Standard Calculator
Evaluate arithmetic expressions with addition, subtraction, multiplication, division, powers, parentheses, and decimals — safely, step by step.
Standard Calculator — input your values
What does this math calculator do?
The standard calculator evaluates a full arithmetic expression that you type, supporting +, −, ×, ÷, exponentiation with ^, parentheses, decimals, and unary minus. The expression is validated character by character and parsed with a recursive-descent parser, so nothing is ever passed to JavaScript's eval.
Operator precedence follows the standard mathematical conventions: parentheses first, then exponents, then multiplication and division, then addition and subtraction. The step-by-step view shows the tokens, the parsing rules, and the final evaluation, which makes it an excellent way to check your own arithmetic homework.
Formula and variables
Multiplication and division have equal precedence and evaluate left to right; addition and subtraction also evaluate left to right.
| Symbol | Meaning |
|---|---|
| op | One of + − * / ^ |
| ( ) | Grouping parentheses, evaluated first |
| ^ | Exponentiation, evaluated right to left |
Worked example
Evaluate the expression (12 + 8) / 5 - 2^3.
- Parentheses first: 12 + 8 = 20.
- Exponent: 2^3 = 8.
- Division: 20 / 5 = 4.
- Subtraction: 4 - 8 = -4.
Answer: (12 + 8) / 5 - 2^3 = -4.
Tips and common mistakes
Tips
- Use parentheses liberally: 2 * 3 + 4 differs from 2 * (3 + 4), and the calculator follows the same order of operations you learn in class.
- Remember the mnemonic PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction) — and note that ×/÷ and +/− are left-to-right peers.
- For powers, use ^: 2^10 = 1024. For roots, use fractional exponents: 16^(1/2) = 4.
- The expression field accepts spaces for readability — they are ignored by the tokenizer.
Common mistakes to avoid
- Using eval-based assumptions: this calculator validates every character, so letters or symbols like %, $, or commas are rejected.
- Forgetting a closing parenthesis, which produces a clear parse error.
- Dividing by zero, which is undefined and reported as an error rather than Infinity.
Standard Calculator — frequently asked questions
Which operators does this calculator support?
Addition (+), subtraction (−), multiplication (*), division (/), exponentiation (^), parentheses, and decimal numbers. Unary minus such as -5 is also supported.
Is the expression evaluated with eval?
No. The expression is validated and parsed with a recursive-descent parser that computes the result using explicit precedence rules, so it is safe and predictable.
What order of operations is used?
Parentheses first, then exponents, then multiplication and division (left to right), then addition and subtraction (left to right).
What happens if I divide by zero?
You get a clear error message. Division by zero is mathematically undefined, so the calculator refuses to report Infinity.
Can I use commas or thousands separators?
No. Use plain digits and a dot for decimals, for example 1,234 should be typed as 1234 and 0.5 as 0.5.
How do I compute something like the square root?
Use a fractional exponent: 16^(1/2) = 4, or 27^(1/3) = 3 for cube roots. The scientific calculator has dedicated root and trig functions.