Mathematical expression evaluator

Usage no npm install needed!

<script type="module">
  import exprEvalStable from 'https://cdn.skypack.dev/expr-eval-stable';


JavaScript Expression Evaluator

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Parses and evaluates mathematical expressions. It's a safer and more math-oriented alternative to using JavaScript’s eval function for mathematical expressions.

It has built-in support for common math operators and functions. Additionally, you can add your own JavaScript functions. Expressions can be evaluated directly, or compiled into native JavaScript functions.


npm install expr-eval

Basic Usage

var Parser = require('expr-eval').Parser;

var parser = new Parser();
var expr = parser.parse('2 * x + 1');
console.log(expr.evaluate({ x: 3 })); // 7

// or
Parser.evaluate('6 * x', { x: 7 }) // 42



Parser is the main class in the library. It has as single parse method, and "static" methods for parsing and evaluating expressions.


Constructs a new Parser instance.

The constructor takes an optional options parameter that allows you to enable or disable operators.

For example, the following will create a Parser that does not allow comparison or logical operators, but does allow in:

var parser = new Parser({
  operators: {
    // These default to true, but are included to be explicit
    add: true,
    concatenate: true,
    conditional: true,
    divide: true,
    factorial: true,
    multiply: true,
    power: true,
    remainder: true,
    subtract: true,

    // Disable and, or, not, <, ==, !=, etc.
    logical: false,
    comparison: false,

    // Disable 'in' and = operators
    'in': false,
    assignment: false

parse(expression: string)

Convert a mathematical expression into an Expression object.

Parser.parse(expression: string)

Static equivalent of new Parser().parse(expression).

Parser.evaluate(expression: string, variables?: object)

Parse and immediately evaluate an expression using the values and functions from the variables object.

Parser.evaluate(expr, vars) is equivalent to calling Parser.parse(expr).evaluate(vars).


Parser.parse(str) returns an Expression object. Expressions are similar to JavaScript functions, i.e. they can be "called" with variables bound to passed-in values. In fact, they can even be converted into JavaScript functions.

evaluate(variables?: object)

Evaluate the expression, with variables bound to the values in {variables}. Each variable in the expression is bound to the corresponding member of the variables object. If there are unbound variables, evaluate will throw an exception.

js> expr = Parser.parse("2 ^ x");
js> expr.evaluate({ x: 3 });

substitute(variable: string, expression: Expression | string | number)

Create a new Expression with the specified variable replaced with another expression. This is similar to function composition. If expression is a string or number, it will be parsed into an Expression.

js> expr = Parser.parse("2 * x + 1");
js> expr.substitute("x", "4 * x");
js> expr2.evaluate({ x: 3 });

simplify(variables: object)

Simplify constant sub-expressions and replace variable references with literal values. This is basically a partial evaluation, that does as much of the calculation as it can with the provided variables. Function calls are not evaluated (except the built-in operator functions), since they may not be deterministic.

Simplify is pretty simple. For example, it doesn’t know that addition and multiplication are associative, so ((2*(4*x))+1) from the previous example cannot be simplified unless you provide a value for x. 2*4*x+1 can however, because it’s parsed as (((2*4)*x)+1), so the (2*4) sub-expression will be replaced with "8", resulting in ((8*x)+1).

js> expr = Parser.parse("x * (y * atan(1))").simplify({ y: 4 });
js> expr.evaluate({ x: 2 });

variables(options?: object)

Get an array of the unbound variables in the expression.

js> expr = Parser.parse("x * (y * atan(1))");
js> expr.variables();
js> expr.simplify({ y: 4 }).variables();

By default, variables will return "top-level" objects, so for example, Parser.parse(x.y.z).variables() returns ['x']. If you want to get the whole chain of object members, you can call it with { withMembers: true }. So Parser.parse(x.y.z).variables({ withMembers: true }) would return ['x.y.z'].

symbols(options?: object)

Get an array of variables, including any built-in functions used in the expression.

js> expr = Parser.parse("min(x, y, z)");
(min(x, y, z))
js> expr.symbols();
js> expr.simplify({ y: 4, z: 5 }).symbols();

Like variables, symbols accepts an option argument { withMembers: true } to include object members.


Convert the expression to a string. toString() surrounds every sub-expression with parentheses (except literal values, variables, and function calls), so it’s useful for debugging precedence errors.

toJSFunction(parameters: array | string, variables?: object)

Convert an Expression object into a callable JavaScript function. parameters is an array of parameter names, or a string, with the names separated by commas.

If the optional variables argument is provided, the expression will be simplified with variables bound to the supplied values.

js> expr = Parser.parse("x + y + z");
((x + y) + z)
js> f = expr.toJSFunction("x,y,z");
[Function] // function (x, y, z) { return x + y + z; };
js> f(1, 2, 3)
js> f = expr.toJSFunction("y,z", { x: 100 });
[Function] // function (y, z) { return 100 + y + z; };
js> f(2, 3)

Expression Syntax

The parser accepts a pretty basic grammar. It's similar to normal JavaScript expressions, but is more math-oriented. For example, the ^ operator is exponentiation, not xor.

Operator Precedence

Operator Associativity Description
(...) None Grouping
f(), x.y, a[i] Left Function call, property access, array indexing
! Left Factorial
^ Right Exponentiation
+, -, not, sqrt, etc. Right Unary prefix operators (see below for the full list)
*, /, % Left Multiplication, division, remainder
+, -, || Left Addition, subtraction, array/list concatenation
==, !=, >=, <=, >, <, in Left Equals, not equals, etc. "in" means "is the left operand included in the right array operand?"
and Left Logical AND
or Left Logical OR
x ? y : z Right Ternary conditional (if x then y else z)
= Right Variable assignment
; Left Expression separator
var parser = new Parser({
  operators: {
    'in': true,
    'assignment': true
// Now parser supports 'x in array' and 'y = 2*x' expressions

Unary operators

The parser has several built-in "functions" that are actually unary operators. The primary difference between these and functions are that they can only accept exactly one argument, and parentheses are optional. With parentheses, they have the same precedence as function calls, but without parentheses, they keep their normal precedence (just below ^). For example, sin(x)^2 is equivalent to (sin x)^2, and sin x^2 is equivalent to sin(x^2).

The unary + and - operators are an exception, and always have their normal precedence.

Operator Description
-x Negation
+x Unary plus. This converts it's operand to a number, but has no other effect.
x! Factorial (x * (x-1) * (x-2) * … * 2 * 1). gamma(x + 1) for non-integers.
abs x Absolute value (magnitude) of x
acos x Arc cosine of x (in radians)
acosh x Hyperbolic arc cosine of x (in radians)
asin x Arc sine of x (in radians)
asinh x Hyperbolic arc sine of x (in radians)
atan x Arc tangent of x (in radians)
atanh x Hyperbolic arc tangent of x (in radians)
cbrt x Cube root of x
ceil x Ceiling of x — the smallest integer that’s >= x
cos x Cosine of x (x is in radians)
cosh x Hyperbolic cosine of x (x is in radians)
exp x e^x (exponential/antilogarithm function with base e)
expm1 x e^x - 1
floor x Floor of x — the largest integer that’s <= x
length x String length of x
ln x Natural logarithm of x
log x Natural logarithm of x (synonym for ln, not base-10)
log10 x Base-10 logarithm of x
log2 x Base-2 logarithm of x
log1p x Natural logarithm of (1 + x)
not x Logical NOT operator
round x X, rounded to the nearest integer, using "grade-school rounding"
sign x Sign of x (-1, 0, or 1 for negative, zero, or positive respectively)
sin x Sine of x (x is in radians)
sinh x Hyperbolic sine of x (x is in radians)
sqrt x Square root of x. Result is NaN (Not a Number) if x is negative.
tan x Tangent of x (x is in radians)
tanh x Hyperbolic tangent of x (x is in radians)
trunc x Integral part of a X, looks like floor(x) unless for negative number

Pre-defined functions

Besides the "operator" functions, there are several pre-defined functions. You can provide your own, by binding variables to normal JavaScript functions. These are not evaluated by simplify.

Function Description
random(n) Get a random number in the range [0, n). If n is zero, or not provided, it defaults to 1.
fac(n) n! (factorial of n: "n * (n-1) * (n-2) * … * 2 * 1") Deprecated. Use the ! operator instead.
min(a,b,…) Get the smallest (minimum) number in the list.
max(a,b,…) Get the largest (maximum) number in the list.
hypot(a,b) Hypotenuse, i.e. the square root of the sum of squares of its arguments.
pyt(a, b) Alias for hypot.
pow(x, y) Equivalent to x^y. For consistency with JavaScript's Math object.
atan2(y, x) Arc tangent of x/y. i.e. the angle between (0, 0) and (x, y) in radians.
roundTo(x, n) Rounds x to n places after the decimal point.
map(f, a) Array map: Pass each element of a the function f, and return an array of the results.
fold(f, y, a) Array fold: Fold/reduce array a into a single value, y by setting y = f(y, x, index) for each element x of the array.
filter(f, a) Array filter: Return an array containing only the values from a where f(x, index) is true.
indexOf(x, a) Return the first index of string or array a matching the value x, or -1 if not found.
join(sep, a) Concatenate the elements of a, separated by sep.
if(c, a, b) Function form of c ? a : b.

Array literals

Arrays can be created by including the elements inside square [] brackets, separated by commas. For example:

[ 1, 2, 3, 2+2, 10/2, 3! ]

Function definitions

You can define functions using the syntax name(params) = expression. When it's evaluated, the name will be added to the passed in scope as a function. You can call it later in the expression, or make it available to other expressions by re-using the same scope object. Functions can support multiple parameters, separated by commas.


square(x) = x*x
add(a, b) = a + b
factorial(x) = x < 2 ? 1 : x * factorial(x - 1)

Custom JavaScript functions

If you need additional functions that aren't supported out of the box, you can easily add them in your own code. Instances of the Parser class have a property called functions that's simply an object with all the functions that are in scope. You can add, replace, or delete any of the properties to customize what's available in the expressions. For example:

var parser = new Parser();

// Add a new function
parser.functions.customAddFunction = function (arg1, arg2) {
  return arg1 + arg2;

// Remove the factorial function
delete parser.functions.fac;

parser.evaluate('customAddFunction(2, 4) == 6'); // true
//parser.evaluate('fac(3)'); // This will fail


The parser also includes a number of pre-defined constants that can be used in expressions. These are shown in the table below:

Constant Description
E The value of Math.E from your JavaScript runtime
PI The value of Math.PI from your JavaScript runtime
true Logical true value
false Logical false value

Pre-defined constants are stored in parser.consts. You can make changes to this property to customise the constants available to your expressions. For example:

var parser = new Parser();
parser.consts.R = 1.234;

console.log(parser.parse('A+B/R').toString());  // ((A + B) / 1.234)

To disable the pre-defined constants, you can replace or delete parser.consts:

var parser = new Parser();
parser.consts = {};


  1. cd to the project directory
  2. Install development dependencies: npm install
  3. Run the tests: npm test