What is PEMDAS vs BODMAS?

PEMDAS stands for Parentheses, Exponents, Multiplication & Division (left-to-right), Addition & Subtraction (left-to-right). BODMAS stands for Brackets, Orders (powers/roots), Division & Multiplication, Addition & Subtraction. Both represent the exact same mathematical priority.

Why do Multiplication and Division have equal priority?

Multiplication and division are inverse operations of equal mathematical precedence. When both appear in an expression without parentheses, evaluate them strictly from left to right.

How do you evaluate 8 ÷ 2(2 + 2)?

1. Parentheses first: (2 + 2) = 4, giving 8 ÷ 2(4). 2. Left-to-right division and multiplication: 8 ÷ 2 = 4. 3. 4 × 4 = 16.

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Order of Operations (PEMDAS / BODMAS) Calculator

Evaluate complex mathematical expressions step-by-step with our Order of Operations Calculator! Applying PEMDAS (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction) and BODMAS rules, this tool highlights the exact operation performed at each step to demystify mathematical operator precedence.

Math Expression Input🔒 Safe Local Solve

Interactive Mathematical Keypad

Popular Study Presets & Demos

Click any preset to instantly evaluate and visualize the order of operations

Mental Math Priority Challenge

Test your mathematical precedence parsing and speed

Test your parsing order. Tapping play launches operations verification questions where you solve step-by-step.

Order of Operations: PEMDAS, BODMAS & Hierarchies

Master standard rules that determine correct operation values inside algebraic equations.

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Parentheses & Brackets (P / B)

The absolute highest priority boundary, isolating expressions to override normal order precedence.

Rule: Evaluate innermost brackets first, working outwards: ( ), [ ], { }.

Usage: Forcing addition to evaluate before multiplication: (3 + 5) * 2 = 16.

x²

Exponents & Orders (E / O)

Indices, roots, powers, and unary factorials that map growth factors. Exploded before standard products.

Rule: Solved top-to-bottom for power towers (right-associative): a^b^c = a^(b^c).

Usage: Evaluating powers and roots: 3 * 2^3 = 3 * 8 = 24.

× / ÷

Multiplication & Division (M / D)

Multiplicative expansions. In standard PEMDAS, they share equal priority and resolve strictly left-to-right.

Rule: Equal priority left-to-right (PEMDAS) vs. Strict Division-First (BODMAS variation).

Usage: Division and products: 12 / 3 * 2 = 4 * 2 = 8.

+ / -

Addition & Subtraction (A / S)

Additive aggregations. Positioned at the lowest tier of algebraic operational hierarchy.

Rule: Evaluated with equal priority from left to right: a - b + c = (a - b) + c.

Usage: Final resolutions: 10 - 4 + 2 = 6 + 2 = 8.

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Why Precedence Matters: The Core Resolution Scale

Equations resolve into completely different numbers if standard mathematical orders are ignored:

Algebraic Expression	Standard PEMDAS Logic	Incorrect Left-to-Right Solve	Practical Curricular Significance
*3 + 5 2**	13 (Multiply first: 3 + 10)	16 (Summed first: 8 * 2)	Shows multiplication's inherent priority over standard addition.
*12 / 3 2**	8 (Left-to-right: 4 * 2)	2 (BODMAS strictly: 12 / 6)	Demonstrates the importance of equal M/D left-to-right priorities.
(2 + 3)^2	25 (Bracket first: 5^2)	11 (Square first: 2 + 9)	Highlights parentheses overriding standard power exponents.
10 - 4 + 3	9 (Left-to-right: 6 + 3)	3 (Subtract first: 10 - 7)	Demonstrates equal A/S priorities solved left-to-right.