Basic Arithmetic

Advanced Scientific Calculator

A CAS-level scientific calculator with graphing, matrices, complex numbers, derivatives, integrals, statistics, and equation solving, all in one.

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Overview

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

How it works

Advanced Scientific Calculator Formula and Method

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

Instructions

How to Use

1
Select a mode tab: Scientific, Grapher, Matrix, Statistics, Calculus, or Solver.
2
In Scientific mode: type expressions directly or use the on-screen keypad; press Enter or = to evaluate.
3
Toggle Deg/Rad for angle units. ANS recalls the last computed result in subsequent expressions.
4
In Grapher: enter f(x) expressions and set axis bounds to plot up to 3 curves simultaneously.
5
In Matrix mode: fill in the grid, optionally add a second matrix, then choose an operation.
6
In Statistics mode: paste a comma-separated number list and click Analyze for full descriptive stats.

Real example

Advanced Scientific Calculator Example

Example expressions in Scientific mode:

sin(45) = 0.7071... (Deg 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.

Guide

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

Answers

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

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