EquaSolver

A calculator and equation solver with 37 tools, worked solutions, six languages and offline support.

Features • Getting Started • Usage • Project Structure • Testing • Contributing

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Overview

EquaSolver is a web calculator for equations, calculus, statistics, graphs and everyday conversions. It is built with vanilla JavaScript, HTML and CSS: no framework, no build step, no runtime dependency except jsPDF for PDF export. It installs as a PWA and keeps working offline.

The interface is light by default and follows the system dark mode, with one accent colour per theme, a serif display face, tabular figures for numbers, and motion that only conveys state.

Features

Calculators

Tool	What it does
Standard calculator	Arithmetic and scientific keys (sin, cos, tan, √, ln, log, eˣ, n!, π, e, x²), degrees / radians switch, memory keys (MC, MR, M+, M−), floating point noise removed from results, Ctrl+Z / Ctrl+Y undo and redo
Expression calculator	Type a whole expression such as 2 + 3 * (4 - 1)^2, sqrt(2) * pi, 5! / 3!; ans is the previous result; insert keys for functions; reusable history of the last results
Percentage	Percent of a value, change between two values, increase and decrease
Ratio & proportion	Simplifies ratios (decimals included) and solves a : b = c : x
Fractions	Simplify, add, subtract, multiply, divide, mixed numbers, decimal value

Equation solvers

• Linear, quadratic, cubic, quartic and quintic equations with real and complex roots shown as a ± bi. Multiple roots are recognised as real roots, and quadratic roots keep full precision when the coefficients differ greatly in size.
• Exact form of quadratic roots: fractions (1, 1/2), radicals ((3 ± √5) / 2) and complex values (-1 ± 2i) next to the decimal results.
• Systems of linear equations: 2×2 and 3×3 with Cramer's rule, and n × n (2 to 5) with Gaussian elimination and partial pivoting, including every row operation as a foldable list of matrices. Detects unique, infinite and impossible systems.
• Inequalities: linear, quadratic and absolute value, with interval notation.
• Absolute value equations |ax + b| = c.
• Trigonometric equations sin x = k, cos x = k, tan x = k on a chosen domain.
• Exponential and logarithmic equations: aˣ = b, a·bˣ = c, eˣ = a, log_a(x) = b, log_a(bx + c) = d, ln x = a, log x = a, with steps.
• LaTeX input: type an equation such as x^2 - 5x + 6 = 0 with live preview; terms that cancel are handled.
• Polynomial division with quotient and remainder, plus the factored form of the dividend over the rationals ((x - 1)(x - 2)(x - 3)).
• Partial fraction decomposition of P(x) / Q(x) in exact fractions, with polynomial part and repeated factors.

Algebra and number tools

• Matrices (2×2 and 3×3): addition, multiplication, determinant, inverse, transpose, trace, rank and eigenvalues (real or complex).
• GCD and LCM of several numbers with prime factorisations.
• Prime numbers: primality test (exact up to 2⁵³ with Miller-Rabin), next and previous prime, list of all primes up to 5 000 000.
• Modular arithmetic: modulo, modular inverse and exponentiation with exact big-number products.
• Combinatorics: factorial, permutations, combinations (no overflow for large n).
• Base converter: binary, octal, decimal, hexadecimal.
• Unit converter: length, mass, temperature, time, area, volume, speed, energy, pressure and digital storage (SI and binary prefixes), with a swap key.

Calculus

• Derivatives: symbolic, at a point, nth order and critical points.
• Integrals: symbolic indefinite integrals and definite integrals (Simpson's rule).
• Limits computed numerically from the left, the right or both sides, including limits at ±∞ and removable singularities such as sin(x)/x.
• Taylor series of sin, cos, eˣ, ln(1 + x) and arctan.
• Numerical integration: trapezoidal and Simpson's rules.
• Sequences: arithmetic, geometric and Fibonacci, with sums and formulas.

Statistics

• Descriptive statistics: mean, median, mode, variance, standard deviation, minimum, quartiles, interquartile range, outliers (Tukey fences) and a histogram.
• Linear regression: fitted line, slope, intercept, r, R², prediction for any x, and a scatter plot with the fitted line.

Graphs

• Function plotter: up to four y = f(x) curves on one canvas. Drag to pan, scroll or pinch to zoom, hover to read values, double-click to reset. Roots, extrema and intersections are detected and listed; curves draw themselves; export to PNG.
• 3D surface: z = f(x, y) with presets, rotate by dragging or with the arrow keys, zoom, height colouring, rise animation.
• Cartesian graph of linear, quadratic and cubic equations, parametric curves (circle, ellipse, spiral, Lissajous) and polar curves (cardioid, roses, spiral, lemniscate).

Sharing, history and export

• Shareable links: the Share button copies a link that reopens the tool with its current values and runs it. #quadratic style links also open a tool directly, and the PWA shortcuts use them.
• Copy result button under every solution.
• History of the last 50 calculations, with favorites that survive clearing.
• PDF export of solutions, graphs and plots (symbols that jsPDF cannot print are transliterated).
• Print stylesheet: only the open tool and its solution are printed.
• Tool search on the home screen, accent and case insensitive.

Interface

• Light, dark or system: follows prefers-color-scheme until you choose, with no flash on load.
• Six accent themes (Cobalt, Graphite, Emerald, Vermilion, Teal, Violet) plus a custom theme builder. Theme and mode changes cross-fade.
• Six languages: English, French, Spanish, German, Italian, Russian. A test keeps every language in sync.
• Decimal comma accepted in numeric fields.
• Keyboard: digits and operators drive the calculator, Enter or = calculates, Escape clears, Backspace deletes, arrow keys rotate the 3D surface, the settings panel traps focus and closes with Escape.
• Responsive layout and reduced-motion support.
• Progressive Web App: installable, precached by a service worker, works offline.
• Safe by design: expressions are parsed by a recursive-descent parser, never evaluated as JavaScript, and user text is escaped before it is shown.

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Getting Started

Prerequisites

• A recent browser. Current Chrome, Edge, Safari and Firefox give the full experience (view transitions, scroll-driven animation, relative colours); older browsers keep working, without the animation.
• Node.js only if you want to run the tests.

Run it

git clone https://github.com/l-at-nnes/EquaSolver.git
cd EquaSolver

Open index.html (it redirects to src/index.html), or serve the folder:

npx serve .
# or
python -m http.server 8000 --directory src

There is no build process. The service worker needs http://localhost or HTTPS to register.

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Usage

1. Pick a tool on the home screen (or type in the search box), or open index.html#plotter directly.
2. Fill the inputs; the equation preview updates as you type.
3. Press Solve / Calculate. Worked steps appear under the result.
4. Use Copy result, Export PDF, Share or print.

Examples

Tool	Input	Result
Quadratic	a = 1, b = -3, c = 1	x ≈ 2.618, 0.382; exact form (3 ± √5) / 2
Expression	2 + 3 * (4 - 1)^2	29
Limit	sin(x)/x at 0	1
Polynomial division	x^3 - 6x^2 + 11x - 6 ÷ x - 1	quotient x² - 5x + 6, factored (x - 1)(x - 2)(x - 3)
Partial fractions	3x + 5 over x^2 - x - 6	1/(5(x + 2)) + 14/(5(x - 3))
Plotter	sin(x) and x^2 / 4 - 1	curves with their intersections marked
Regression	1 2, 2 4, 3 5, 4 4, 5 5	y = 0.6x + 2.2, R² = 0.6

Keyboard shortcuts

Key	Action
0-9, ., + - * /	Calculator input (standard calculator open)
Enter, =	Calculate
Backspace	Delete the last digit
Escape	Clear the calculator / close the settings panel
Ctrl/Cmd + Z, Ctrl/Cmd + Y	Undo, redo
Arrow keys	Rotate the 3D surface when the canvas has focus

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Project Structure

EquaSolver/
|-- index.html                    # Redirect to src/index.html
|-- src/
|   |-- index.html                # The application
|   |-- manifest.json, sw.js      # PWA manifest and service worker
|   |-- assets/                   # Icons
|   |-- css/
|   |   |-- base.css              # Layers, design tokens, themes, shared controls
|   |   |-- home.css              # Hero and tool tiles
|   |   |-- calculator.css        # Tabs, keypad, history, expression calculator
|   |   |-- forms.css             # Inputs, matrices, unit swap
|   |   |-- results.css           # Solutions, steps, histogram, Gauss steps
|   |   |-- plotter.css           # Plotter, 3D surface, regression
|   |   |-- settings.css          # Settings panel and theme swatches
|   |   |-- print.css             # Print stylesheet
|   |-- js/
|       |-- script.js             # Application entry point (browser)
|       |-- index.js              # CommonJS entry point for the tests
|       |-- math/                 # complex, matrix, linear-system, gcd-lcm, primes, modular,
|       |                         # combinatorics, fractions, exact, statistics, regression, sequences
|       |-- solvers/              # inequality, absolute, trigonometric, exponential-log,
|       |                         # polynomial-division, factor, partial-fractions
|       |-- calculus/             # derivatives-integrals, limits, taylor, numerical-integration
|       |-- converters/           # base, units
|       |-- parsers/              # expression (safe parser), latex
|       |-- graphing/             # cartesian, parametric, polar, plotter, surface
|       |-- ui/                   # calculator, expression-calc, history, themes, export, clipboard,
|       |                         # router, search, motion, inputs, system-n, regression, animations, ...
|       |-- i18n/                 # en, fr, es, de, it, ru
|-- tests/
|   |-- unit/                     # Jest, 57 suites
|   |-- e2e/                      # Playwright spec
|   |-- manual/test.html          # In-browser checks
|-- docs/                         # API.md, TESTING.md
|-- TODO.md                       # Roadmap
|-- PRODUCT.md, DESIGN.md         # Product and design notes

Technology

• HTML5, CSS3, vanilla JavaScript; Canvas 2D for every plot, including the 3D surface (software projection and painter's algorithm).
• CSS: cascade layers, @property registered colours (theme changes interpolate), light-dark(), OKLCH with relative colour syntax, container queries, :has(), view transitions, scroll-driven animation, native nesting.
• jsPDF for PDF export (loaded from a CDN, cached by the service worker).
• No framework, no bundler, no web font: system font stacks only.

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Testing

npm install
npm test               # all unit tests
npm run test:watch
npm run test:coverage

1411 tests in 57 suites cover:

• the mathematics: every solver, the parser, calculus, statistics, matrices, primes, conversions, factoring and partial fractions;
• the interface logic: calculator state machine, history and favorites, themes and settings, routing and share links, search, clipboard, PDF export, graph drawing;
• a smoke test that loads the real index.html with every script in jsdom and presses all the solve buttons;
• translation parity: every language has the same keys and every key used by the page exists;
• the service worker precache list and the print stylesheet.

The Playwright spec in tests/e2e/ needs @playwright/test, which is not a dependency of the project. tests/manual/test.html runs checks in a real browser.

See docs/TESTING.md for details and docs/API.md for the function reference.

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Mathematical Methods

Problem	Method
Quadratic	Discriminant, with the numerically stable form of the quadratic formula; exact form from integer discriminant and square-free part
Cubic	Cardano with tolerances relative to the size of the roots, trigonometric form for three real roots
Quartic, quintic	Durand-Kerner iteration; tight clusters of roots are averaged so multiple roots come out real
Linear systems	Cramer's rule (2×2, 3×3); Gaussian elimination with partial pivoting (n × n)
Eigenvalues	Characteristic polynomial (trace, sum of principal minors, determinant)
Factoring	Rational root theorem with exact integer arithmetic and multiplicities
Partial fractions	Basis terms per factor power, solved as an exact rational linear system (BigInt)
Limits	One-sided sampling toward the point with Richardson extrapolation; divergence and oscillation detection
Roots and extrema on plots	Sign changes refined by bisection; poles rejected by checking the value at the converged point
Primality	Deterministic Miller-Rabin for all safe integers
Regression	Ordinary least squares on centred data
Expressions	Recursive-descent parser: unary minus, right-associative powers, implicit multiplication, constants and functions

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Contributing

Contributions are welcome. Read CONTRIBUTING.md first.

1. Fork the repository and create a branch (git checkout -b feature/YourFeature).
2. Add tests with your change and run npm test.
3. Keep translations in sync: add keys to all six files in src/js/i18n/ (a test enforces it).
4. If you add a script or stylesheet, list it in src/index.html, in the precache list of src/sw.js and bump the cache version.
5. Open a pull request.

Ideas are tracked in TODO.md.

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License

MIT. See LICENSE.

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Built with precision and attention to detail

© 2026 EquaSolver | Report Issue | Request Feature