Many operations in Ethereum operation on numbers which are outside the range of safe values to use in JavaScript.

A **BigNumber** is an object which safely allows mathematic operations on numbers of any magnitude.

Most operations which need to return a value will return a **BigNumber** and parameters which accept values will generally accept them.

Many functions and methods in this library take in values which can be non-ambiguously and safely converted to a BigNumber. These values can be sepcified as:

*string*A HexString or a decimal string, either of which may be negative.

*BytesLike*A BytesLike Object, such as an Array or Uint8Array.

*BigNumber*An existing BigNumber instance.

*number*A number that is within the safe range for JavaScript numbers.

*BigInt*A JavaScript BigInt object, on environments that support BigInt.

The constructor of BigNumber cannot be called directly. Instead, Use the static `BigNumber.from`

.

Returns an instance of a **BigNumber** for *aBigNumberish*.

### Examples:

The BigNumber class is immutable, so no operations can change the value it represents.

Returns a BigNumber with the value of *BigNumber* **+** *otherValue*.

Returns a BigNumber with the value of *BigNumber* **-** *otherValue*.

Returns a BigNumber with the value of *BigNumber* **×** *otherValue*.

Returns a BigNumber with the value of *BigNumber* **÷** *divisor*.

Returns a BigNumber with the value of the **remainder** of *BigNumber* ÷ *divisor*.

Returns a BigNumber with the value of *BigNumber* to the power of *exponent*.

Returns a BigNumber with the value of *BigNumber* with bits beyond the *bitcount* least significant bits set to zero.

Two's Complicment is an elegant method used to encode and decode fixed-width signed values while efficiently preserving mathematic operations. Most users will not need to interact with these.

Returns a BigNumber with the value of *BigNumber* converted from twos-compliment with *bitwidth*.

Returns a BigNumber with the value of *BigNumber* converted to twos-compliment with *bitwidth*.

Returns true if and only if the value of *BigNumber* is equal to *otherValue*.

Returns true if and only if the value of *BigNumber* **<** *otherValue*.

Returns true if and only if the value of *BigNumber* **≤** *otherValue*.

Returns true if and only if the value of *BigNumber* **>** *otherValue*.

Returns true if and only if the value of *BigNumber* **≥** *otherValue*.

Returns true if and only if the value of *BigNumber* is zero.

Returns the value of *BigNumber* as a JavaScript value.

This will **throw an error** if the value is greater than or equal to *Number.MAX_SAFE_INTEGER* or less than or equal to *Number.MIN_SAFE_INTEGER*.

Returns the value of *BigNumber* as a base-10 string.

Returns the value of *BigNumber* as a base-16, `0x`

-prefixed DataHexString.

Returns true if and only if the *object* is a BigNumber object.

This section is a for a couple of questions that come up frequently.

The first problem many encounter when dealing with Ethereum is the concept of numbers. Most common currencies are broken down with very little granularity. For example, there are only 100 cents in a single dollar. However, there are 10^{18} **wei** in a single **ether**.

JavaScript uses IEEE 754 double-precision binary floating point numbers to represent numeric values. As a result, there are *holes* in the integer set after 9,007,199,254,740,991; which is problematic for *Ethereum* because that is only around 0.009 ether (in wei), which means any value over that will begin to experience rounding errors.

To demonstrate how this may be an issue in your code, consider:

To remedy this, all numbers (which can be large) are stored and manipulated as Big Numbers.

The functions parseEther( etherString ) and formatEther( wei ) can be used to convert between string representations, which are displayed to or entered by the user and Big Number representations which can have mathematical operations handled safely.

Everyone has their own favourite Big Number library, and once someone has choosen one, it becomes part of their identity, like their editor, vi vs emacs. There are over 100 Big Number libraries on npm.

One of the biggest differences between the Ethers BigNumber object and other libraries is that it is immutable, which is very important when dealing with the asynchronous nature of the blockchain.

Capturing the value is not safe in async functions, so immutability protects us from easy to make mistakes, which is not possible on the low-level library's objects which supports myriad in-place operations.

Second, the Ethers BigNumber provides all the functionality required internally and should generally be sufficient for most developers while not exposing some of the more advanced and rare functionality. So it will be eaiser to swap out the underlying library without impacting consumers.

For example, if BN.js was exposed, someone may use the greatest-common-denominator functions, which would then be functionality the replacing library should also provide to ensure anyone depending on that functionality is not broken.

The reason why BN.js is used internally as the big number is because that is the library used by elliptic.

Therefore it **must** be included regardless, so we leverage that library rather than adding another Big Number library, which would mean two different libraries offering the same functionality.

This has saved about 85kb (80% of this library size) of library size over other libraries which include separate Big Number libraries for various purposes.

Another comment that comes up frequently is tha desire to specify a global user-defined Big Number library, which all functions would return.

This becomes problematic since your code may live along side other libraries or code that use Ethers. In fact, even Ethers uses a lot of the public functions internally.

If you, for example, used a library that used `a.plus(b)`

instead of `a.add(b)`

, this would break Ethers when it tries to compute fees internally, and other libraries likely have similar logic.

But, the BigNumber prototype is exposed, so you can always add a `toMyCustomBigNumber()`

method to all BigNumber's globally which is safe.