Calculator
Use numbers, decimals, parentheses, pi, e, and operators + - * / ^.
Formula Used
Value(node) = Value(left child) operator Value(right child)
Depth(node) = 1 + max(Depth(left child), Depth(right child))
Nodes(tree) = 1 + Nodes(left subtree) + Nodes(right subtree)
Prefix visits root first. Infix visits root between children. Postfix visits root last.
The calculator first tokenizes the expression, then converts infix to postfix with operator precedence and associativity. Next, it builds the binary expression tree from postfix order and evaluates the final result recursively.
How to Use This Calculator
Enter a valid mathematical expression in the expression field.
Choose the decimal precision for the displayed result.
Select how node labels should appear in the graph.
Optionally load a preset example for quick testing.
Click Build Expression Tree to generate the result.
Review the normalized infix, postfix, prefix, and tree metrics.
Use the CSV button to save result data as a table.
Use the PDF button to save the result section as a document.
Example Data Table
| Expression | Postfix | Result | Depth |
|---|---|---|---|
| (7 + 3) * 2 | 7 3 + 2 * | 20 | 3 |
| ((7 + 3) * 2) / (5 - 1) | 7 3 + 2 * 5 1 - / | 5 | 4 |
| 3 ^ 2 + (8 / 4) | 3 2 ^ 8 4 / + | 11 | 4 |
| ((12.5 - 4.5) * (3 + 2)) / 5 | 12.5 4.5 - 3 2 + * 5 / | 8 | 4 |
Frequently Asked Questions
1. What is an expression tree?
An expression tree is a binary tree that stores operands in leaves and operators in internal nodes. It helps visualize evaluation order and operator precedence clearly.
2. Which operators does this calculator support?
It supports addition, subtraction, multiplication, division, and exponentiation. Parentheses are supported too. You can also use decimals, negative values, pi, and e.
3. Why is postfix generated first?
Postfix notation removes parentheses and makes tree construction straightforward. Each operator simply combines the latest two available operands or subtrees from the stack.
4. What do prefix, infix, and postfix mean?
They are three traversal styles. Prefix visits root first, infix visits root between children, and postfix visits root after both children.
5. Can this calculator solve algebraic variables?
No. This page evaluates numeric expressions only. It does not perform symbolic algebra, unknown solving, or variable simplification beyond the constants pi and e.
6. What causes an invalid expression error?
Common causes include mismatched parentheses, missing operators, unsupported characters, incomplete expressions, or division by zero during evaluation.
7. How is tree depth useful?
Tree depth shows how many levels the expression spans. A deeper tree often means more nesting and a more complex evaluation structure.
8. What do the CSV and PDF options save?
CSV saves the main result metrics in a spreadsheet-friendly format. PDF saves the result section, including the graph, as a printable document.