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A JavaScript Formula Parser

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fparser provides a Formula class that parses strings containing mathematical formulas (e.g. x*sin(PI*x/2)) into an evaluationable object. One can then provide values for all unknown variables / functions and evaluate a numeric value from the formula.

For an example application, see https://fparser.alexi.ch/.


Parses a mathematical formula from a string. Known expressions:

  • Numbers in the form [-]digits[.digits], e.g. "-133.2945"
  • simple operators: '+','-','*','/', '^' expanded in correct order
  • parentheses '(', ')' for grouping (e.g. "5*(3+2)")
  • all JavaScript Math object functions (e.g. "sin(3.14)")
  • all JavaScript Math constants like PI, E
  • the use of own functions
  • the use of single-char variables (like '2x')
  • the use of named variables (like '2*[myVar]')
  • the use of path named variables and functions (like '2*[myVar.property.innerProperty]')
  • memoization: store already evaluated results for faster re-calcs
  • use it in Web pages, as ES6 module or as NodeJS module
  • Example:


Include directly in your web page:

<!-- Within a web page: Load the fparser library: -->
<script src="dist/fparser.js"></script>
<script>const f = new Formula('x+3');</script>

Install it from npmjs.org:

# Install it using npm:
$ npm install --save fparser

Then use as ES6 module (recommended):

import Formula from 'fparser';

or use it as UMD module:

const Formula = require('fparser');

... and finally use it:

// 1. Create a Formula object instance by passing a formula string:
const fObj = new Formula('2^x');

// 2. evaluate the formula, delivering a value object for each unknown entity:
let result = fObj.evaluate({ x: 3 }); // result = 8

// or deliver multiple value objects to return multiple results:
let results = fObj.evaluate([{ x: 2 }, { x: 4 }, { x: 8 }]); // results = [4,16,256]

// You can also directly evaluate a value if you only need a one-shot result:
let result = Formula.calc('2^x', { x: 3 }); // result = 8
let results = Formula.calc('2^x', [{ x: 2 }, { x: 4 }, { x: 8 }]); // results = [4,16,256]

More options

Using multiple variables

const fObj = new Formula('a*x^2 + b*x + c');

// Just pass a value object containing a value for each unknown variable:
let result = fObj.evaluate({ a: 2, b: -1, c: 3, x: 3 }); // result = 18

Using named variables

Instead of single-char variables (like 2x+y), you can also use named variables in brackets:

const fObj = new Formula('2*[var1] + sin([var2]+PI)');

// Just pass a value object containing a value for each named variable:
let result = fObj.evaluate({ var1: 5, var2: 0.7 });

The reason for the bracket syntax is the support of shortcut multiplication of single vars, e.g. 2xy is a shorthand for 2*x*y. As the parser cannot decide if xy means "the variable named xy", or calc x*y`, we had to introduce the bracket syntax.

Using named object path variables

Named variables in brackets can also describe an object property path:

const fObj = new Formula('2*[var1.propertyA] + 3*[var2.propertyB.propertyC]');

// Just pass a value object containing a value for each named variable:
let result = fObj.evaluate({ var1: { propertyA: 3 }, var2: { propertyB: { propertyC: 9 } } });

This even works for array values: Instead of the property name, use a 0-based index in an array:

// var2.propertyB is an array, so we can use an index for the 3rd entry of propertyB:
const fObj = new Formula('2*[var1.propertyA] + 3*[var2.propertyB.2]');
let result = fObj.evaluate({ var1: { propertyA: 3 }, var2: { propertyB: [2, 4, 6] } });

Using user-defined functions

const fObj = new Formula('sin(inverse(x))');

//Define the function(s) on the Formula object, then use it multiple times:
fObj.inverse = (value) => 1/value;
let results = fObj.evaluate({x: 1,x:2,x:3});

// Or pass it in the value object, and OVERRIDE an existing function:
let result = fObj.evaluate({
	x: 2/Math.PI,
	inverse: (value) =>  (-1*value)

If defined in the value object AND on the formula object, the Value object has the precedence

Functions also support the object path syntax:

// in an evaluate() value object:
const fObj = new Formula('sin(lib.inverse(x))');
const res = fObj.evaluate({
	lib: { inverse: (value) => 1/value }

// or set it on the Formula instance:
const fObj2 = new Formula('sin(lib.inverse(x))');
fObj2.lib = { inverse: (value) => 1/value };
const res2 = fObj.evaluate();

Re-use a Formula object

You can instantiate a Formula object without formula, and set it later, and even re-use the existing object:

const fObj = new Formula();
// ...
fObj.setFormula('2*x^2 + 5*x + 3');
let res = fObj.evaluate({ x: 3 });
// ...
res = fObj.evaluate({ x: 2, y: 4 });


To avoid re-calculation of already evaluated results, the formula parser object supports memoization: it stores already evaluated results for given expression parameters.


const fObj = new Formula('x * y', { memoization: true });
let res1 = fObj.evaluate({ x: 2, y: 3 }); // 6, evaluated by calculating x*y
let res2 = fObj.evaluate({ x: 2, y: 3 }); // 6, from memory

You can enable / disable memoization on the object:

const fObj = new Formula('x * y');
let res1 = fObj.evaluate({ x: 2, y: 3 }); // 6, evaluated by calculating x*y
let res2 = fObj.evaluate({ x: 2, y: 3 }); // 6, evaluated by calculating x*y
let res3 = fObj.evaluate({ x: 2, y: 3 }); // 6, from memory

Blacklisted functions

The Formula class blacklists its internal functions like evaluate, parse etc. You cannot create a formula that calls an internal Formula function:

// Internal functions cannot be used in formulas:
const fObj = new Formula('evaluate(x)');
fObj.evaluate({ x: 5 }); // throws an Error

// This also counts for function aliases / references to internal functions:
const fObj = new Formula('ex(x)');
fObj.ex = fObj.evaluate;
fObj.evaluate({ x: 5 }); // still throws an Error: ex is an alias of evaluate

The Formula object keeps a function reference of all blacklisted functions in the Formula.functionBlacklist array.

You can get a list of all blacklisted functions:

let blacklistNames = Formula.functionBlacklist.map((f) => f.name));

Or you can check if a specific function is in the blacklist:

fObj = new Formula('x * y');
// fObj.evaluate is a Function pointer to an internal, blacklisted function:

If you want to provide your own function for a blacklisted internal function, provide it with the evaluate function:

fObj = new Formula('evaluate(x * y)');
fObj.evaluate({ x: 1, y: 2, evaluate: (x, y) => x + y });

Now, evaluate in your formula uses your own version of this function.

Get all used variables

// Get all used variables in the order of their appereance:
const f4 = new Formula('x*sin(PI*y) + y / (2-x*[var1]) + [var2]');
console.log(f4.getVariables()); // ['x','y','var1','var2']

Get the parsed formula string

After parsing, get the formula string as parsed:

// Get all used variables in the order of their appereance:
const f = new Formula('x      * (  y  +    9 )');
console.log(f.getExpressionString()); // 'x * (y + 9)'



  • [Bugfix] Fixing main entry in package.json: The 3.0.0 build could not be used as ES 6 module import with the non-existing main entry.


This is a long-wanted "migrate to typescript and modernize build infrastrucure" release. It introduces some few breaking changes, which hopefully are simple to adapt in existing code, or does not affect end users at all (I hope).

  • [Breaking]: new build system (vitejs instead of webpack)
  • [Breaking]: UMD module version available as dist/fparser.umd.js instead of dist/fparser.js: If you need the UMD version, use dist/fparser.umd.js instead of dist/fparser.js.
  • [Breaking]: An empty formula now throws an Error when parsed.
  • [Breaking]: VariableExpression class now needs Formula instance in constructor. This should not affect any end-user, but I did not test all edge cases.
  • [Change]: Migrating source code to TypeScript. This should not affect end-users.
  • [Feature]: Variables and functions now both support object paths (e.g. obj.fn(3*[obj.value]))


  • [Breaking]: Blacklisting internal functions: You cannot use internal functions as formula function anymore.
  • [Feature]: Supporting object paths as variable values (e.g. 3*[obj1.property1.innerProperty]), thanks to SamStonehouse
  • [Change]: Updated build infrastructure: upped versions of build tools


  • Fixing Issue #22: If the formula started with a single negate variable (e.g. -z*t), the parser got confused.


This release is a complete re-vamp, see below. it should be completely backward compatible to the 1.x versions, but I did not test all edge cases.

  • Switched to MIT license
  • complete refactoring of the parsing and evaluating part: The parser now creates an Expression Tree (AST) that saves extra time while evaluating - Evaluation now only traverses the AST, which is much faster.
  • added getExpressionString() function to get a formatted string from the formula
  • adding support for memoization: store already evaluated results
  • Switched bundler to webpack
  • fixed some parser bugs


  • Adding support for named variables (2x + [var1])
  • switched testing to chromium runner instead of PhantomJS


  • modernized library: The source is now ES6 code, and transpiled in a dist ES5+ library.
  • Make sure you include dist/fparser.js if you are using it as a browser library.
  • Drop support for Bower, as there are more modern approaches (npm) for package dependency nowadays


Licensed under the MIT license, see LICENSE file.

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