Advanced Scientific Calculator
A CAS-level scientific calculator with graphing, matrices, complex numbers, derivatives, integrals, statistics, and equation solving, all in one.
What Is the Advanced Scientific Calculator?
This advanced scientific calculator brings CAS-level capabilities to your browser across six specialized modes: Scientific, Grapher, Matrix, Statistics, Calculus, and Equation Solver. All calculations run locally, no data leaves your device. Built on the mathjs library for high-precision arithmetic, symbolic differentiation, and matrix decomposition.
- ›Scientific mode: full keypad with trig, log, exp, constants (π, e, φ), history
- ›Grapher: plot any f(x) expression, up to 3 functions in different colors
- ›Matrix: add, multiply, transpose, invert, determinant up to 4×4
- ›Statistics: mean, median, mode, SD (σ and s), variance, IQR, histogram
- ›Calculus: symbolic first derivative and numerical definite integral
- ›Solver: linear, quadratic, and linear system (2×2, 3×3) solvers
Formula
Six Calculation Modes
Scientific
Full keypad, Deg/Rad, ANS recall, history
Grapher
Plot f(x), up to 3 functions simultaneously
Matrix
Add, multiply, inverse, det for up to 4×4
Statistics
Mean, SD, IQR, histogram from data list
Calculus
Derivatives f′(x), integrals ∫f(x)dx
Solver
Linear, quadratic, 2×2 and 3×3 systems
How to Use
- 1Select a mode tab: Scientific, Grapher, Matrix, Statistics, Calculus, or Solver
- 2Scientific mode: type expressions directly or use the on-screen keypad; press Enter or = to evaluate
- 3Toggle Deg/Rad for angle units; ANS recalls the last computed result
- 4Grapher: enter f(x) expressions and set axis bounds to plot curves
- 5Matrix mode: fill in the grid, optionally enter matrix B, then choose an operation
- 6Statistics: paste a comma-separated number list and click Analyze
Example Calculation
Example expressions in Scientific mode:
sin(pi/4) = 0.7071... (Rad mode)
log(1000) = 3 (log₁₀)
ln(e^5) = 5
sqrt(2)^2 = 2
(3+4i) * (1-2i) = 11-2i (complex)
ANS * 2 (uses previous result)
Calculus mode example
Enter f(x) = x³ + 2*x² − x + 5 and click Differentiate. Result: 3*x² + 4*x − 1 (symbolic first derivative). For the integral, enter bounds a=0, b=2: ∫₀² (x³+2x²−x+5) dx ≈ 18.
Understanding Advanced Scientific
Scientific Calculator Function Reference
| Function | Syntax | Example | Result |
|---|---|---|---|
| Sine | sin(x) | sin(30) [Deg] | 0.5 |
| Cosine | cos(x) | cos(pi/3) [Rad] | 0.5 |
| Natural log | ln(x) | ln(e^3) | 3 |
| Log base 10 | log(x) | log(1000) | 3 |
| Square root | sqrt(x) | sqrt(144) | 12 |
| Power | x^n | 2^10 | 1024 |
| Factorial | n! | 10! | 3628800 |
| Absolute value | abs(x) | abs(-7.5) | 7.5 |
Frequently Asked Questions
What is a CAS scientific calculator?
This calculator uses mathjs for symbolic differentiation and matrix algebra, combining CAS capabilities with high-precision numerical computation, all in the browser.
- ›Symbolic differentiation: d/dx(x³+2x²) = 3x²+4x (exact algebraic result)
- ›Numerical integration: Simpson's rule with 10,000 intervals for accuracy
- ›Matrix operations: exact results using LU decomposition
- ›Complex arithmetic: full support for imaginary and complex numbers
How do I enter mathematical expressions?
The expression parser is flexible and handles standard math notation. All on-screen buttons insert the correct syntax automatically.
- ›Multiplication: 2*x or 2x (implicit multiply also works)
- ›Powers: x^2, x^(1/3), sqrt(x)
- ›Trig: sin(30) in Deg mode, sin(pi/6) in Rad mode
- ›Logarithm: log(x) = log₁₀(x), ln(x) = natural log
Does this calculator support complex numbers?
Full complex arithmetic is supported in the Scientific mode. Results are displayed in standard a+bi form.
- ›(2+3i) + (1-i) = 3+2i
- ›(3+4i)*(1-2i) = 11-2i
- ›sqrt(-1) = i (imaginary unit)
- ›e^(pi*i) = -1 (Euler's famous identity)
How does the graphing calculator work?
The grapher samples 1,000+ points across the visible x range and draws smooth lines, handling discontinuities by detecting large jumps between adjacent points.
- ›Enter any expression in x: sin(x), x^2-4, sqrt(1-x^2)
- ›Adjust xMin/xMax/yMin/yMax to zoom or pan
- ›Different colors distinguish the three function slots
- ›Asymptotes and discontinuities are handled gracefully
What statistical functions are available?
Enter a comma-separated list of numbers and click Analyze. All descriptive statistics are computed instantly, plus a simple frequency histogram.
- ›Input format: 12, 15, 18, 22, 19, 14 (comma-separated)
- ›Population SD σ: divides by n; Sample SD s: divides by n−1
- ›IQR = Q3 − Q1 (interquartile range, robust spread measure)
- ›Histogram: auto-binned frequency chart for the data set
How are matrix operations computed?
LU decomposition decomposes a matrix into lower and upper triangular factors, enabling stable computation of inverses and linear system solutions even for near-singular matrices.
- ›Matrix A×B: standard matrix multiplication (conformability required)
- ›Inverse A⁻¹: LU decomposition, defined only for square non-singular matrices
- ›Determinant: product of diagonal elements of U in LU decomposition
- ›Transpose Aᵀ: rows and columns swapped
Does keyboard input work?
Keyboard support makes the Scientific mode as fast as a physical calculator for power users who prefer typing to clicking buttons.
- ›Enter / = : evaluate the current expression
- ›Escape: clear the current input without resetting history
- ›↑ / ↓: navigate through calculation history
- ›Type function names directly: sin(, cos(, sqrt(, log(, ln(, abs(, exp(
What built-in constants are available?
Constants are accessible by typing their names or clicking the dedicated buttons. Physics constants are dimensioned in SI units.
- ›pi = 3.14159265358979...
- ›e = 2.71828182845904...
- ›phi = 1.61803398874989... (golden ratio)
- ›c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, NA = 6.02214076×10²³ mol⁻¹
Can I solve systems of equations?
The Solver applies Gaussian elimination (equivalent to LU decomposition) for linear systems, ensuring consistent and reliable solutions for well-determined systems.
- ›Linear: ax + b = c → x = (c−b)/a
- ›Quadratic: ax²+bx+c=0 → x = [−b ± √(b²−4ac)] / 2a
- ›2×2 system: ax+by=e, cx+dy=f → solved by elimination/substitution
- ›3×3 system: three equations in three unknowns → Gaussian elimination
How accurate are the numerical results?
Double-precision arithmetic is sufficient for virtually all scientific, engineering, and educational calculations. The only limitations are inherent floating-point rounding (like 0.1+0.2 = 0.30000000000000004).
- ›15–17 significant digits for basic arithmetic
- ›Simpson's rule integrals: ~10–12 digits for smooth functions
- ›Numerical derivatives: central difference with h=0.0001 for ~8 digits
- ›Matrix operations: LU decomposition maintains accuracy for well-conditioned matrices