Order of Operations Calculator
Order of Operations Calculator
Evaluate arithmetic expressions using parentheses, multiplication, division, addition and subtraction in the correct order.
Enter your expression
Enter an expression and select Calculate.
Order of Operations Calculator – Solve Maths Expressions Step by Step
Use this free Order of Operations Calculator to evaluate arithmetic expressions correctly. The order of operations tells you which calculation to perform first when an expression contains more than one operation. It prevents different interpretations of the same expression and helps you solve maths problems consistently. Enter an expression containing parentheses, multiplication, division, addition or subtraction to calculate its value.
The standard order is often remembered through PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division, Multiplication, Addition and Subtraction). This calculator supports basic arithmetic and parentheses only; it does not calculate exponents, variables or mathematical functions.
How to use this order of operations calculator
- Enter a mathematical expression in the Arithmetic expression field, for example (2 + 3) * 4 - 6 / 2.
- Use parentheses to group the calculations that must be completed first.
- Use the supported arithmetic symbols for addition (+), subtraction (-), multiplication (*) and division (/).
- Select Calculate to evaluate the expression according to the correct operation priority.
- Select Clear to remove the expression before entering another one.
Order of operations rules: PEMDAS and BODMAS
Follow these rules when evaluating an arithmetic expression:
- Parentheses or Brackets: Calculate the expression inside grouping symbols first. If brackets are nested, start with the innermost group.
- Multiplication and Division: These operations have equal priority. Work from left to right, performing whichever appears first.
- Addition and Subtraction: These operations also have equal priority. Work from left to right.
A common mistake is to assume multiplication must always happen before division, or addition before subtraction. They share the same priority, so their left-to-right order matters. PEMDAS and BODMAS describe the same essential convention; the letters should not be read as meaning that multiplication always outranks division.
Order of operations formula and priority
Priority: Parentheses → Multiplication and Division (left to right) → Addition and Subtraction (left to right).
Example expression: (2 + 3) × 4 − 6 ÷ 2
Evaluation: 5 × 4 − 3 = 20 − 3 = 17.
There is no single arithmetic formula for every expression. Instead, the order of operations is a set of rules for deciding the sequence in which the individual operations are evaluated.
Worked examples of order of operations
Example 1: Multiplication before addition
Expression: 5 + 3 × 4
First multiply: 3 × 4 = 12. Then add: 5 + 12 = 17.
Example 2: Parentheses first
Expression: (8 − 2) × 5
First calculate the brackets: 8 − 2 = 6. Then multiply: 6 × 5 = 30.
Example 3: Division and multiplication from left to right
Expression: 24 ÷ 6 × 2
Both operations have equal priority. Work left to right: 24 ÷ 6 = 4, then 4 × 2 = 8.
Example 4: Addition and subtraction from left to right
Expression: 18 − 5 + 2
Work left to right: 18 − 5 = 13, then 13 + 2 = 15.
Why is the order of operations important?
The order of operations gives everyone a consistent way to interpret mathematical expressions. It is useful for school maths, homework, arithmetic practice, checking calculations and understanding expressions that contain several operations. Applying the rules correctly avoids errors caused by calculating from left to right without considering operation priority.
Frequently asked questions
1. What is the order of operations in maths?
The order of operations is the set of rules used to decide which part of an arithmetic expression to calculate first. Evaluate parentheses first, then multiplication and division from left to right, and finally addition and subtraction from left to right.
2. What does PEMDAS stand for?
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. It is a memory aid for the standard order of operations. Multiplication and division share a priority level, as do addition and subtraction.
3. What does BODMAS mean?
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction. It is another way to remember operation priority. Division and multiplication are performed from left to right when they appear together.
4. Do you multiply before you divide?
No. Multiplication and division have equal priority. When both appear in an expression, calculate them in the order they occur from left to right.
5. Do you add before you subtract?
No. Addition and subtraction have equal priority. Work from left to right, performing whichever operation appears first.
6. What comes first, parentheses or multiplication?
Parentheses come first. Complete the calculation inside the parentheses before applying multiplication, division, addition or subtraction to the remaining expression.
7. How do you solve an expression with multiple operations?
Start with the innermost parentheses, then complete multiplication and division from left to right. Finish by completing addition and subtraction from left to right.
8. What is the answer to 5 + 3 × 4?
The answer is 17. Multiply 3 by 4 first to get 12, then add 5 to get 17.
9. Are PEMDAS and BODMAS the same?
They are different memory aids for the same basic order-of-operations convention. Both indicate that grouping symbols are handled first, followed by higher-priority operations and then addition and subtraction. Operations at the same priority are evaluated from left to right.
10. Can this calculator solve exponents or algebraic expressions?
No. This calculator is designed for basic arithmetic expressions with parentheses, addition, subtraction, multiplication and division. It does not support variables, functions or exponent operators.