A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.

• Features
• Build
• Load
• Use
• Test
• Minify
• Licence

Features

• Integers and decimals
• Simple API but full-featured
• Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
• 8 KB minified and gzipped
• 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 has fewer configuration options than this library, and does not allow NaN or Infinity.

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.

Build

bignumber.js is the single source file, and bignumber.d.ts contains the type declarations for it. The build script, build.js, creates targeted builds in a dist directory for ES module, CommonJS, and browser usage.

To run the build script (requires Node.js ≥ 14.14.0):

npm install
npm run build
# or: node build.js

A dist directory will be created containing the following:

Load

Browser

<script src='dist/bignumber.js'></script>

or, minified from a CDN (Content Delivery Network):

<script src='https://cdn.jsdelivr.net/npm/bignumber.js@latest/dist/bignumber.min.js'></script>

ES module

<script type="module">
import BigNumber from './dist/bignumber.mjs';
// ...
</script>

or, minified from a CDN:

<script type="module">
import BigNumber from 'https://cdn.jsdelivr.net/npm/bignumber.js@latest/+esm'
// ...
</script>

Node.js

npm install bignumber.js

CommonJS

const BigNumber = require('bignumber.js');

// or, testing from a local repo:
const BigNumber = require('./dist/bignumber.cjs');

ES module

import BigNumber from 'bignumber.js';

// or
import { BigNumber } from 'bignumber.js';

// or, testing from a local repo:
import { BigNumber } from './dist/bignumber.mjs';

Deno

// @deno-types="https://raw.githubusercontent.com/MikeMcl/bignumber.js/main/dist/bignumber.d.mts"
import BigNumber from 'https://raw.githubusercontent.com/MikeMcl/bignumber.js/main/dist/bignumber.mjs';

// or
// @deno-types="https://unpkg.com/bignumber.js@latest/dist/bignumber.d.mts"
import { BigNumber } from 'https://unpkg.com/bignumber.js@latest/dist/bignumber.mjs';

Use

The library exports a single constructor function, BigNumber, which accepts a value of type Number, String, BigInt or BigNumber,

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

An error will be thrown if an invalid value is passed to the constructor.

To get the string value of a BigNumber use toString() or toFixed(). Using toFixed() prevents exponential notation being returned, no matter how large or small the value.

let x = new BigNumber('1111222233334444555566');
x.toString();                       // "1.111222233334444555566e+21"
x.toFixed();                        // "1111222233334444555566"

If the limited precision of Number values is not well understood, it is recommended to create BigNumbers from String values rather than Number values to avoid a potential loss of precision.

In all further examples below, let, 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.

// Precision loss from using numeric literals with more than 15 significant digits.
new BigNumber(1.0000000000000001)         // '1'
new BigNumber(88259496234518.57)          // '88259496234518.56'
new BigNumber(99999999999999999999)       // '100000000000000000000'

// Precision loss from using numeric literals outside the range of Number values.
new BigNumber(2e+308)                     // 'Infinity'
new BigNumber(1e-324)                     // '0'

// Precision loss from the unexpected result of arithmetic with Number values.
new BigNumber(0.7 + 0.1)                  // '0.7999999999999999'

When creating a BigNumber from a Number, note that a BigNumber is created from a Number's decimal toString() value not from its underlying binary value. If the latter is required, then pass the Number's toString(2) value and specify base 2.

new BigNumber(Number.MAX_VALUE.toString(2), 2)

BigNumbers can be created from string values in bases from 2 to 36. See ALPHABET to extend this range.

a = new BigNumber('1011', 2)        // "11"
b = new BigNumber('zz.9', 36)       // "1295.25"
c = a.plus(b)                       // "1306.25"

Explicitly passing base 10 is not recommended as it will cause the slower base conversion path to be used, which is only necessary if an unconventional ALPHABET has been specified.

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.

x.dividedBy(y).plus(z).times(9)
x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').integerValue()

Some of the longer method names have a shorter alias.

x.squareRoot().dividedBy(y).exponentiatedBy(3).isEqualTo(x.sqrt().div(y).pow(3))    // true
x.modulo(y).multipliedBy(z).eq(x.mod(y).times(z))                                   // true

As with 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

A base can be specified for toString.

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

Again, explicitly passing base 10 is not recommended as it will cause the slower base conversion path to be used, which is only necessary if an unconventional ALPHABET has been specified.

There is 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 set or config method of the BigNumber constructor.

The other arithmetic operations always give the exact result.

BigNumber.set({ DECIMAL_PLACES: 10, ROUNDING_MODE: 4 })

x = new BigNumber(2)
y = new BigNumber(3)
z = x.dividedBy(y)                        // "0.6666666667"
z.squareRoot()                            // "0.8164965809"
z.exponentiatedBy(-3)                     // "3.3749999995"
z.toString(2)                             // "0.1010101011"
z.multipliedBy(z)                         // "0.44444444448888888889"
z.multipliedBy(z).decimalPlaces(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

For advanced usage, multiple BigNumber constructors can be created, each with its own independent configuration.

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

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

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

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

To avoid having to call toString or valueOf on a BigNumber to get its value in the Node.js REPL or when using console.log use

BigNumber.prototype[require('util').inspect.custom] = BigNumber.prototype.valueOf;

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

Test

The test/methods directory contains the test scripts for each method.

The tests can be run with Node.js or a browser. The tests require the CommonJS distributable, so build before testing:

npm run build
npm test
# or: node test/test

To test a single method, use, for example

node test/methods/toFraction

For the browser, open test/test.html.

There are also some old programs in perf that still work and can be useful for testing and cross-checking results over large sets of random inputs.

TypeScript

The test/typescript directory contains TypeScript compilation tests that verify the type declarations and imports work correctly for each module format. Run them with:

npm run typecheck

Minify

To minify using, for example, terser:

npm install -g terser

Minify the browser/global bundle:

terser dist/bignumber.js -c -m -o dist/bignumber.min.js

Licence

The MIT Licence.

See LICENCE.