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Calculator Answers

PEMDAS Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A PEMDAS calculator is an algebraic tool that simplifies expressions according to the standard order of operations. It resolves nested parentheses, applies exponents, evaluates multiplication and division from left to right, and solves addition and subtraction from left to right. This ensures a single, mathematically correct result.

Evaluate any mathematical expression step-by-step using the PEMDAS / BODMAS order of operations rules. Features full intermediate equations showing the priority path.

Quick Answer

Evaluate mathematical expressions step-by-step. Enter any formula using standard arithmetic operators and parentheses to see the order of operations breakdown.

Mathematical Expression

Allowed operators: + - * / ^ ( )

PEMDAS Rule Priority

  1. Parentheses (innermost groups first)
  2. Exponents (power calculations)
  3. Multiplication & Division (evaluated left-to-right)
  4. Addition & Subtraction (evaluated left-to-right)
Evaluation Summary

Result

9

PEMDAS order applied step-by-step.

Original Expression3 + 4 * 2 - (5 - 3)^2 / 2
Steps Count5

Order of operations ensures that math expressions have a single, unambiguous result.

Step-by-Step Order of Operations

[1]Parentheses: Solve (5 − 3) = 2 → 3 + 4 × 2 − 2 ^ 2 ÷ 2
[2] - Subtract: 5 − 3 = 2 → 2
[3]Exponent: -2^2 = 4 → 3 + 4 × 24 ÷ 2
[4]Multiply: 4 × 24 = 96 → 396 ÷ 2
[5]Divide: 396 ÷ 2 = 198 → 198
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Examples

Expression with Parentheses and Powers: 3 + 4 * 2 - (5 - 3)^2 / 2

Simplify (5 - 3) = 2 · Apply power 2^2 = 4 · Multiply 4 × 2 = 8 · Divide 4 ÷ 2 = 2 · Final additions: 3 + 8 - 2 = 9

Left-to-right division and multiplication: 12 / 3 * 2

Since / and * are equal priority, go left to right: 12 ÷ 3 = 4 · 4 × 2 = 8

How it works

Math expressions are simplified by applying operator priorities in order:

The PEMDAS / BODMAS Mnemonic

PParentheses
EExponents
MMultiply
DDivide
AAddition
SSubtract

Left-to-Right Priority Rules

A common misconception is that Multiplication always comes before Division, and Addition always comes before Subtraction because of the letter order of the PEMDAS acronym. In reality, Multiplication and Division form a single group with equal priority, and they must be resolved strictly from left to right. Similarly, Addition and Subtraction have equal priority and are evaluated from left to right. Our calculator models this standard algebraic hierarchy.

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Frequently asked questions

PEMDAS is an acronym helper that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It represents the standard mathematical convention for the order in which operations must be performed to evaluate an expression correctly.

They are the exact same mathematical rules under different regional names. BODMAS is used commonly in the UK, India, and Australia, and stands for Brackets, Orders (exponents), Division, Multiplication, Addition, and Subtraction. Note that Division and Multiplication have equal priority, as do Addition and Subtraction.

Multiplication and Division have equal priority. When both appear in an expression, you perform them from left to right as they appear. For example, in 12 ÷ 3 × 2, you divide first to get 4, then multiply by 2 to get 8.

Without a standard order of operations, a single math expression could evaluate to multiple different answers. For example, 3 + 4 × 2 could be 14 (if you add first) or 11 (if you multiply first). The order of operations ensures everyone gets the same correct result (11).