PEMDAS Calculator - Order of Operations Solver

PEMDAS Calculator

Use standard operators: +, -, *, /, % (modulo), ** (exponent), ().

Result:

What is PEMDAS? (Order of Operations)

PEMDAS is an acronym used to help remember the standard order of operations for evaluating mathematical expressions. It ensures that everyone gets the same result when calculating the same expression. The acronym stands for:

  • Parentheses (or Brackets): Evaluate expressions inside parentheses or brackets first. Work from the innermost set outwards.
  • Exponents (or Orders / Indices): Evaluate powers and roots next.
  • Multiplication and Division: Perform multiplication and division from left to right as they appear. They have equal priority.
  • Addition and Subtraction: Perform addition and subtraction last, from left to right as they appear. They also have equal priority.

Other common acronyms representing the same order include BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) and BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction). The key takeaway is the hierarchy of operations and the left-to-right rule for operations of equal priority.

For example, in the expression 2 + 3 * 4, multiplication is done before addition according to PEMDAS, so the result is 2 + 12 = 14, not (2 + 3) * 4 = 20.

How This PEMDAS Calculator Works

This calculator evaluates the mathematical expression you enter, strictly following the PEMDAS order of operations.

  1. Input Expression: Type the mathematical expression you want to evaluate into the input field. Use standard numerical digits, operators (+, -, *, /, % for modulo, ** for exponentiation), and parentheses ().
  2. Click Calculate: Press the "Calculate" button.
  3. Validation (Basic): The calculator performs a basic check for obviously invalid or potentially unsafe characters. It primarily expects numbers, operators, parentheses, and whitespace.
  4. Evaluation: The calculator uses JavaScript's built-in mathematical evaluation engine, which naturally follows the standard order of operations (PEMDAS), to compute the result of the expression.
  5. Display Result: The calculated numerical result is displayed. If there's a syntax error in your expression (like unmatched parentheses) or an invalid operation (like division by zero resulting in Infinity), an error message will be shown instead.
Security Note: This calculator uses JavaScript's new Function() constructor (similar to eval()) to evaluate the mathematical expression. While convenient for simple calculations and generally safe if only mathematical operators/numbers are used, executing arbitrary code from user input can be a security risk in broader contexts. We have added basic input filtering, but complex malicious code might bypass simple checks. Use responsibly.

Frequently Asked Questions (FAQs)

Q1: What's the difference between PEMDAS, BODMAS, and BEDMAS?

They all represent the same standard order of operations. The differences are just in the terminology:

  • PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
  • BODMAS: Brackets, Orders (or Of), Division, Multiplication, Addition, Subtraction
  • BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction

The calculation rules are identical.

Q2: How are Multiplication/Division and Addition/Subtraction handled if they have the same priority?

Operations with the same priority (Multiplication and Division; Addition and Subtraction) are evaluated from left to right as they appear in the expression.
Example: 10 / 2 * 5 is evaluated as (10 / 2) * 5 = 5 * 5 = 25.
Example: 10 - 3 + 2 is evaluated as (10 - 3) + 2 = 7 + 2 = 9.

Q3: Does the calculator support nested parentheses?

Yes. Expressions within the innermost set of parentheses are evaluated first, following PEMDAS rules within those parentheses, then working outwards. Example: 10 * (4 - (1 + 1)) becomes 10 * (4 - 2) which becomes 10 * 2 = 20.

Q4: Can I use decimals and negative numbers?

Yes. The calculator handles standard decimal numbers (e.g., 3.14) and negative numbers (e.g., -5). Be mindful of syntax, for example: 3 + (-5) or simply 3 - 5.

Q5: What operators are supported?

The calculator supports basic arithmetic operators:

  • + (Addition)
  • - (Subtraction)
  • * (Multiplication)
  • / (Division)
  • % (Modulo - remainder after division)
  • ** (Exponentiation - raise to the power of, e.g., 2**3 is 2³)
  • () (Parentheses for grouping)

It does *not* support functions like sin(), cos(), sqrt(), or variables.

Q6: What happens if I enter an invalid expression?

If the expression has a syntax error (e.g., unmatched parentheses (5+2, invalid operators 5++2) or attempts an invalid mathematical operation recognized by the engine (like division by zero which yields Infinity), the calculator will either display the result (like Infinity) or show an error message indicating that the expression is invalid or could not be evaluated.