BODMAS / PEMDAS Calculator – Order of Operations Solver
Solve any math expression using the correct order of operations with our free BODMAS/PEMDAS calculator. Get step-by-step breakdowns to understand exactly how each expression is evaluated.
Supports: + - * / ^ ( ) and decimals
BODMAS / PEMDAS Calculator – Order of Operations Solver
Order of operations rules tell us which part of a mathematical expression to calculate first. Without these rules, the same expression could have multiple answers. This calculator follows BODMAS/PEMDAS rules and shows every step so you can follow along and learn the process.
Enter any expression with numbers, basic operations (+, −, ×, ÷), exponents, and parentheses. The calculator evaluates it in the correct order, explaining each step. You'll see parentheses handled first, then exponents, then multiplication and division, and finally addition and subtraction.
BODMAS vs PEMDAS
BODMAS (UK, Australia, others)
PEMDAS (US)
Both acronyms mean the same thing. Division and multiplication have equal priority – work left to right. Same for addition and subtraction. The different letters just reflect different regional terminology.
Key Rules
1. Parentheses/Brackets First
Always evaluate what's inside parentheses or brackets before anything else. If there are nested parentheses, start with the innermost pair.
2. Exponents/Orders Next
Calculate powers and roots after parentheses. This includes squares, cubes, and any other exponents.
3. Multiplication and Division (Left to Right)
These have equal priority. Work from left to right, not multiplication before division.
4. Addition and Subtraction (Left to Right)
These also have equal priority. Work from left to right.
Worked Examples
Example 1: 2 + 3 x 4
Example 2: (5 + 3) x 2
Example 3: 10 - 2³
Example 4: 4 + 6 / 2 x 3
Example 5: (8 - 2) x (3 + 1)
Common Mistakes
Adding before multiplying
Wrong: 2 + 3 x 4 = 5 x 4 = 20
Right: 2 + 3 x 4 = 2 + 12 = 14
Doing multiplication before division
Wrong: 12 / 3 x 2 = 12 / 6 = 2
Right: 12 / 3 x 2 = 4 x 2 = 8 (left to right)
Ignoring parentheses
Wrong: (5 + 3) x 2 = 5 + 6 = 11
Right: (5 + 3) x 2 = 8 x 2 = 16
Subtracting before adding
Wrong: 10 - 3 + 2 = 10 - 5 = 5
Right: 10 - 3 + 2 = 7 + 2 = 9 (left to right)
Frequently Asked Questions
Why does order of operations matter?
Without agreed-upon rules, the same expression could have different answers. Order of operations ensures everyone gets the same result when solving mathematical expressions.
Do calculators follow order of operations?
Scientific calculators do. Basic four-function calculators often don't – they calculate as you type. That's why 2 + 3 x 4 gives 14 on a scientific calculator but 20 on a basic one.
What about fractions in expressions?
Treat the numerator and denominator as if they're in parentheses. Evaluate each separately, then divide. For example, (2 + 3) / (4 - 1) = 5 / 3.
How do I remember the order?
Use the mnemonic PEMDAS: "Please Excuse My Dear Aunt Sally." Or BODMAS for British English. Remember that M/D and A/S are equal priority – go left to right.
What about implicit multiplication?
Expressions like 2(3 + 4) mean 2 x (3 + 4). The multiplication is implied. Some calculators give implicit multiplication higher priority, but standard PEMDAS treats it the same as explicit multiplication.
Are there exceptions to these rules?
The standard order is universal in mathematics. However, some programming languages have additional operators with their own precedence rules. Always check your language's documentation for complex expressions.
Other Free Tools
Long Division Calculator – Step-by-Step Division with Remainder
Solve long division problems step by step with our free online long division calculator. See every step of the division process including quotient and remainder – ideal for learning.
Long Multiplication Calculator – Step-by-Step Multiplication
Multiply large numbers with full step-by-step working using our free online long multiplication calculator. See every step laid out clearly – perfect for students learning multiplication.
Free Online Standard Calculator – Fast & Easy Math
Use our free standard calculator online to perform quick arithmetic operations including addition, subtraction, multiplication, and division. Simple, fast, and accurate for everyday math needs.
Absolute Value Calculator – Find |x| of Any Number
Calculate the absolute value of any number or expression instantly with our free online absolute value calculator. Supports positive, negative, and decimal numbers.
Simplify Expression Calculator – Simplify Algebraic Expressions
Simplify any basic algebraic expression instantly with our free online simplify expression calculator. Combine like terms and reduce expressions to their simplest form with ease.
Free Online Scientific Calculator – Advanced Math Functions
Perform complex scientific calculations online with our free scientific calculator. Supports trigonometry, logarithms, exponents, roots, and more – ideal for students and professionals.
Equation Balancer – Balance Simple Equations Online
Balance simple chemical or algebraic equations automatically with our free online equation balancer. Enter your equation and get correctly balanced coefficients in seconds.
Linear Equation Solver – Solve ax + b = c Online
Solve any linear equation of the form ax + b = c instantly with our free online linear equation solver. Get step-by-step solutions for one-variable linear equations.