Example Data Table
| RPN Expression |
Purpose |
Expected Result |
Parsing Check |
| 5 1 2 + 4 * + 3 - |
Nested arithmetic |
14 |
Ends with one stack item |
| 9 sqrt 2 ^ |
Unary and power operations |
81 |
Every operator has operands |
| 3 4 > 10 2 / 5 == and |
Logic after comparisons |
0 |
Boolean result is numeric |
| x y + 2 * |
Variable based expression |
Depends on variables |
Unknown names must be defined |
Formula Used
The calculator uses a stack evaluation rule. If a token is a number, boolean, or variable, it is pushed onto the stack. If a token is a unary operator, one value is popped and replaced with the operator result. If a token is a binary operator, two values are popped in left to right order.
operand: push(value)
unary: a = pop(); push(op(a))
binary: b = pop(); a = pop(); push(a op b)
valid: final stack count must equal 1
For logical operators, zero is treated as false. Any nonzero value is treated as true. Comparison operators return 1 for true and 0 for false.
How To Use This Calculator
- Enter one RPN expression with spaces between all tokens.
- Add variables if your expression uses named values.
- Select precision and angle unit for special functions.
- Press the submit button to check parsing and calculate.
- Review the result, stack trace, and infix check.
- Download the CSV or PDF file for records.
Why This RPN Parsing Tool Helps
Reverse Polish notation removes parentheses by placing operators after values. That style is compact. It is also easy to misread. A missing number can break the whole expression. This calculator checks the logic before it trusts the answer. Each token is read in order. Numbers, booleans, and variables enter the stack. Operators consume stack items. The tool reports every change, so you can see why a result appears.
Practical Uses
RPN is useful in engineering tools, financial models, classroom exercises, and parser testing. It can test arithmetic, comparisons, and simple logic. You can enter expressions like 5 2 +, or combine checks like 3 4 > true and. The parser records token count, maximum stack depth, final expression form, and any issue found. These details help students, developers, and reviewers catch mistakes early.
Better Error Checking
The main value is validation. The calculator warns when an operator has too few operands. It stops unsafe actions, such as division by zero. It also rejects unknown tokens unless you define them as variables. When the stack ends with more than one item, the expression is incomplete. This makes the output useful for debugging, not just calculation.
Clean Review Workflow
Use the precision box when you need rounded numeric output. Choose degrees or radians for trigonometric functions. Add variables on separate lines, such as rate=7.5 or approved=true. After calculation, export a CSV file for spreadsheets. You can also create a PDF summary for reports. The example table gives starter expressions for quick testing.
Recommended Checks
Start with short expressions. Confirm the stack trace. Then add one operator at a time. Watch the maximum depth, because deep stacks can hide input order mistakes. Compare the infix view with your intended logic. If both match, the parsed answer is much easier to trust.
Input Quality Tips
Use spaces between every value and operator. Write negative numbers as normal values, such as -5. Use the neg operator only when you want to change the sign of an existing stack value. Keep variable names simple. Avoid commas inside expressions. These habits make the parser more predictable and make exported records easier to compare across tests during careful review sessions.
FAQs
What is an RPN expression?
It is an expression where operators come after operands. For example, 4 5 + means 4 plus 5. This style removes the need for most parentheses.
Why does the parser use a stack?
A stack matches RPN order. Values are pushed first. Operators then pop the required values, calculate a new value, and push it back.
How are logic values handled?
The calculator treats zero as false. Any nonzero number is true. Logical and comparison operators return 1 for true and 0 for false.
Can I use variables?
Yes. Add variables in the variable box using name=value format. Use one variable per line. Values may be numbers, true, or false.
What causes a parsing error?
Common causes include unknown tokens, too few operands, division by zero, invalid variables, or extra values left on the stack after parsing.
Does the calculator support trigonometry?
Yes. It supports sin, cos, and tan as unary operators. You can choose degrees or radians before submitting the expression.
What does maximum stack depth mean?
It is the largest number of items held during parsing. A high depth can show complex logic or possible ordering problems.
Why export CSV or PDF?
CSV helps spreadsheet review. PDF creates a simple report with the expression, status, answer, and stack trace summary.