Order of operations calculator

What is an order of operations calculator?

The order of operations calculator evaluates an arithmetic expression exactly the way mathematicians agree it should be read. Instead of working strictly from left to right, it applies the standard priority rules — parentheses first, then exponents, then multiplication and division, and finally addition and subtraction. Type an expression such as 2+3*4 and the calculator returns the single correct value, so you never have to wonder whether a result was computed in the right sequence.

PEMDAS and BODMAS

The priority rules are usually remembered through an acronym. In the United States it is PEMDAS — Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. In the United Kingdom and many other countries it is BODMAS — Brackets, Orders, Division and Multiplication, Addition and Subtraction. The two acronyms describe the very same convention: multiplication and division share one level (evaluated left to right), and addition and subtraction share the level below them (also left to right).

How does the order of operations calculator work?

You enter a full expression in a single field. The calculator accepts digits, decimals, parentheses, and the operators +, -, * (or ×), / (or ÷), and ^ for exponents. It parses the expression with a safe evaluator that honours precedence and associativity, then displays the result. If the expression is incomplete or malformed, the result simply stays empty until you fix it. For repeated single operations you can also use the dedicated addition calculator or multiplication calculator.

The order of operations

The calculator resolves an expression in this priority, highest first:

• Parentheses: anything inside ( ) is evaluated first, from the innermost pair outward.
• Exponents: powers written with ^ are applied next, and they group from right to left.
• Multiplication and division: performed together, scanning left to right.
• Addition and subtraction: performed last, also scanning left to right.

Worked examples

1. Multiplication before addition: $2 + 3 \times 4 = 14$ Because multiplication ranks above addition, $3 \times 4 = 12$ is computed first and then added to 2.

2. Parentheses change everything: $(2 + 3) \times 4 = 20$ The brackets force the addition to happen first, giving $5 \times 4 = 20$.

3. Exponents group right to left: $2^{3^{2}} = 2^{9} = 512$ The top exponent is resolved first: $3^{2} = 9$, and then $2^{9} = 512$.

4. Exponent before multiplication: $2^{3} \times 2 = 8 \times 2 = 16$ The power is evaluated before the multiplication, so the answer is 16, not 64.

5. Subtraction left to right: $10 - 4 - 3 = 3$ Reading left to right, $10 - 4 = 6$ and then $6 - 3 = 3$.

6. Division left to right: $8 / 4 / 2 = 1$ Left to right gives $8 / 4 = 2$ and then $2 / 2 = 1$.

7. Everything together: $2 \times (3 + 4)^{2} = 2 \times 49 = 98$ Parentheses first ($3 + 4 = 7$), then the exponent ($7^{2} = 49$), then the multiplication.

8. Decimals: $1.5 \times 2 = 3$ Decimal values follow exactly the same precedence rules as whole numbers.

Practical notes

• Use parentheses when in doubt: brackets make your intent explicit and remove any ambiguity from a long expression.
• Multiplication and division are equal: they are resolved strictly left to right, so $8 / 4 / 2$ is 1, not 4.
• Powers are right-associative: $2^{3^{2}}$ means $2^{(3^{2})}$, which is 512, not $(2^{3})^{2} = 64$.

Frequently asked questions

Does the calculator follow PEMDAS or BODMAS?

Both. PEMDAS and BODMAS are two names for the same rule set, so the calculator produces identical results regardless of which acronym you were taught.

Why is 2+3×4 equal to 14 and not 20?

Multiplication has higher priority than addition, so $3 \times 4 = 12$ is calculated before adding 2, giving 14. You would only get 20 if you wrote $(2 + 3) \times 4$.

Is the exponent evaluated left to right or right to left?

Exponents are right-associative. In $2^{3^{2}}$ the calculator evaluates $3^{2} = 9$ first and then $2^{9} = 512$.

What symbols can I type?

Digits, a decimal point, parentheses, and the operators +, -, *, /, and ^. The unicode symbols × and ÷ are also accepted and treated as * and /.

What happens with an invalid expression?

If the expression is incomplete or contains an unexpected symbol — for example 2++ or (3+ — the result stays empty. Correct the expression and the answer appears immediately.