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Calculator Expressions, Order of Operations, and Safety

A trustworthy calculator should explain how it reads an expression and reject input it cannot safely or mathematically support.

Short answer

What you need to know

Use parentheses when the intended order could be unclear. The shared calculator engine accepts an allowlisted mathematical grammar, reports the position of malformed input, checks function domains and finite results, and never evaluates entered text as JavaScript code.

Open the Scientific Calculator

Order and associativity

Functions and parentheses group values first, followed by factorial and powers, unary signs, multiplication and division, then addition and subtraction. Powers associate from the right, so 2^3^2 means 2^(3^2).

A leading minus applies after exponentiation in the shared grammar: −2^2 is −4. Write (−2)^2 when the negative value is the base.

Supported language is deliberately small

Numbers may use decimal or scientific notation. Named constants are pi and e. Reviewed functions include roots, absolute value, logarithms, exponentials, and common trigonometric functions. Unknown names, implicit multiplication, assignment, property access, and executable syntax are rejected.

Domains and finite results

Division by zero is undefined. Real square roots require non-negative inputs, logarithms require positive inputs, and inverse sine and cosine accept values from −1 through 1. Overflow and non-finite results are errors rather than displayed as NaN or infinity.

Bounded work

The engine limits input length, token count, nesting, exponent magnitude, and factorial input. These boundaries make behavior testable and prevent a short-looking input from demanding unbounded work.

Why parsing is safer than execution

The tokenizer recognizes only reviewed token types. The parser creates a mathematical expression tree, and the evaluator walks only known node types. It does not use eval, Function, dynamic imports, or treat entered text as a program.

Try these before revealing the answers

What is 2 + 3 × 4?

Show worked answer

Multiplication comes first, so the result is 14.

Why does sqrt(−1) fail here?

Show worked answer

The first release evaluates real numbers only, and −1 is outside the real square-root domain.

What does 2^3^2 mean?

Show worked answer

Powers associate from the right: 2^(3^2) = 512.

Important limitation

Verify important findings

The shared engine is an educational real-number calculator core, not an arbitrary programming language, symbolic algebra system, complex-number package, or certified numerical system.

Open the Scientific Calculator Review the methodology

Further reading

Authoritative references

These primary sources support the concepts and reference information in this guide. Their inclusion does not imply endorsement of Hidden Word Scanner.