 + 3) * 4 - Useful in parsing and symbolic processing
Postfix (Reverse Polish)
- Operator comes last:
2 3 + 4 * - Also represents
(2 + 3) * 4 - Very efficient for stack-based evaluation
How to Use This Polish Calculator
- Select Prefix or Postfix.
- Type tokens separated by spaces.
- Click Calculate.
- Read the result and step-by-step stack operations.
If you receive an error, it usually means there is an unsupported token, insufficient operands, or an incomplete expression.
Operator Reference
- Binary:
+,-,*,/,^,% - Unary:
neg(negation),sqrt,abs,sin,cos,tan,ln,log - Constants:
pi,e
Trigonometric functions use radians. For example, sin pi in prefix returns approximately zero.
Why Polish Notation Matters
Polish notation is more than a classroom concept. It appears in:
- Expression parsers and interpreters
- Compiler internals
- Stack machines and virtual machines
- Embedded systems with limited resources
Because operator precedence is encoded by position, evaluation can happen in a single pass with a stack. That makes implementations clean, fast, and reliable.
Common Mistakes and Fixes
1) Missing spaces
Write + 2 3, not +2 3. Tokens must be separated clearly.
2) Too few operands
For *, you need two numbers. For sqrt, one number is enough.
3) Wrong notation mode
2 3 + should run in Postfix mode, not Prefix mode.
4) Invalid domains
sqrt of a negative number or ln of zero/negative values is undefined in real numbers and will return an error.
Practice Expressions
- Prefix:
- * 10 5 12→ 38 - Postfix:
10 5 * 12 -→ 38 - Prefix:
+ ^ 2 3 7→ 15 - Postfix:
2 3 ^ 7 +→ 15
Use the built-in examples above to test quickly, then create your own expressions.