PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, and it is the standard American mnemonic for the order of operations: the agreed-upon sequence that tells you which part of a math expression to evaluate first.
Without a shared rule, the expression 2 + 3 * 4 could reasonably yield 20 (if you add first) or 14 (if you multiply first). Mathematicians settled on 14. PEMDAS is just the memory tool that encodes that settlement.
Work through an expression in this sequence:
Parentheses come first. Any operation inside grouping symbols, whether round brackets, square brackets, or curly braces, gets resolved before anything outside them. Nested parentheses work from the inside out.
Exponents are next. After the brackets are cleared, raise any bases to their powers. This includes square roots and other radicals, which are fractional exponents in disguise.
Multiplication and Division sit at the same level of priority. They do not form a strict left-before-right hierarchy between themselves. When both appear in an expression, you read left to right and handle whichever comes first. This is the point most people get wrong.
Addition and Subtraction are the final tier, also sharing equal rank. Again, read left to right. Subtraction is just adding a negative number, so there is no reason to treat them differently.
The hierarchy in shorthand: (P) then (E) then (MD left to right) then (AS left to right).
Consider 2 + 3 * 4.
If you had added first (2 + 3 = 5, then 5 * 4 = 20), you would get 20. That answer violates the convention and would be marked wrong on any standard exam. The multiplication step had higher priority and had to go first.
Now try something that exercises every level: (2 + 3)^2 / 5 - 1 * 3 + 8 / 4.
Notice that in step 3, division and multiplication were handled strictly left to right across the whole expression, not as two separate passes. That single rule prevents a lot of errors.
If you regularly work with sets of numbers rather than single expressions, the average calculator on this site can handle those computations quickly. For problems involving common factors, the GCF calculator covers that ground.
In the United Kingdom, Australia, India, and several other countries, the same hierarchy goes by BODMAS or BIDMAS. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. BIDMAS swaps "Orders" for "Indices," which means exponents.
The math is identical. Both systems produce the same result for every expression. The only real difference is that BODMAS lists division before multiplication, which can mislead students into thinking division outranks multiplication. It does not. They remain co-equal, resolved left to right. PEMDAS has the same trap in reverse: listing multiplication before division does not elevate it. Both mnemonics are imperfect abbreviations of a more nuanced rule.
Some teachers in the UK now use BIDMAS specifically to avoid the impression that "O for Orders" is somehow broader or different from exponents. In practice, any of the three terms gets you to the right answer if you remember the left-to-right rule for the paired tiers.
In 2019, the expression 8 / 2(2+2) went viral. Half the internet said the answer was 1. The other half said 16. Comment sections turned ugly.
Under standard PEMDAS, the answer is 16. Here is why.
First, resolve the parentheses: (2+2) = 4. The expression becomes 8 / 2 * 4.
Now apply the left-to-right rule for multiplication and division. Reading left to right: 8 / 2 = 4, then 4 * 4 = 16.
The camp that got 1 treated 2(4) as a single unit, effectively reading the expression as 8 / (2 * 4) = 8 / 8 = 1. That interpretation applies a convention sometimes called "implicit multiplication has higher priority," which some older textbooks and certain calculators do follow. It is not wrong in every context. But it is not the standard rule taught in most schools or implemented in most modern calculators and programming languages.
The deeper lesson is that the expression is genuinely ambiguous. A well-written expression would use explicit parentheses to remove all doubt: either (8 / 2) * (2+2) = 16 or 8 / (2 * (2+2)) = 1. If your expression requires a debate, the expression needs a rewrite.
Order of operations is not just a school exercise. Every spreadsheet formula, every line of code, every scientific calculator applies these rules automatically. If you type =2+3*4 into a spreadsheet cell, you will get 14, not 20. If you expect 20 and budget accordingly, that is a real error with real consequences.
Programming languages like Python, JavaScript, and C all follow the same hierarchy, with minor variations for bitwise operators. Financial models built in Excel can contain subtle order-of-operations bugs that are hard to spot precisely because the software follows the rules correctly while the human author did not.
Understanding why 3 * 4 goes before 2 + 3 is not about memorizing a mnemonic. It is about knowing what your tools are doing with the numbers you give them.
If you need to find the mean of a set of numbers, the average calculator handles it in one step, with the formula shown.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is the standard mnemonic used in the United States to remember the order in which operations must be performed in a math expression.
Yes. Multiplication and division share the same rank in the order of operations. When both appear in an expression, you work through them left to right, not multiplication first. The same rule applies to addition and subtraction.
They describe the same rule. BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is used in the UK, Australia, and other countries. BIDMAS is another variant. The underlying math is identical.
Because changing the order changes the answer. In 2 + 3 * 4, doing the addition first gives 20, but the correct answer under standard rules is 14, because multiplication is evaluated before addition. Consistent rules let every mathematician and computer reach the same result from the same expression.
Editor at Encore Editorial, Chris Terry sets the editorial standards here and turns dense topics into plain English. He has written widely on education, finance, and consumer markets.