Enter −2² and different calculators give −4 and 4. The answer here is −4, because exponentiation binds more tightly than the unary minus, so the expression reads as −(2²) rather than as (−2)². Calculators that answer 4 are treating the minus as part of the number rather than as an operator applied to the result.
Neither behaviour is a bug. They are different parsing conventions, and knowing which one you are holding is more useful than knowing which is correct.
What is the actual precedence order?
Brackets first, then exponents, then multiplication and division, then addition and subtraction — with unary minus sitting between exponentiation and multiplication in the convention used here and in most programming languages and computer algebra systems.
| Expression | Reads as | Result |
|---|---|---|
| −2² | −(2²) | −4 |
| (−2)² | (−2)² | 4 |
| 2^3^2 | 2^(3^2) | 512 |
| (2^3)^2 | (2^3)^2 | 64 |
The brackets are not decoration in either case. They are the only way to state the other reading, which is exactly what they are for.
Why do powers group from the right?
Because the left-grouped reading is redundant. If 2^3^2 meant (2^3)^2, it would equal 2^(3×2) — which anyone can already write as 2^6. Right grouping gives 2^(3^2) = 2^9 = 512, a value that has no shorter form, so the convention preserves expressive power rather than throwing it away.
This is the same reasoning behind most notational conventions: the ambiguous case resolves toward the reading that cannot be written any other way.
What about implicit multiplication?
It is the deepest source of disagreement between calculators, and it has no settled answer. Some models treat 6÷2(3) as 6÷2×3 = 9; others treat the juxtaposition as binding tighter, giving 6÷(2×3) = 1.
Physics and mathematics typesetting generally favour the tighter binding — nobody reads 1/2π as (1/2)×π. Most calculators and programming languages do not, because their parsers treat implicit multiplication as ordinary multiplication.
The practical position is that any expression relying on this is ambiguous regardless of what your calculator does, and the fix is a bracket rather than an argument. An expression a reader has to guess at is one the author should have punctuated.
Do brackets have to be closed?
Not in most calculators, including this one — unclosed brackets are closed implicitly at the end of the expression, so 2×(3+4 evaluates as 2×(3+4) = 14. It is a convenience for typing on a phone and it hides one specific class of error, where a bracket was opened in the wrong place and the implicit close puts it somewhere you did not intend.
When an answer looks wrong and the expression is long, closing the brackets explicitly is the fastest diagnostic.
One further wrinkle: subtraction and division are left-associative, so 12−4−3 is (12−4)−3 = 5, and 24÷4÷2 is (24÷4)÷2 = 3. Nobody argues about these, and they are the reason exponentiation grouping the other way is worth stating explicitly rather than assuming.
Does the percentage key mean anything consistent?
Not across models, no. On many calculators % divides by a hundred and nothing else, so 50+10% is 50.1. On others it is context-sensitive, taking 10 per cent of the preceding value to give 55.
The context-sensitive behaviour is convenient in a shop and unpredictable in an equation, which is why expression-based calculators tend to define it as plain division by a hundred and leave percentage questions to a tool built for them. If a percentage matters, computing it explicitly removes the ambiguity entirely.
Memory keys have their own quiet convention. M+ adds the displayed value to whatever is already stored rather than replacing it, so pressing it twice on the same result stores double. Anyone treating it as a save button will eventually recall a number that is a sum of things they meant to overwrite.
What about degrees and radians?
The single most common source of a wrong trigonometric answer. sin(30) is 0.5 in degrees and −0.988 in radians, and the calculator will report whichever mode it happens to be in without complaint.
The mode indicator is worth checking before any trigonometry rather than after, because a plausible wrong answer is much harder to spot than an implausible one. Calculus and most programming work in radians; geometry, surveying and school trigonometry generally in degrees.
Questions people ask
Which convention is right for −2²? Both are defensible, and −(2²) is the reading used by mathematical typesetting, spreadsheets’ underlying convention aside, and most programming languages. Writing (−2)² when you mean it removes the question.
Why does my spreadsheet disagree? Some spreadsheet software binds unary minus more tightly than exponentiation, so =-2^2 returns 4. It is a documented and long-standing difference from the mathematical convention.
Is floating-point arithmetic exact? No. Results are computed in double precision, so a value such as sin(30) can come back as 0.49999999999999994 before display rounding. That is the hardware, not the tool.
Can I work from the keyboard alone? Yes — digits, operators, brackets and Enter all map to their obvious keys, which is faster than clicking for anything more than two operations.
Why does the history let me tap an old answer? Because reusing a result is more common than retyping it, and retyping is where transcription errors come from. Tapping a previous answer puts the full-precision value back into the field, not the rounded one that was displayed.
Precedence is a convention, brackets are how you override it, and the mode indicator decides your trigonometry. The scientific calculator evaluates whole expressions so the precedence is visible before you commit, the percentage calculator removes the percentage-key ambiguity, and the fraction calculator keeps exact values exact.