Example from start to finish
For 3 + 4 × (2 − 1)³, the parentheses give 1, the power remains 1, multiplication gives 4, and the last addition produces 7. This Order of Operations example can be compared with exponent rules.
Math calculator
Order of Operations Calculator
Evaluate an arithmetic expression with parentheses, exponents, multiplication, division, addition, and subtraction in the correct order. Formula and expression value remain visible in one place for independent verification.
Order of Operations inputs
Calculation inputs
Mathematical foundation
Operation precedence removes ambiguity from a line containing several operations. Parentheses come first, followed by powers, multiplication or division, and finally addition or subtraction; equal-ranking operations proceed from left to right.
Reading expression value in Order of Operations requires the relationship defined above.
Steps without the calculator
Copy the expression and simplify one precedence level at a time. Replace every completed subexpression with its result while leaving the untouched structure visible. To extend Order of Operations, open fraction multiplication.
Boundaries and common traps
The exponent operator is evaluated from right to left, so 2^3^2 means 2^(3²). A minus sign directly before a value is treated as unary negation. If the Order of Operations assumptions do not fit, consider signed arithmetic.
Reversing the displayed steps offers a quick independent check on this order of operations result.
Situations that fit the model
Spreadsheet formulas, programming expressions, and textbook arithmetic all rely on a declared precedence system. Writing explicit parentheses remains the clearest approach when a result will be reviewed by someone else.
Reading sensitivity and precision
The input labels—arithmetic expression—encode the model used on this page. Write those labels beside source values when transferring a problem from paper or a spreadsheet. That small step catches transposed quantities and mixed units before they become a polished-looking expression value.
Changing parentheses can alter the operation tree even when every number and operator remains present. A one-field trial makes this relationship visible without reworking the entire example.
Choose rounding after considering how the result will be used. Comparison may need only a few significant digits, while a later multi-step calculation benefits from carrying more. In either case, retain the page's formula with the expression value so the underlying definition remains visible.
This evaluator follows arithmetic precedence; an algebra solver additionally manipulates unknown quantities. The distinction determines whether this page fits the original question.
If the number moves into a spreadsheet, give its cell a expression value heading and retain the source values arithmetic expression nearby. Context matters more than extra displayed digits.
Questions about Order of Operations
Does division always come before multiplication?
No. They have equal precedence and are handled from left to right.
Can I enter implicit multiplication such as 2(3)?
No. Enter 2*(3) so the operation is explicit.
Why are letters rejected?
This calculator evaluates numerical arithmetic, not algebraic variables.
Are nested parentheses allowed?
Yes, provided every opening parenthesis has a matching closing one.
What happens when I divide by zero?
The expression is rejected because the result is not finite.