A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.
[](https://www.npmjs.com/package/bignumber.js)
[](https://www.npmjs.com/package/bignumber.js)
## 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](http://mikemcl.github.io/bignumber.js/) and test set
If a smaller and simpler library is required see [big.js](https://github.com/MikeMcl/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](https://github.com/MikeMcl/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
```html
```
> ES module
```html
```
### [Node.js](http://nodejs.org)
```bash
npm install bignumber.js
```
```javascript
const BigNumber = require('bignumber.js');
```
> ES module
```javascript
import BigNumber from "bignumber.js";
import { BigNumber } from "./node_modules/bignumber.js/bignumber.mjs";
```
### [Deno](https://deno.land/)
```javascript
import BigNumber from 'https://raw.githubusercontent.com/mikemcl/bignumber.js/v9.1.0/bignumber.mjs';
import BigNumber from 'https://unpkg.com/bignumber.js@latest/bignumber.mjs';
```
## Use
The library exports a single constructor function, [`BigNumber`](http://mikemcl.github.io/bignumber.js/#bignumber), which accepts a value of type Number, String or BigNumber,
```javascript
let x = new BigDecimal(123.4567);
let y = BigDecimal('123456.7e-3');
let z = new BigDecimal(x);
x.isEqualTo(y) && y.isEqualTo(z) && x.isEqualTo(z); // true
```
To get the string value of a BigNumber use [`toString()`](http://mikemcl.github.io/bignumber.js/#toS) or [`toFixed()`](http://mikemcl.github.io/bignumber.js/#toFix). Using `toFixed()` prevents exponential notation being returned, no matter how large or small the value.
```javascript
let x = new BigDecimal('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.*
```javascript
// Precision loss from using numeric literals with more than 15 significant digits.
new BigDecimal(1.0000000000000001) // '1'
new BigDecimal(88259496234518.57) // '88259496234518.56'
new BigDecimal(99999999999999999999) // '100000000000000000000'
// Precision loss from using numeric literals outside the range of Number values.
new BigDecimal(2e+308) // 'Infinity'
new BigDecimal(1e-324) // '0'
// Precision loss from the unexpected result of arithmetic with Number values.
new BigDecimal(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.
```javascript
new BigDecimal(Number.MAX_VALUE.toString(2), 2)
```
BigNumbers can be created from values in bases from 2 to 36. See [`ALPHABET`](http://mikemcl.github.io/bignumber.js/#alphabet) to extend this range.
```javascript
a = new BigDecimal(1011, 2) // "11"
b = new BigDecimal('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`](http://mikemcl.github.io/bignumber.js/#decimal-places) setting.*
A BigNumber is immutable in the sense that it is not changed by its methods.
```javascript
0.3 - 0.1 // 0.19999999999999998
x = new BigDecimal(0.3)
x.minus(0.1) // "0.2"
x // "0.3"
```
The methods that return a BigNumber can be chained.
```javascript
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.
```javascript
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`](http://mikemcl.github.io/bignumber.js/#toE), [`toFixed`](http://mikemcl.github.io/bignumber.js/#toFix) and [`toPrecision`](http://mikemcl.github.io/bignumber.js/#toP) methods.
```javascript
x = new BigDecimal(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`](http://mikemcl.github.io/bignumber.js/#toS).
*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`](http://mikemcl.github.io/bignumber.js/#decimal-places) setting.*
```javascript
x.toString(16) // "ff.8"
```
There is a [`toFormat`](http://mikemcl.github.io/bignumber.js/#toFor) method which may be useful for internationalisation.
```javascript
y = new BigDecimal('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.
```javascript
BigDecimal.set({DECIMAL_PLACES: 10, ROUNDING_MODE: 4})
x = new BigDecimal(2)
y = new BigDecimal(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`](http://mikemcl.github.io/bignumber.js/#toFr) method with an optional *maximum denominator* argument
```javascript
y = new BigDecimal(355)
pi = y.dividedBy(113) // "3.1415929204"
pi.toFraction() // [ "7853982301", "2500000000" ]
pi.toFraction(1000) // [ "355", "113" ]
```
and [`isNaN`](http://mikemcl.github.io/bignumber.js/#isNaN) and [`isFinite`](http://mikemcl.github.io/bignumber.js/#isF) methods, as `NaN` and `Infinity` are valid `BigNumber` values.
```javascript
x = new BigDecimal(NaN) // "NaN"
y = new BigDecimal(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.
```javascript
x = new BigDecimal(-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.
```javascript
// Set DECIMAL_PLACES for the original BigNumber constructor
BigDecimal.set({DECIMAL_PLACES: 10})
// Create another BigNumber constructor, optionally passing in a configuration object
BN = BigDecimal.clone({DECIMAL_PLACES: 5})
x = new BigDecimal(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
```javascript
BigDecimal.prototype[require('util').inspect.custom] = BigDecimal.prototype.valueOf;
```
For further information see the [API](http://mikemcl.github.io/bignumber.js/) 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
```bash
npm test
```
or
```bash
node test/test
```
To test a single method, use, for example
```bash
node test/methods/toFraction
```
For the browser, open *test/test.html*.
## Minify
To minify using, for example, [terser](https://github.com/terser/terser)
```bash
npm install -g terser
```
```bash
terser big.js -c -m -o big.min.js
```
## Licence
The MIT Licence.
See [LICENCE](https://github.com/MikeMcl/bignumber.js/blob/master/LICENCE).