About

LaTeX is the standard typesetting language for mathematical notation, but it carries zero computational meaning. Pasting a LaTeX fraction into a JavaScript runtime produces a syntax error, not a number. This converter parses raw LaTeX input through a recursive-descent algorithm and emits valid JavaScript math syntax targeting the math.js evaluation engine. It handles \frac, \sqrt, \sin, \cos, \tan, \log, \ln, nth roots via \sqrt[n]{x}, and nested exponentiation via caret notation. The parser respects operator precedence and implicit multiplication rules common in mathematical writing.

Manual transcription of formulas is error-prone. A single misplaced parenthesis in a nested fraction silently corrupts every downstream calculation. This tool eliminates that risk by enforcing balanced brace matching and producing structurally correct output. Note: the converter assumes well-formed LaTeX. Ambiguous constructs like bare superscripts without bases will produce a parse error rather than a guess. Variable names are passed through verbatim. Greek letters such as π are mapped to their math.js constant equivalents.

Formulas

The converter implements a three-stage pipeline common in compiler design: Lexical Analysis, Parsing, and Code Generation.

LaTeX String → Tokenizer → Token[] → Parser → AST → Generator → JS String

Operator precedence follows standard mathematical convention, implemented via recursive descent:

Level 1 (lowest): + −
Level 2: × ÷ (explicit and implicit)
Level 3: unary − +
Level 4 (highest): ^ (right-associative)

Fraction conversion rule:

\frac{a}{b} → (a) ÷ (b)

Nth root conversion rule:

\sqrt[n]{x} → nthRoot(x, n)

Power conversion rule:

xⁿ → pow(x, n)

Implicit multiplication is inserted when a number is directly followed by a variable or opening parenthesis, or when a closing parenthesis is followed by an opening parenthesis or variable. For example, 2x becomes 2 × x.

Reference Data

LaTeX Input	JavaScript Output	Description
`\frac{a}{b}`	`(a) / (b)`	Simple fraction
`\frac{x + 1}{y - 2}`	`(x + 1) / (y - 2)`	Fraction with expressions
`\sqrt{x}`	`sqrt(x)`	Square root
`\sqrt[3]{x}`	`nthRoot(x, 3)`	Cube root (nth root)
`\sqrt[n]{x + 1}`	`nthRoot(x + 1, n)`	Nth root with variable index
`x^{2}`	`pow(x, 2)`	Exponentiation
`x^{n+1}`	`pow(x, n + 1)`	Exponent with expression
`\sin{x}`	`sin(x)`	Sine function
`\cos{\theta}`	`cos(theta)`	Cosine with Greek letter
`\tan{x}`	`tan(x)`	Tangent function
`\log{x}`	`log10(x)`	Base-10 logarithm
`\ln{x}`	`log(x)`	Natural logarithm
`\pi`	`pi`	Pi constant
`e^{x}`	`pow(e, x)`	Euler's number exponent
`2x`	`2 * x`	Implicit multiplication
`\frac{\sin{x}}{\cos{x}}`	`(sin(x)) / (cos(x))`	Nested functions in fraction
`\sqrt{x^{2} + y^{2}}`	`sqrt(pow(x, 2) + pow(y, 2))`	Pythagorean expression
`-x^{2}`	`-pow(x, 2)`	Unary minus with power
`\frac{-b + \sqrt{b^{2} - 4ac}}{2a}`	`(-b + sqrt(pow(b, 2) - 4 * a * c)) / (2 * a)`	Quadratic formula
`(a + b)(c + d)`	`(a + b) * (c + d)`	Implicit mult. with parens
`\sin^{2}{x}`	`pow(sin(x), 2)`	Squared trig function
`\left(x\right)`	`(x)`	Left/right delimiters
`3.14`	`3.14`	Decimal number passthrough
`\frac{1}{\sqrt{2}}`	`(1) / (sqrt(2))`	Fraction over square root
`x_{1}`	`x_1`	Subscripted variable
`\alpha + \beta`	`alpha + beta`	Greek letter variables

Frequently Asked Questions

The tokenizer detects adjacency patterns where multiplication is implied but not written. When a number token is immediately followed by a variable or opening parenthesis, or when a closing parenthesis precedes an opening parenthesis or variable, the parser inserts an explicit multiplication operator. So 2x becomes 2 * x and (a)(b) becomes (a) * (b). This mirrors standard mathematical notation conventions.

The parser performs strict brace counting during tokenization. If an opening brace { has no matching closing brace }, or if a command like \frac receives only one argument instead of two, the converter throws a descriptive error indicating the position in the input where the problem was detected. It will never silently produce incorrect output from malformed input.

Yes. The parser is recursive by design. Each LaTeX command argument is parsed as a complete sub-expression. This means \sqrt{\frac{a}{b}} correctly produces sqrt((a) / (b)), and arbitrarily deep nesting is handled. The AST naturally represents this tree structure, and the code generator walks it recursively to emit the correct parenthesized JavaScript.

In standard mathematical convention, \log without a specified base typically means base-10 logarithm, while \ln denotes the natural logarithm. The math.js library follows this convention: log10() for base-10 and log() for natural logarithm (base e). The converter maps \log to log10() and \ln to log() to maintain consistency with both LaTeX semantics and math.js function names.

Greek letter commands like \alpha, \beta, \theta, \omega are stripped of the backslash and output as their English name (alpha, beta, theta, omega), which math.js recognizes as variable names. Special constants \pi and e are output as pi and e respectively, which math.js maps to their numerical values (3.14159... and 2.71828...). Subscripted variables like x_{1} are output as x_1.

Yes. When the parser encounters a trigonometric function command followed by a superscript before its argument (e.g., \sin^{2}{x}), it interprets this as the function applied to the argument, then raised to the given power. The output is pow(sin(x), 2). This correctly represents the standard mathematical meaning of sin²(x).

The converter focuses on computational expressions. It does not support display-only commands like \sum, \int, \lim, \prod (summation, integration, limits, products) because these require iteration bounds that have no direct single-expression equivalent in JavaScript. It also does not support matrix environments (\begin{matrix}), text commands (\text), or spacing commands (\quad, \,). The tool will report an error if it encounters an unsupported command.