The 40-second answer
PEMDAS, BODMAS, BIDMAS, and BEDMAS are the same rule with different names. PEMDAS (used in the US) says Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BODMAS (used in the UK, India, Australia) says Brackets, Orders, Division, Multiplication, Addition, Subtraction. The order is identical: brackets/parentheses first, then powers, then multiplication and division together left to right, then addition and subtraction together left to right. If you learned BODMAS and someone says PEMDAS, nothing changes — solve the expression exactly the same way. Verify any expression with a free order of operations calculator.
Why so many names for one rule?
The order of operations is a global agreement, but the mnemonic children memorize is local. The United States teaches PEMDAS (“Please Excuse My Dear Aunt Sally”). The UK, India, Australia, and much of the Commonwealth teach BODMAS or BIDMAS. Canada and New Zealand often teach BEDMAS. A student moving from London to Los Angeles can feel like the rules changed overnight — they did not. Only the letters changed.
Here are the four common mnemonics side by side:
| PEMDAS (US) | BODMAS (UK/India/Aus) | BIDMAS (UK) | BEDMAS (Canada/NZ) | |
|---|---|---|---|---|
| 1 | Parentheses | Brackets | Brackets | Brackets |
| 2 | Exponents | Orders | Indices | Exponents |
| 3 | Multiplication | Division | Division | Division |
| 4 | Division | Multiplication | Multiplication | Multiplication |
| 5 | Addition | Addition | Addition | Addition |
| 6 | Subtraction | Subtraction | Subtraction | Subtraction |
Three observations matter here. First, “brackets,” “parentheses,” “orders,” “indices,” and “exponents” all describe the same two priority levels. Second, every mnemonic lists multiplication and division adjacent — because they are one level. Third, every mnemonic lists addition and subtraction adjacent — because they are also one level. The letters differ; the mathematics does not.
The one rule they all share
Strip away the acronyms and every version of the rule is this:
- Grouping symbols first — parentheses (), brackets [], braces {}, fraction bars.
- Powers and roots — exponents, indices, orders: all the same thing (see our exponent calculator for powers worked step by step).
- Multiplication and division together, left to right. Not multiplication before division. Together.
- Addition and subtraction together, left to right. Not addition before subtraction. Together.
Step 3 is where the mnemonics mislead. PEMDAS puts M before D; BODMAS puts D before M. If you read either acronym as a strict sequence, the two mnemonics seem to disagree about 8 ÷ 2 × 4. They do not — both teach that × and ÷ are equals, resolved in reading order. The acronyms are memory aids, not algorithms. The algorithm is the four-step list above.
Worked examples in both dialects
The best proof that the rule is one rule: the same expression, solved the same way, under either name.
Example 1: 8 ÷ 2(2+2) — the viral one
PEMDAS wording: Parentheses first — 2 + 2 = 4 → 8 ÷ 2 × 4. Multiplication and division left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.
BODMAS wording: Brackets first — 2 + 2 = 4 → 8 ÷ 2 × 4. Division and multiplication left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.
Same answer. For the full story of why some people insist the answer is 1, see our explainer on why 8 divided by 2(2+2) equals 16.
Example 2: 33 − 12 + 4²
PEMDAS wording: Exponents — 4² = 16 → 33 − 12 + 16. Addition and subtraction left to right: 33 − 12 = 21, then 21 + 16 = 37.
BODMAS wording: Orders — 4² = 16 → 33 − 12 + 16. Addition and subtraction left to right: 37.
Note the trap BODMAS students face too: the acronym lists A before S, but 12 + 16 must NOT be done first. Left to right. Always.
Example 3: 30 ÷ 5 × 3 — the left-to-right tiebreaker
This is the expression that exposes the acronym’s lie: PEMDAS lists M before D, BODMAS lists D before M. If either letter order were the rule, the two mnemonics would disagree here. They do not.
PEMDAS wording: No parentheses, no exponents. Multiplication and division are one level — go left to right: 30 ÷ 5 = 6, then 6 × 3 = 18.
BIDMAS wording: No brackets, no indices. Division and multiplication are one level — go left to right: 18. Identical.
The letters never decided anything. The level rule did.
Where students actually get confused
The confusion is rarely about the letters. It is about three deeper misunderstandings, and they are the same in every country:
1. Thinking the acronym is a strict sequence. “M comes before D, so I multiply first.” No — they are one level. 8 ÷ 2 × 4 goes left to right regardless of which mnemonic you learned.
2. Treating implied multiplication as special. Writing 2(4) instead of 2 × 4 changes nothing about priority. This is the engine of the whole 16-vs-1 internet war, and it has nothing to do with PEMDAS vs BODMAS.
3. Forgetting that subtraction is left-to-right too. In 33 − 12 + 16, students who add first get 5. The correct answer is 37.
If any of these sound familiar, run your expression through Calcrio’s pemdas calculator — it shows each step with the rule that justifies it, which is exactly how the confusion gets fixed.
A brief history: why the US and UK split the letters
The order of operations hardened into a standard in the early 20th century as mathematics textbooks converged internationally. American publishers settled on Parentheses and Exponents; British publishers on Brackets and Orders (from the older term “orders of” powers). Neither side’s math was ever different — this is pure vocabulary drift, like “trunk” vs “boot” on a car. International standards such as ISO 80000-1 describe the notation conventions without taking sides in the mnemonic war, because there is no war to take sides in.
Which mnemonic should you teach or learn?
Use whichever your curriculum uses — your teacher, exam, or country decides. What matters is teaching the two equal-level rules explicitly, because every mnemonic hides them:
- × and ÷ are one level: left to right.
- + and − are one level: left to right.
A student who knows those two sentences can use PEMDAS, BODMAS, BIDMAS, or BEDMAS interchangeably. A student who only memorized “Please Excuse My Dear Aunt Sally” as a strict sequence will still get 8 ÷ 2 × 4 wrong.
PEMDAS around the world: who uses what
The mnemonic map roughly follows language and colonial history, but the math underneath is identical everywhere:
| Region | Common mnemonic | Notes |
|---|---|---|
| United States | PEMDAS | “Please Excuse My Dear Aunt Sally” — the classic |
| United Kingdom | BODMAS / BIDMAS | “Orders” (older term) vs “Indices” (modern term) |
| Canada, New Zealand | BEDMAS | Brackets, Exponents, Division, Multiplication, Addition, Subtraction |
| India, Australia, Pakistan | BODMAS | Same as UK usage |
| Much of continental Europe | No single mnemonic | The rule is taught directly as “punkt vor strich” (Germany: “point before line” — ×/÷ before +/−) |
Germany’s version is worth noticing: “Punkt vor Strich” (dots before dashes) teaches the concept — multiplication and division before addition and subtraction — without any acronym at all. It sidesteps the exact trap the acronyms create, because there are no letters to misread as a strict sequence. That is the real lesson of the mnemonic wars: the letters were never the point. The priority levels are.
One more practical note for students who move between systems: exams grade the rule, never the mnemonic. A BODMAS student who learned “brackets, orders, division-and-multiplication left to right” gets full marks on a PEMDAS test, because the grader checks the steps, not the acronym.
Frequently asked questions
Is BODMAS the same as PEMDAS?
Yes. They describe the identical order of operations. PEMDAS says Parentheses/Exponents; BODMAS says Brackets/Orders. Multiplication and division share a level (left to right) and addition and subtraction share a level (left to right) in both.
What is BIDMAS?
BIDMAS is the UK variant that says “Indices” instead of “Orders” — Brackets, Indices, Division, Multiplication, Addition, Subtraction. Same rule as BODMAS and PEMDAS.
Which countries use BODMAS vs PEMDAS?
The US teaches PEMDAS. The UK, India, Australia, and much of the Commonwealth teach BODMAS or BIDMAS. Canada and New Zealand commonly teach BEDMAS. The underlying rule is the same everywhere.
Does the order of the letters M and D matter?
No. In PEMDAS, M precedes D; in BODMAS, D precedes M. Both mnemonics teach that multiplication and division are a single level evaluated left to right, so the letter order changes nothing.
Is 8 ÷ 2(2+2) = 16 under BODMAS too?
Yes — 16 under every mnemonic. Brackets first (4), then division and multiplication left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.
One rule, four names, zero ambiguity. Check any expression — in any dialect — with the free pemdas calculator.