Evaluate mathematical expressions with trigonometry, logarithms, factorials, exponentiation, and order-of-operations parsing.
Click "Calculate" or press Enter to evaluate expression.
An electrical engineer calculates phase angles in an AC circuit: atan(12 / 5) * (180 / π). A physics student determines kinetic energy: 0.5 * 1200 * 25^2. A chemistry student computes pH from hydronium ion concentration: -log(1.5 * 10^-4). Each task requires performing advanced mathematical calculations beyond basic addition and multiplication.
A scientific calculator evaluates complex mathematical expressions containing trigonometric, logarithmic, exponential, and factorial functions. Unlike basic 4-function calculators that execute operations sequentially, a scientific calculator respects operator precedence (PEMDAS / BODMAS) and parses nested parentheses.
This online tool uses a client-side recursive-descent expression parser. It evaluates inputs containing trigonometric functions in either Degrees or Radians, computes logarithms in base 10 and natural log (base e), and processes large factorials. The following sections explain the underlying parser architecture, supported functions, and real-world applications across science, technology, engineering, and mathematics (STEM).
When an expression is submitted, the engine tokenizes the input string into numbers, operators, functions, and parentheses. It then evaluates the token stream using standard operator precedence rules.
1. Tokenization: Converts string 2 * sin(45) + 3^2 into token sequence: [2, *, sin, (, 45, ), +, 3, ^, 2].
2. Operator Precedence Order:
() and Function calls! and Exponents ^*, Division /, Modulo %+, Subtraction -3. Trigonometric Angle Conversion: In DEG mode, inputs to sin(x) are converted to radians: x_rad = x * (π / 180) before invoking JavaScript's Math.sin(x_rad).
4. Factorial Evaluation: For non-negative integers: n! = n × (n-1) × ... × 1. For non-integer inputs, the engine computes the Gamma function approximation Γ(n+1).
Physics and kinematics calculations. Students calculate projectile trajectories, orbital velocities, and wave frequencies using trigonometric and power functions.
Chemistry and thermodynamics. Chemistry labs calculate solution pH (-log[H+]), radioactive half-life decay rates, and Arrhenius activation energy equations.
Electrical and electronic engineering. Engineers compute impedance (Z = √(R² + X²)), resonant frequencies (f = 1 / (2π√(LC))), and decibel gain ratios (20 * log(Vout / Vin)).
Finance and statistics. Quantitative analysts compute continuous compound interest (P * e^(rt)), option pricing models, and probability density functions.
Always verify whether your trigonometric calculation requires Degrees or Radians. Click the ANGLE: DEG / RAD button at the top of the calculator to toggle modes.
Use parentheses liberally to enforce explicit grouping in complex rational expressions. For example, write (a + b) / (c + d) instead of a + b / c + d.
For solving systems of linear equations or matrix operations, use our Matrix Calculator or System of Equations Solver.
The parser operates in client-side JavaScript using IEEE 754 64-bit floating-point numbers. Expressions evaluate in sub-millisecond time.
| Feature | This Tool | Hand Scientific Calculator | Basic 4-Function |
|---|---|---|---|
| Expression Parsing | Full PEMDAS string parser | Button-by-button buffer | Immediate execution |
| Trig Modes | DEG and RAD toggle | DEG / RAD / GRAD | None |
| Logarithms | log10 and natural ln | log and ln keys | None |
| Memory Keys | MC, MR, M+, MS | M+, MR, MC | M+, M- |
| Execution Time | <1ms | Hardware chip | Immediate |
| Privacy | Client-side browser | Local hardware | Local hardware |
Expressions like 2(3 + 4) or 2pi are automatically converted to 2 * (3 + 4) and 2 * pi during tokenization.
log(x) evaluates the common logarithm in base 10 (10^y = x). ln(x) evaluates the natural logarithm in base e ≈ 2.71828 (e^y = x).
Yes. Supported inverse trig functions include asin (arcsin), acos (arccos), and atan (arctan).
The tangent of 90 degrees (π/2 radians) is mathematically undefined (division by zero in sin/cos). The calculator detects asymptote boundaries and reports an error.
Logarithm Calculator — Calculates logarithms in custom bases with change-of-base step breakdown.
Factorial Calculator — Computes large factorials with BigInt arbitrary precision.
Quadratic Solver — Solves second-order polynomial equations with real and complex roots.