Expression Calculator
Need to evaluate a complex mathematical formula without doing it by hand? An expression calculator interprets a string of mathematical input – from simple arithmetic to nested functions – and gives you the exact numeric answer. The free online tool below lets you type any valid mathematical expression and get the result instantly.
Start by entering a calculation: 2 + 3 * sin(pi/4), sqrt(16) + log(100), or even a custom expression with variables like x = 5; 2 * x^2 - 3*x + 1. The calculator parses your input according to standard mathematical rules and returns the final value.
Supported Functions & Constants
| Category | Functions |
|---|---|
| Trigonometric | sin(x), cos(x), tan(x), asin(x),
acos(x), atan(x) |
| Hyperbolic | sinh(x), cosh(x), tanh(x) |
| Exponential & Log | exp(x), ln(x), log(x) (base 10),
log10(x) |
| Power & Root | sqrt(x), pow(x, y) |
| Rounding | abs(x), round(x), floor(x), ceil(x) |
Constants: pi (π ≈ 3.1415926535), e (≈ 2.7182818284)
Operator Precedence
| Priority | Operators / Elements |
|---|---|
| 1 (highest) | Parentheses () |
| 2 | Unary minus, functions |
| 3 | Exponentiation ^ (right‑associative) |
| 4 | Multiplication *, division /, modulo % |
| 5 (lowest) | Addition +, subtraction - |
Examples
2+3*4→ 14 (multiplication before addition)(2+3)*4→ 20 (parentheses change order)sin(pi/2)→ 1 (radians assumed)sqrt(16)+log(100)→ 6 (√16 = 4, log₁₀100 = 2)2^3^2→ 512 (right‑associative: 2^(3²))x=10; 2*x→ 20 (variable assignment)
How to Use the Expression Calculator?
The expression calculator above reads the text you enter, identifies numbers, operators, functions, and constants, and evaluates them following the conventional order of operations. Here are the basics:
- Type any expression using digits, operators (
+,-,*,/,^), parentheses, and supported function names. - Assign variables with
=if needed (the variable must appear on the left side, e.g.,a = 10), then use it in subsequent expressions. - Watch the result – the calculator computes the value and displays it as soon as the input is valid. No need to press a separate button (though a “Calculate” action may be available for clarity).
- Fix mistakes – if there’s a syntax error, the tool shows a brief message; simply adjust your input.
The calculator respects standard precedence: parentheses have the highest priority, followed by functions and exponentiation, then multiplication / division, and finally addition / subtraction.
Supported Mathematical Functions
The expression calculator includes built-in elementary functions that go far beyond basic arithmetic. All trigonometric functions expect angles in radians.
| Category | Functions |
|---|---|
| Trigonometric | sin(x), cos(x), tan(x), asin(x), acos(x), atan(x) |
| Hyperbolic | sinh(x), cosh(x), tanh(x) |
| Exponential & Log | exp(x), ln(x), log(x) (base 10), log10(x) |
| Power & Root | sqrt(x), pow(x, y) (equivalent to x^y) |
| Rounding | abs(x), round(x), floor(x), ceil(x) |
You can also directly use constants:
pi– the number π (≈ 3.1415926535)e– Euler’s number (≈ 2.7182818284)
Operator Precedence and Syntax Rules
When you type 2+3*4, the calculator understands that multiplication comes before addition and returns 14, not 20. Below is the full precedence table, from highest to lowest priority.
| Precedence | Operators / Elements |
|---|---|
| 1 (highest) | Parentheses () |
| 2 | Unary minus -, functions |
| 3 | Exponentiation ^ (right‑associative) |
| 4 | Multiplication *, division /, modulo % |
| 5 (lowest) | Addition +, subtraction - |
Exponentiation is right‑associative, so 2^3^2 is interpreted as 2^(3^2) = 512. Use parentheses to make the order explicit when needed.
Expressions That Often Confuse
Here are a few examples that illustrate common patterns – and how the expression calculator handles them.
2+3*4→ 14 (multiplication first)(2+3)*4→ 20 (parentheses change order)sin(pi/2)→ 1 (radians assumed)sqrt(16)+log(100)→ 6 (square root = 4, log base 10 = 2)2^3^2→ 512 (right‑associative exponentiation)x=10; 2*x→ 20 after the assignment (semicolons separate multiple expressions)
What If the Expression Contains Errors?
If you miss a closing parenthesis, write an unknown function name, or use symbols incorrectly, the expression calculator will flag the problem. A short error message appears, pointing out the likely issue – for example, “Unexpected token” for a stray operator, or “Undefined function” for a misspelled word. Correct the input and the calculation automatically updates.
The error messages are designed to be simple and actionable, so you can quickly get back to the math you need.