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

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.

Load

The library is the single JavaScript file bignumber.js or ES module bignumber.mjs.

Browser

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

ES module

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

Get a minified version from a CDN:

<script src='https://cdn.jsdelivr.net/npm/bignumber.js@9.3.1/bignumber.min.js'></script>

Node.js

npm install bignumber.js

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

ES module

import BigNumber from "bignumber.js";

Deno

// @deno-types="https://raw.githubusercontent.com/mikemcl/bignumber.js/v9.3.1/bignumber.d.mts"
import BigNumber from 'https://raw.githubusercontent.com/mikemcl/bignumber.js/v9.3.1/bignumber.mjs';

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

Use

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

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 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"

Performance is better if base 10 is NOT specified for decimal values. Only specify base 10 when you want to limit the number of decimal places of the input value to the current DECIMAL_PLACES setting.

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.

Performance is better if base 10 is NOT specified, i.e. use toString() not toString(10). Only specify base 10 when you want to limit the number of decimal places of the string to the current DECIMAL_PLACES setting.

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

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/modules directory contains the test scripts for each method.

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

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.

Minify

To minify using, for example, terser

npm install -g terser

terser big.js -c -m -o big.min.js

Licence

The MIT Licence.

See LICENCE.

An arbitrary-precision Decimal type for JavaScript.

Features

• Integers and floats
• Simple but full-featured API
• Replicates many of the methods of JavaScript's Number.prototype and Math objects
• Also handles hexadecimal, binary and octal values
• Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
• No dependencies
• Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
• Comprehensive documentation and test set
• Used under the hood by math.js
• Includes a TypeScript declaration file: decimal.d.ts

The library is similar to bignumber.js, but here precision is specified in terms of significant digits rather than decimal places, and all calculations are rounded to the precision (similar to Python's decimal module) rather than just those involving division.

This library also adds the trigonometric functions, among others, and supports non-integer powers, which makes it a significantly larger library than bignumber.js and the even smaller big.js.

For a lighter version of this library without the trigonometric functions see decimal.js-light.

Load

The library is the single JavaScript file decimal.js or ES module decimal.mjs.

Browser:

<script src='path/to/decimal.js'></script>

<script type="module">
  import Decimal from './path/to/decimal.mjs';
  ...
</script>

Node.js:

npm install decimal.js

const Decimal = require('decimal.js');

import Decimal from 'decimal.js';

import {Decimal} from 'decimal.js';

Use

In all examples below, 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 constructor function, Decimal, which expects a single argument that is a number, string or Decimal instance.

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

If using values with more than a few digits, it is recommended to pass strings rather than numbers to avoid a potential loss of precision.

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

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

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

As with JavaScript numbers, strings can contain underscores as separators to improve readability.

x = new Decimal('2_147_483_647')

String values in binary, hexadecimal or octal notation are also accepted if the appropriate prefix is included.

x = new Decimal('0xff.f')            // '255.9375'
y = new Decimal('0b10101100')        // '172'
z = x.plus(y)                        // '427.9375'

z.toBinary()                         // '0b110101011.1111'
z.toBinary(13)                       // '0b1.101010111111p+8'

// Using binary exponential notation to create a Decimal with the value of `Number.MAX_VALUE`.
x = new Decimal('0b1.1111111111111111111111111111111111111111111111111111p+1023')
// '1.7976931348623157081e+308'

Decimal instances are immutable in the sense that they are not changed by their methods.

0.3 - 0.1                     // 0.19999999999999998
x = new Decimal(0.3)
x.minus(0.1)                  // '0.2'
x                             // '0.3'

The methods that return a Decimal can be chained.

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

Many method names have a shorter alias.

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

Most of the methods of JavaScript's Number.prototype and Math objects are replicated.

x = new Decimal(255.5)
x.toExponential(5)                       // '2.55500e+2'
x.toFixed(5)                             // '255.50000'
x.toPrecision(5)                         // '255.50'

Decimal.sqrt('6.98372465832e+9823')      // '8.3568682281821340204e+4911'
Decimal.pow(2, 0.0979843)                // '1.0702770511687781839'

// Using `toFixed()` to avoid exponential notation:
x = new Decimal('0.0000001')
x.toString()                             // '1e-7'
x.toFixed()                              // '0.0000001'

And there are isNaN and isFinite methods, as NaN and Infinity are valid Decimal values.

x = new Decimal(NaN)                                           // 'NaN'
y = new Decimal(Infinity)                                      // 'Infinity'
x.isNaN() && !y.isNaN() && !x.isFinite() && !y.isFinite()      // true

There is also a toFraction method with an optional maximum denominator argument.

z = new Decimal(355)
pi = z.dividedBy(113)        // '3.1415929204'
pi.toFraction()              // [ '7853982301', '2500000000' ]
pi.toFraction(1000)          // [ '355', '113' ]

All calculations are rounded according to the number of significant digits and rounding mode specified by the precision and rounding properties of the Decimal constructor.

For advanced usage, multiple Decimal constructors can be created, each with their own independent configuration which applies to all Decimal numbers created from it.

// Set the precision and rounding of the default Decimal constructor
Decimal.set({ precision: 5, rounding: 4 })

// Create another Decimal constructor, optionally passing in a configuration object
Dec = Decimal.clone({ precision: 9, rounding: 1 })

x = new Decimal(5)
y = new Dec(5)

x.div(3)                           // '1.6667'
y.div(3)                           // '1.66666666'

The value of a Decimal is stored in a floating point format in terms of its digits, exponent and sign, but these properties should be considered read-only.

x = new Decimal(-12345.67);
x.d                            // [ 12345, 6700000 ]    digits (base 10000000)
x.e                            // 4                     exponent (base 10)
x.s                            // -1                    sign

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

Test

To run the tests using Node.js from the root directory:

npm test

Each separate test module can also be executed individually, for example:

node test/modules/toFraction

To run the tests in a browser, open test/test.html.

Minify

Two minification examples:

Using uglify-js to minify the decimal.js file:

npm install uglify-js -g
uglifyjs decimal.js --source-map url=decimal.min.js.map -c -m -o decimal.min.js

Using terser to minify the ES module version, decimal.mjs:

npm install terser -g
terser decimal.mjs --source-map url=decimal.min.mjs.map -c -m --toplevel -o decimal.min.mjs

import Decimal from './decimal.min.mjs';

Licence

The MIT Licence