Mathematics · Basics
BODMAS Calculator
Type an expression with brackets, powers, roots, “of”, ×, ÷, + and − and see it solved one operation at a time in BODMAS order — the same working a teacher expects, with exact fractions so there are no rounding surprises.
Your inputs
Quick start — try a typical case
Type it or use the keypad. * or x also mean ×, / means ÷, ^ is a power, √ or sqrt a square root, % a percentage. Brackets can be ( ), [ ] or { }.
Your result Live
Answer
6
20 − 3 × (8 − 2)^2 ÷ 6 + 4 = 6
- Steps
- 6
- Read as
- 20 − 3 × (8 − 2)^2 ÷ 6 + 4
Step-by-step working (BODMAS)
Start: 20 − 3 × (8 − 2)^2 ÷ 6 + 4
B: Step 1 · Brackets — subtraction inside ( )
8 − 2 = 6
Expression becomes 20 − 3 × 6^2 ÷ 6 + 4
O: Step 2 · Orders — power
6^2 = 36
Expression becomes 20 − 3 × 36 ÷ 6 + 4
M: Step 3 · Multiplication
3 × 36 = 108
Expression becomes 20 − 108 ÷ 6 + 4
D: Step 4 · Division
108 ÷ 6 = 18
Expression becomes 20 − 18 + 4
S: Step 5 · Subtraction
20 − 18 = 2
Expression becomes 2 + 4
A: Step 6 · Addition
2 + 4 = 6
Expression becomes 6
Answer = 6
How this is calculated
Brackets → Orders → Division / Multiplication → Addition / Subtraction
- B
- Brackets ( ), [ ], { } — innermost first
- O
- Orders: powers ^ and roots √, plus “of”
- D M
- Division and multiplication — equal priority, left to right
- A S
- Addition and subtraction — equal priority, left to right
BODMAS is the agreed order for working out an expression with several operations, so everyone reaches the same answer. It's the same rule as PEMDAS (US), BEDMAS (Canada) and BIDMAS (UK). This calculator never jumps ahead: it finds the single operation BODMAS says comes next, does it, rewrites the expression, and repeats — exactly the working you'd write out by hand. Arithmetic uses exact fractions, so 1 ÷ 3 × 3 comes out as exactly 1, not 0.9999999999.
Common questions
What does BODMAS stand for?
Brackets, Orders (powers and roots — in many Indian textbooks the O is “Of”), Division, Multiplication, Addition, Subtraction. PEMDAS, BEDMAS and BIDMAS are the same rule with different names.
Is division always done before multiplication?
No — this is the most common BODMAS mistake. Division and multiplication have equal priority and are done left to right, so 8 ÷ 2 × 4 = 4 × 4 = 16, not 1. Addition and subtraction work the same way: 10 − 3 + 2 = 9.
What is 6 ÷ 2(1 + 2)?
Here it's 9: the bracket gives 3, and 2(3) means 2 × 3 with the same priority as ÷, so 6 ÷ 2 × 3 = 3 × 3 = 9. Some textbooks give a number written next to a bracket a higher priority, which would give 1 — that's why the puzzle goes viral. Add brackets to make your meaning unambiguous.
How does “of” work?
“of” means multiply and is done before division and multiplication: 60 ÷ 3 of 4 = 60 ÷ 12 = 5. Percentages work naturally with it: 50% of 200 = 100. For a fraction of a number, bracket the fraction: (1/2) of 10 = 5.
Which brackets can I use?
Round ( ), square [ ] and curly { } brackets, nested as deeply as you like. The innermost bracket is solved first, then the next one out. Each opening bracket must be closed by the same kind.
Can I see the answer as a fraction?
Yes — switch “Show the answer as” to Fraction. Every step then shows exact fractions (like 5/6) instead of decimals, and the result also shows a mixed number such as 2 1/3 where that applies.