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A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic
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Merge pull request #63 from droppedoncaprica/master

Fix README's location of JS map.
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LICENCE Initial commit. Publish. Fix README's location of JS map.
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A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.

Build Status


  • Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
  • 8 KB minified and gzipped
  • Simple API but full-featured
  • Works with numbers with or without fraction digits in bases from 2 to 64 inclusive
  • Replicates the toExponential, toFixed, toPrecision and toString methods of JavaScript's Number type
  • Includes a toFraction and a correctly-rounded squareRoot method
  • Supports cryptographically-secure pseudo-random number generation
  • No dependencies
  • Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
  • Comprehensive documentation and test set


If a smaller and simpler library is required see big.js. It's less than half the size but only works with decimal numbers and only has half the methods. It also does not allow NaN or Infinity, or have the configuration options of this library.

See also decimal.js, which among other things adds support for non-integer powers, and performs all operations to a specified number of significant digits.


The library is the single JavaScript file bignumber.js (or minified, bignumber.min.js).

<script src='relative/path/to/bignumber.js'></script>

For Node.js or io.js, the library is available from the npm registry

$ npm install bignumber.js
var BigNumber = require('bignumber.js');

To load with AMD loader libraries such as requireJS:

require(['path/to/bignumber'], function(BigNumber) {  
    // Use BigNumber here in local scope. No global BigNumber.


In all examples below, var, semicolons and toString calls are not shown. If a commented-out value is in quotes it means toString has been called on the preceding expression.

The library exports a single function: BigNumber, the constructor of BigNumber instances.

It accepts a value of type number (up to 15 significant digits only), string or BigNumber object,

x = new BigNumber(123.4567)
y = BigNumber('123456.7e-3')
z = new BigNumber(x)
x.equals(y) && y.equals(z) && x.equals(z)      // true

and a base from 2 to 64 inclusive can be specified.

x = new BigNumber(1011, 2)          // "11"
y = new BigNumber('zz.9', 36)       // "1295.25"
z =                       // "1306.25"

A BigNumber is immutable in the sense that it is not changed by its methods.

0.3 - 0.1                           // 0.19999999999999998  
x = new BigNumber(0.3)
x.minus(0.1)                        // "0.2"
x                                   // "0.3"

The methods that return a BigNumber can be chained.


Many method names have a shorter alias.

x.squareRoot().dividedBy(y).toPower(3).equals(x.sqrt().div(y).pow(3))         // true
x.cmp(y.mod(z).neg()) == 1 && x.comparedTo(y.modulo(z).negated()) == 1        // true

Like JavaScript's number type, there are toExponential, toFixed and toPrecision methods

x = new BigNumber(255.5)
x.toExponential(5)                  // "2.55500e+2"
x.toFixed(5)                        // "255.50000"
x.toPrecision(5)                    // "255.50"
x.toNumber()                        // 255.5

and a base can be specified for toString.

 x.toString(16)                     // "ff.8"

There is also a toFormat method which may be useful for internationalisation

y = new BigNumber('1234567.898765')
y.toFormat(2)                       // "1,234,567.90"

The maximum number of decimal places of the result of an operation involving division (i.e. a division, square root, base conversion or negative power operation) is set using the config method of the BigNumber constructor.

The other arithmetic operations always give the exact result.

BigNumber.config({ DECIMAL_PLACES: 10, ROUNDING_MODE: 4 })
// Alternatively, BigNumber.config( 10, 4 );

x = new BigNumber(2);
y = new BigNumber(3);
z = x.div(y)                        // "0.6666666667"
z.sqrt()                            // "0.8164965809"
z.pow(-3)                           // "3.3749999995"
z.toString(2)                       // "0.1010101011"
z.times(z)                          // "0.44444444448888888889"
z.times(z).round(10)                // "0.4444444445"

There is a toFraction method with an optional maximum denominator argument

y = new BigNumber(355)
pi = y.dividedBy(113)               // "3.1415929204"
pi.toFraction()                     // [ "7853982301", "2500000000" ]
pi.toFraction(1000)                 // [ "355", "113" ]

and isNaN and isFinite methods, as NaN and Infinity are valid BigNumber values.

x = new BigNumber(NaN)                                           // "NaN"
y = new BigNumber(Infinity)                                      // "Infinity"
x.isNaN() && !y.isNaN() && !x.isFinite() && !y.isFinite()        // true

The value of a BigNumber is stored in a decimal floating point format in terms of a coefficient, exponent and sign.

x = new BigNumber(-123.456);
x.c                                 // [ 123, 45600000000000 ]  coefficient (i.e. significand)
x.e                                 // 2                        exponent
x.s                                 // -1                       sign

Multiple BigNumber constructors can be created, each with their own independent configuration which applies to all BigNumber's created from it.

// Set DECIMAL_PLACES for the original BigNumber constructor
BigNumber.config({ DECIMAL_PLACES: 10 })

// Create another BigNumber constructor, optionally passing in a configuration object
BN = BigNumber.another({ DECIMAL_PLACES: 5 })

x = new BigNumber(1)
y = new BN(1)

x.div(3)                            // '0.3333333333'
y.div(3)                            // '0.33333'

For futher information see the API reference in the doc directory.


The test directory contains the test scripts for each method.

The tests can be run with Node or a browser. For Node use

$ npm test


$ node test/every-test

To test a single method, e.g.

$ node test/toFraction

For the browser, see every-test.html and single-test.html in the test/browser directory.

bignumber-vs-number.html enables some of the methods of bignumber.js to be compared with those of JavaScript's number type.


This is version 2.x.x of the library, for version 1.x.x see the tagged releases or switch to the 'original' branch. The advantages of version 2 are that it is considerably faster for numbers with many digits and that there are a some added methods (see Change Log below). The disadvantages are more lines of code and increased code complexity, and the loss of simplicity in no longer having the coefficient of a BigNumber stored in base 10. The 'original' version will continue to be supported.


See the README in the perf directory.


For Node, if uglify-js is installed

npm install uglify-js -g


npm run build

will create bignumber.min.js.

A source map will also be created in the root directory.


Open an issue, or email





Change Log


  • 31/03/2015
  • Add bower.json. Tweak division after in-depth review.


  • 25/03/2015
  • Amend README. Remove bitcoin address.


  • 25/03/2015
  • Critical bugfix #58: division.


  • 18/02/2015
  • Amend README. Add source map.


  • 18/02/2015
  • Correct links.


  • 18/02/2015
  • Add max, min, precision, random, shift, toDigits and truncated methods.
  • Add the short-forms: add, mul, sd, sub and trunc.
  • Add an another method to enable multiple independent constructors to be created.
  • Add support for the base 2, 8 and 16 prefixes 0b, 0o and 0x.
  • Enable a rounding mode to be specified as a second parameter to toExponential, toFixed, toFormat and toPrecision.
  • Add a CRYPTO configuration property so cryptographically-secure pseudo-random number generation can be specified.
  • Add a MODULO_MODE configuration property to enable the rounding mode used by the modulo operation to be specified.
  • Add a POW_PRECISION configuration property to enable the number of significant digits calculated by the power operation to be limited.
  • Improve code quality.
  • Improve documentation.


  • 29/12/2014
  • Add dividedToIntegerBy, isInteger and toFormat methods.
  • Remove the following short-forms: isF, isZ, toE, toF, toFr, toN, toP, toS.
  • Store a BigNumber's coefficient in base 1e14, rather than base 10.
  • Add fast path for integers to BigNumber constructor.
  • Incorporate the library into the online documentation.


  • 13/11/2014
  • Add toJSON and decimalPlaces methods.


  • 08/06/2014
  • Amend README.


  • 08/05/2014
  • Add toNumber.


  • 08/11/2013
  • Ensure correct rounding of sqrt in all, rather than almost all, cases.
  • Maximum radix to 64.


  • 17/10/2013
  • Sign of zero when x < 0 and x + (-x) = 0.


  • 19/9/2013
  • Throw Error objects for stack.


  • 22/8/2013
  • Show original value in constructor error message.


  • 1/8/2013
  • Allow numbers with trailing radix point.


  • Bugfix: error messages with incorrect method name


  • 8/11/2012
  • Initial release
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