bignumber.js CONSTRUCTOR Methods Properties INSTANCE Methods Properties Zero, NaN & Infinity Errors FAQ

bignumber.js

A JavaScript library for arbitrary-precision arithmetic.

Hosted on GitHub.

API

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

CONSTRUCTOR

BigNumberBigNumber(value [, base]) ⇒ BigNumber
value
number|string|BigNumber : See RANGE for range.
A numeric value.
Legitimate values include ±0, ±Infinity and NaN.
Values of type number with more than 15 significant digits are considered invalid as calling toString or valueOf on such numbers may not result in the intended value. 
console.log( 823456789123456.3 );    // 823456789123456.2
There is no limit to the number of digits of a value of type string (other than that of JavaScript's maximum array size).
Decimal string values may be in exponential, as well as normal (fixed-point) notation. Non-decimal values must be in normal notation.
String values in hexadecimal literal form, e.g. '0xff', are invalid, and string values in octal literal form will be interpreted as decimals, e.g. '011' is interpreted as 11, not 9.
Values in any base may have fraction digits.
For bases from 10 to 36, lower and/or upper case letters can be used to represent values from 10 to 35. For bases above 36, a-z represents values from 10 to 35, A-Z from 36 to 61, and $ and _ represent 62 and 63 respectively (this can be changed by editing the DIGITS variable near the top of the source file).
base
number : integer, 2 to 64 inclusive
The base of value.
If base is omitted, or is null or undefined, base 10 is assumed.

Returns a new instance of a BigNumber object.

If a base is specified, the value is rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings. Usefully, this means the decimal places of a decimal value passed to the constructor can be limited by explicitly specifying base 10.

See Errors for the treatment of an invalid value or base. 

x = new BigNumber(9)                       // '9'
y = new BigNumber(x)                       // '9'
BigNumber(435.345)                         // 'new' is optional
new BigNumber('5032485723458348569331745.33434346346912144534543')
new BigNumber('4.321e+4')                  // '43210'
new BigNumber('-735.0918e-430')            // '-7.350918e-428'
new BigNumber(Infinity)                    // 'Infinity'
new BigNumber(NaN)                         // 'NaN'
new BigNumber('.5')                        // '0.5'
new BigNumber('+2')                        // '2'
new BigNumber(-10110100.1, 2)              // '-180.5'
new BigNumber('123412421.234324', 5)       // '607236.557696'
new BigNumber('ff.8', 16)                  // '255.5'

new BigNumber(9, 2)
// Throws 'not a base 2 number' if ERRORS is true, otherwise 'NaN'

new BigNumber(96517860459076817.4395)
// Throws 'number type has more than 15 significant digits'
// if ERRORS is true, otherwise '96517860459076820'

new BigNumber('blurgh')
// Throws 'not a number' if ERRORS is true, otherwise 'NaN'

BigNumber.config({DECIMAL_PLACES: 5})
new BigNumber(1.23456789)                  // '1.23456789'
new BigNumber(1.23456789, 10)              // '1.23457'

Methods

The BigNumber constructor has one added method, config, which configures the library-wide settings for arithmetic, formatting and errors.

configconfig([settings]) ⇒ object
Note: the settings can also be supplied as an argument list, see below.
settings
object
An object that contains some or all of the following properties:
DECIMAL_PLACES
number : integer, 0 to 1e+9 inclusive
Default value: 20
The maximum number of decimal places of the results of division, square root and base conversion operations, and power operations with negative exponents.
I.e. aside from the base conversion which may be involved with any method that accepts a base argument, the value is only relevant to the dividedBy, squareRoot and toPower methods. 
BigNumber.config({ DECIMAL_PLACES: 5 })
BigNumber.config(5)    // equivalent
ROUNDING_MODE
number : integer, 0 to 8 inclusive
Default value: 4 (ROUND_HALF_UP)
The rounding mode used in the above operations and by round, toExponential, toFixed, toFormat and toPrecision.
The modes are available as enumerated properties of the BigNumber constructor. 
BigNumber.config({ ROUNDING_MODE: 0 })
BigNumber.config(null, BigNumber.ROUND_UP)    // equivalent
EXPONENTIAL_AT
number : integer, magnitude 0 to 1e+9 inclusive, or
number[] : [ integer -1e+9 to 0 inclusive, integer 0 to 1e+9 inclusive ]
Default value: [-7, 20]
The exponent value(s) at which toString returns exponential notation.
If a single number is assigned, the value is the exponent magnitude.
If an array of two numbers is assigned then the first number is the negative exponent value at and beneath which exponential notation is used, and the second number is the positive exponent value at and above which the same.
For example, to emulate JavaScript numbers in terms of the exponent values at which they begin to use exponential notation, use [-7, 20]. 
BigNumber.config({ EXPONENTIAL_AT: 2 })
new BigNumber(12.3)         // '12.3'        e is only 1
new BigNumber(123)          // '1.23e+2'
new BigNumber(0.123)        // '0.123'       e is only -1
new BigNumber(0.0123)       // '1.23e-2'

BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
new BigNumber(123456789)    // '123456789'   e is only 8
new BigNumber(0.000000123)  // '1.23e-7'

// Almost never return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 1e+9 })

// Always return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 0 })
Regardless of the value of EXPONENTIAL_AT, the toFixed method will always return a value in normal notation and the toExponential method will always return a value in exponential form.
Calling toString with a base argument, e.g. toString(10), will also always return normal notation.
RANGE
number : integer, magnitude 1 to 1e+9 inclusive, or
number[] : [ integer -1e+9 to -1 inclusive, integer 1 to 1e+9 inclusive ]
Default value: [-1e+9, 1e+9]
The exponent value(s) beyond which overflow to Infinity and underflow to zero occurs.
If a single number is assigned, it is the maximum exponent magnitude: values wth a positive exponent of greater magnitude become Infinity and those with a negative exponent of greater magnitude become zero.
If an array of two numbers is assigned then the first number is the negative exponent limit and the second number is the positive exponent limit.
For example, to emulate JavaScript numbers in terms of the exponent values at which they become zero and Infinity, use [-324, 308]. 
BigNumber.config({ RANGE: 500 })
BigNumber.config().RANGE     // [ -500, 500 ]
new BigNumber('9.999e499')   // '9.999e+499'
new BigNumber('1e500')       // 'Infinity'
new BigNumber('1e-499')      // '1e-499'
new BigNumber('1e-500')      // '0'

BigNumber.config({ RANGE: [-3, 4] })
new BigNumber(99999)         // '99999'      e is only 4
new BigNumber(100000)        // 'Infinity'   e is 5
new BigNumber(0.001)         // '0.01'       e is only -3
new BigNumber(0.0001)        // '0'          e is -4
The largest possible magnitude of a finite BigNumber is
9.999...e+1000000000
The smallest possible magnitude of a non-zero BigNumber is
1e-1000000000
ERRORS
boolean/number : true, false, 1 or 0
Default value: true
The value that determines whether BigNumber Errors are thrown.
If ERRORS is false, this library will not throw errors.
See Errors. 
BigNumber.config({ ERRORS: false })
FORMAT
object
The FORMAT object configures the format of the string returned by the toFormat method.
The example below shows the properties of the FORMAT object that are recognised, and their default values.
Unlike when changing other settings, the values of the properties of the FORMAT object will not be checked for validity. The existing FORMAT object will simply be replaced by the object that is passed in. Note that all the properties shown below do not have to be included.
See toFormat for examples of usage. 
BigNumber.config({
    FORMAT: {
        // the decimal separator
        decimalSeparator : '.',
        // the grouping separator of the integer part
        groupSeparator : ',',
        // the primary grouping size of the integer part
        groupSize : 3,
        // the secondary grouping size of the integer part
        secondaryGroupSize : 0,
        // the grouping separator of the fraction part
        fractionGroupSeparator : ' ',
        // the grouping size of the fraction part
        fractionGroupSize : 0
    }
});


Returns an object with the above properties and their current values.

If the value to be assigned to any of the above properties is null or undefined it is ignored. See Errors for the treatment of invalid values. 

BigNumber.config({
    DECIMAL_PLACES: 40,
    ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
    EXPONENTIAL_AT: [-10, 20],
    RANGE: [-500, 500],
    ERRORS: true
});

// Alternatively but equivalently:
BigNumber.config( 40, 7, [-10, 20], 500, 1 )

obj = BigNumber.config();
obj.ERRORS       // true
obj.RANGE        // [-500, 500]

Properties

The library's enumerated rounding modes are stored as properties of the constructor.
They are not referenced internally by the library itself.

Rounding modes 0 to 6 (inclusive) are the same as those of Java's BigDecimal class.

Property Value Description
ROUND_UP 0 Rounds away from zero
ROUND_DOWN 1 Rounds towards zero
ROUND_CEIL 2 Rounds towards Infinity
ROUND_FLOOR 3 Rounds towards -Infinity
ROUND_HALF_UP 4 Rounds towards nearest neighbour.
If equidistant, rounds away from zero
ROUND_HALF_DOWN 5 Rounds towards nearest neighbour.
If equidistant, rounds towards zero
ROUND_HALF_EVEN 6 Rounds towards nearest neighbour.
If equidistant, rounds towards even neighbour
ROUND_HALF_CEIL 7 Rounds towards nearest neighbour.
If equidistant, rounds towards Infinity
ROUND_HALF_FLOOR 8 Rounds towards nearest neighbour.
If equidistant, rounds towards -Infinity 
BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })
BigNumber.config({ ROUNDING_MODE: 2 })     // equivalent

INSTANCE

Methods

The methods inherited by a BigNumber instance from its constructor's prototype object.

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

The treatment of ±0, ±Infinity and NaN is consistent with how JavaScript treats these values.

Many method names have a shorter alias.
Internally, the library always uses the shorter method names.

absoluteValue.abs() ⇒ BigNumber

Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of this BigNumber. 

x = new BigNumber(-0.8)
y = x.absoluteValue()         // '0.8'
z = y.abs()                   // '0.8'
ceil.ceil() ⇒ BigNumber

Returns a BigNumber whose value is the value of this BigNumber rounded to a whole number in the direction of Infinity. 

x = new BigNumber(1.3)
x.ceil()                      // '2'
y = new BigNumber(-1.8)
y.ceil()                      // '-1'
comparedTo.cmp(n [, base]) ⇒ number

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns  
1 If the value of this BigNumber is greater than the value of n
-1 If the value of this BigNumber is less than the value of n
0 If this BigNumber and n have the same value
null if the value of either this BigNumber or n is NaN 
x = new BigNumber(Infinity)
y = new BigNumber(5)
x.comparedTo(y)                // 1
x.comparedTo(x.minus(1))       // 0
y.cmp(NaN)                     // null
y.cmp('110', 2)                // -1
decimalPlaces.dp() ⇒ number

Return the number of decimal places of the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN. 

x = new BigNumber(123.45)
x.decimalPlaces()             // 2
y = new BigNumber('9.9e-101')
y.dp()                        // 102
dividedBy.div(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns a BigNumber whose value is the value of this BigNumber divided by n, rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings. 

x = new BigNumber(355)
y = new BigNumber(113)
x.dividedBy(y)             // '3.14159292035398230088'
x.div(5)                   // '71'
x.div(47, 16)              // '5'
dividedToIntegerBy.divToInt(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Return a BigNumber whose value is the integer part (truncating towards zero) of dividing the value of this BigNumber by n. 

x = new BigNumber(5)
y = new BigNumber(3)
x.dividedToIntegerBy(y)         // '1'
x.divToInt(0.7)                 // '7'
x.divToInt('0.f', 16)           // '5'
equals.eq(n [, base]) ⇒ boolean

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns true if the value of this BigNumber equals the value of n, otherwise returns false.
As with JavaScript, NaN does not equal NaN.
Note : This method uses the comparedTo method internally. 

0 === 1e-324                    // true
x = new BigNumber(0)
x.equals('1e-324')              // false
BigNumber(-0).eq(x)             // true  ( -0 === 0 )
BigNumber(255).eq('ff', 16)     // true

y = new BigNumber(NaN)
y.equals(NaN)                   // false
floor.floor() ⇒ BigNumber

Returns a BigNumber whose value is the value of this BigNumber rounded to a whole number in the direction of -Infinity. 

x = new BigNumber(1.8)
x.floor()                     // '1'
y = new BigNumber(-1.3)
y.floor()                     // '-2'
greaterThan.gt(n [, base]) ⇒ boolean

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns true if the value of this BigNumber is greater than the value of n, otherwise returns false.
Note : This method uses the comparedTo method internally. 

0.1 > (0.3 - 0.2)                           // true
x = new BigNumber(0.1)
x.greaterThan(BigNumber(0.3).minus(0.2))    // false
BigNumber(0).gt(x)                          // false
BigNumber(11, 3).gt(11.1, 2)                // true
greaterThanOrEqualTo.gte(n [, base]) ⇒ boolean

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns true if the value of this BigNumber is greater than or equal to the value of n, otherwise returns false.
Note : This method uses the comparedTo method internally. 

(0.3 - 0.2) >= 0.1                   // false
x = new BigNumber(0.3).minus(0.2)
x.greaterThanOrEqualTo(0.1)          // true
BigNumber(1).gte(x)                  // true
BigNumber(10, 18).gte('i', 36)       // true
isFinite.isFinite() ⇒ boolean

Returns true if the value of this BigNumber is a finite number, otherwise returns false.
The only possible non-finite values of a BigNumber are NaN, Infinity and -Infinity. 

x = new BigNumber(1)
x.isFinite()                  // true
y = new BigNumber(Infinity)
y.isFinite()                  // false

Note: The native method isFinite() can be used if n <= Number.MAX_VALUE.

isInteger.isInt() ⇒ boolean

Returns true if the value of this BigNumber is a whole number, otherwise returns false. 

x = new BigNumber(1)
x.isInteger()                 // true
y = new BigNumber(123.456)
y.isInt()                     // false
isNaN.isNaN() ⇒ boolean

Returns true if the value of this BigNumber is NaN, otherwise returns false.

x = new BigNumber(NaN)
x.isNaN()                     // true
y = new BigNumber('Infinity')
y.isNaN()                     // false

Note: The native method isNaN() can also be used.

isNegative.isNeg() ⇒ boolean

Returns true if the value of this BigNumber is negative, otherwise returns false.

x = new BigNumber(-0)
x.isNegative()                // true
y = new BigNumber(2)
y.isNeg                       // false

Note: n < 0 can be used if n <= -Number.MIN_VALUE.

isZero.isZero() ⇒ boolean

Returns true if the value of this BigNumber is zero or minus zero, otherwise returns false.

x = new BigNumber(-0)
x.isZero() && x.isNeg()        // true
y = new BigNumber(Infinity)
y.isZero()                     // false

Note: n == 0 can be used if n >= Number.MIN_VALUE.

lessThan.lt(n [, base]) ⇒ boolean

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns true if the value of this BigNumber is less than the value of n, otherwise returns false.
Note : This method uses the comparedTo method internally. 

(0.3 - 0.2) < 0.1                    // true
x = new BigNumber(0.3).minus(0.2)
x.lessThan(0.1)                      // false
BigNumber(0).lt(x)                   // true
BigNumber(11.1, 2).lt(11, 3)         // true
lessThanOrEqualTo.lte(n [, base]) ⇒ boolean

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns true if the value of this BigNumber is less than or equal to the value of n, otherwise returns false.
Note : This method uses the comparedTo method internally. 

0.1 <= (0.3 - 0.2)                                // false
x = new BigNumber(0.1)
x.lessThanOrEqualTo(BigNumber(0.3).minus(0.2))    // true
BigNumber(-1).lte(x)                              // true
BigNumber(10, 18).lte('i', 36)                    // true
minus.minus(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns a BigNumber whose value is the value of this BigNumber minus n. 

0.3 - 0.1                  // 0.19999999999999998
x = new BigNumber(0.3)
x.minus(0.1)               // '0.2'
x.minus(0.6, 20)           // '0'
modulo.mod(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns a BigNumber whose value is the value of this BigNumber modulo n, i.e. the integer remainder of dividing this BigNumber by n.

The result will have the same sign as this BigNumber, and it will match that of JavaScript's % operator (within the limits of its precision) and BigDecimal's remainder method. 

1 % 0.9                    // 0.09999999999999998
x = new BigNumber(1)
x.modulo(0.9)              // '0.1'
y = new BigNumber(33)
y.mod('a', 33)             // '3'
negated.neg() ⇒ BigNumber

Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by -1. 

x = new BigNumber(1.8)
x.negated()                   // '-1.8'
y = new BigNumber(-1.3)
y.neg()                       // '1.3'
plus.plus(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns a BigNumber whose value is the value of this BigNumber plus n. 

0.1 + 0.2                       // 0.30000000000000004
x = new BigNumber(0.1)
y = x.plus(0.2)                 // '0.3'
BigNumber(0.7).plus(x).plus(y)  // '1'
x.plus('0.1', 8)                // '0.225'
round .round([dp [, rm]]) ⇒ BigNumber

dp : number : integer, 0 to 1e+9 inclusive
rm : number : integer, 0 to 8 inclusive

Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode rm to a maximum of dp decimal places.

if dp is omitted, or is null or undefined, the return value is n rounded to a whole number.

if rm is omitted, or is null or undefined, the current ROUNDING_MODE setting is used.

See Errors for the treatment of other non-integer or out of range dp or rm values. 

x = 1234.56
Math.round(x)                             // 1235

y = new BigNumber(x)
y.round()                                 // '1235'
y.round(1)                                // '1234.6'
y.round(2)                                // '1234.56'
y.round(10)                               // '1234.56'
y.round(0, 1)                             // '1234'
y.round(0, 6)                             // '1235'
y.round(1, 1)                             // '1234.5'
y.round(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'
y                                         // '1234.56'
squareRoot.sqrt() ⇒ BigNumber

Returns a BigNumber whose value is the square root of this BigNumber, correctly rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings. 

x = new BigNumber(16)
x.squareRoot()                // '4'
y = new BigNumber(3)
y.sqrt()                      // '1.73205080756887729353'
times.times(n [, base]) ⇒ BigNumber

n : number|string|BigNumber
base : number
See constructor for further parameter details.

Returns a BigNumber whose value is the value of this BigNumber times n. 

0.6 * 3                         // 1.7999999999999998
x = new BigNumber(0.6)
y = x.times(3)                  // '1.8'
BigNumber('7e+500').times(y)    // '1.26e+501'
x.times('-a', 16)               // '-6'
toExponential.toExponential([dp]) ⇒ string

dp : number : integer, 0 to 1e+9 inclusive

Returns a string representing the value of this BigNumber in exponential notation to the specified decimal places, i.e with one digit before the decimal point and dp digits after it. If rounding is necessary, the current ROUNDING_MODE is used.

If the value of this BigNumber in exponential notation has fewer fraction digits then is specified by dp, the return value will be appended with zeros accordingly.

If dp is omitted, or is null or undefined, the number of digits after the decimal point defaults to the minimum number of digits necessary to represent the value exactly.

See Errors for the treatment of other non-integer or out of range dp values. 

x = 45.6
y = new BigNumber(x)
x.toExponential()         // '4.56e+1'
y.toExponential()         // '4.56e+1'
x.toExponential(0)        // '5e+1'
y.toExponential(0)        // '5e+1'
x.toExponential(1)        // '4.6e+1'
y.toExponential(1)        // '4.6e+1'
x.toExponential(3)        // '4.560e+1'
y.toExponential(3)        // '4.560e+1'
toFixed.toFixed([dp]) ⇒ string

dp : number : integer, 0 to 1e+9 inclusive

Returns a string representing the value of this BigNumber in normal notation to the specified fixed number of decimal places, i.e. with dp digits after the decimal point. If rounding is necessary, the current ROUNDING_MODE setting is used.

If the value of this BigNumber in normal notation has fewer fraction digits then is specified by dp, the return value will be appended with zeros accordingly.

Unlike Number.prototype.toFixed, which returns exponential notation if a number is greater or equal to 1021, this method will always return normal notation.

If dp is omitted, or is null or undefined, then the return value is the same as n.toString(). This is also unlike Number.prototype.toFixed, which returns the value to zero decimal places.

See Errors for the treatment of other non-integer or out of range dp values. 

x = 45.6
y = new BigNumber(x)
x.toFixed()              // '46'
y.toFixed()              // '45.6'
y.toFixed(0)             // '46'
x.toFixed(3)             // '45.600'
y.toFixed(3)             // '45.600'
toFormat.toFormat([dp]) ⇒ string

dp : number : integer, 0 to 1e+9 inclusive

Returns a string representing the value of this BigNumber in normal notation rounded to dp decimal places using the current ROUNDING_MODE, and formatted according to the properties of the FORMAT object.

See the examples below for the properties of the FORMAT object, their types and their usage.

If dp is omitted or is null or undefined, then the return value is not rounded to a fixed number of decimal places. 

format = {
    decimalSeparator: '.',
    groupSeparator: ',',
    groupSize: 3,
    secondaryGroupSize: 0,
    fractionGroupSeparator: ' ',
    fractionGroupSize: 0
}
BigNumber.config({ FORMAT: format })

x = new BigNumber('123456789.123456789')
x.toFormat()             // '123,456,789.123456789'
x.toFormat(1)            // '123,456,789.1'

// If a reference to the object assigned to FORMAT has been retained,
// the format properties can be changed directly
format.groupSeparator = ' '
format.fractionGroupSize = 5
x.toFormat()             // '123 456 789.12345 6789'

BigNumber.config({
    FORMAT: {
        decimalSeparator = ',',
        groupSeparator = '.',
        groupSize = 3,
        secondaryGroupSize = 2
    }
})

x.toFormat(6)             // '12.34.56.789,123'
toFraction.toFraction([max_denominator]) ⇒ [string, string]

max_denominator : number|string|BigNumber : integer >= 1 and < Infinity

Returns a string array representing the value of this BigNumber as a simple fraction with an integer numerator and an integer denominator. The denominator will be a positive non-zero value less than or equal to max_denominator.

If a maximum denominator is not specified, or is null or undefined, the denominator will be the lowest value necessary to represent the number exactly.

See Errors for the treatment of other non-integer or out of range max_denominator values. 

x = new BigNumber(1.75)
x.toFraction()            // '7, 4'

pi = new BigNumber('3.14159265358')
pi.toFraction()                 // '157079632679,50000000000'
pi.toFraction(100000)           // '312689, 99532'
pi.toFraction(10000)            // '355, 113'
pi.toFraction(100)              // '311, 99'
pi.toFraction(10)               // '22, 7'
pi.toFraction(1)                // '3, 1'
toJSON.toJSON() ⇒ string

As toString. 

x = new BigNumber('123.4e+567')
str = JSON.stringify(x)
toNumber.toNumber() ⇒ number

Returns the value of this BigNumber as a number primitive.

Type coercion with, for example, JavaScript's unary plus operator can alternatively be used, but then a BigNumber with the value minus zero will convert to positive zero. 

x = new BigNumber(456.789)
x.toNumber()                   // 456.789
+x                             // 456.789

y = new BigNumber('45987349857634085409857349856430985')
y.toNumber()                   // 4.598734985763409e+34

z = new BigNumber(-0)
1 / +z                         // Infinity
1 / z.toNumber()               // -Infinity
toPower.pow(n) ⇒ BigNumber

n : number : integer, -1e+6 to 1e+6 inclusive

Returns a BigNumber whose value is the value of this BigNumber raised to the power n.

If n is negative the result is rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings.

If n is not an integer or is out of range:

If ERRORS is true a BigNumber Error is thrown,
else if n is greater than 1e+6, it is interpreted as Infinity;
else if n is less than -1e+6, it is interpreted as -Infinity;
else if n is otherwise a number, it is truncated to an integer;
else it is interpreted as NaN.

Note: High value exponents may cause this method to be slow to return. 

Math.pow(0.7, 2)             // 0.48999999999999994
x = new BigNumber(0.7)
x.toPower(2)                 // '0.49'
BigNumber(3).pow(-2)         // '0.11111111111111111111'

new BigNumber(2).toPower(100000).toString().length    // 30111
toPrecision.toPrecision([sd]) ⇒ string

sd : number : integer, 1 to 1e+9 inclusive

Returns a string representing the value of this BigNumber to sd significant digits. If rounding is necessary, the current ROUNDING_MODE setting is used.

If sd is less than the number of digits necessary to represent the integer part of the value in normal notation, then exponential notation is used.

If sd is omitted, or is null or undefined, then the return value is the same as n.toString().

See Errors for the treatment of other non-integer or out of range sd values. 

x = 45.6
y = new BigNumber(x)
x.toPrecision()           // '45.6'
y.toPrecision()           // '45.6'
x.toPrecision(1)          // '5e+1'
y.toPrecision(1)          // '5e+1'
x.toPrecision(5)          // '45.600'
y.toPrecision(5)          // '45.600'
toString.toString([base]) ⇒ string

base : number : integer, 2 to 64 inclusive

Returns a string representing the value of this BigNumber in the specified base, or base 10 if base is omitted. For bases above 10, values from 10 to 35 are represented by a-z (as with Number.toString), 36 to 61 by A-Z, and 62 and 63 by $ and _ respectively.

If a base is specified the value is rounded according to the current DECIMAL_PLACES and ROUNDING_MODE settings.

If a base is not specified, and this BigNumber has a positive exponent that is equal to or greater than the positive component of the current EXPONENTIAL_AT setting, or a negative exponent equal to or less than the negative component of the setting, then exponential notation is returned.

If base is null or undefined it is ignored.
See Errors for the treatment of other non-integer or out of range base values. 

x = new BigNumber(750000)
x.toString()                    // '750000'
BigNumber.config({ EXPONENTIAL_AT: 5 })
x.toString()                    // '7.5e+5'

y = new BigNumber(362.875)
y.toString(2)                   // '101101010.111'
y.toString(9)                   // '442.77777777777777777778'
y.toString(32)                  // 'ba.s'

BigNumber.config({ DECIMAL_PLACES: 4 });
z = new BigNumber('1.23456789')
z.toString()                    // '1.23456789'
z.toString(10)                  // '1.2346'
valueOf.valueOf() ⇒ string

As toString, but does not accept a base argument. 

x = new BigNumber('1.777e+457')
x.valueOf()                      // '1.777e+457'

Properties

A BigNumber is an object with three properties:

Property Description Type Value
c coefficient* number[] Array of base 1e14 numbers
e exponent number Integer, -1e9 to 1e9 inclusive
s sign number -1 or 1

*significand

The value of any of the three properties may also be null.

From version 2 of this library, the value of the coefficient of a BigNumber is stored in a normalised base 100000000000000 floating point format, as opposed to the base 10 format used in version 1.

This change means the properties of a BigNumber are now best considered to be read-only. Previously it was acceptable to change the exponent of a BigNumber by writing to its exponent property directly, but this is no longer recommended as the number of digits in the first element of the coefficient array is dependent on the exponent, so the coefficient would also need to be altered.

Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are not preserved. 

x = new BigNumber(0.123)              // '0.123'
x.toExponential()                     // '1.23e-1'
x.c                                   // '1,2,3'
x.e                                   // -1
x.s                                   // 1

y = new Number(-123.4567000e+2)       // '-12345.67'
y.toExponential()                     // '-1.234567e+4'
z = new BigNumber('-123.4567000e+2')  // '-12345.67'
z.toExponential()                     // '-1.234567e+4'
z.c                                   // '1,2,3,4,5,6,7'
z.e                                   // 4
z.s                                   // -1

Zero, NaN and Infinity

The table below shows how ±0, NaN and ±Infinity are stored.

c e s
±0 [0] 0 ±1
NaN null null null
±Infinity null null ±1 
x = new Number(-0)      // 0
1 / x == -Infinity     // true

y = new BigNumber(-0)   // '0'
y.c                     // '0' ( [0].toString() )
y.e                     // 0
y.s                     // -1

Errors

The errors that are thrown are generic Error objects with name BigNumber Error. The table below shows the errors that may be thrown if ERRORS is true, and the action taken if ERRORS is false.

Method(s) ERRORS: true
Throw BigNumber Error		 ERRORS: false
Action on invalid argument
BigNumber
comparedTo
dividedBy
dividedToIntegerBy
equals
greaterThan
greaterThanOrEqualTo
lessThan
lessThanOrEqualTo
minus
mod
plus
times		 number type has more than
15 significant digits		 Accept.
not a base... number Substitute NaN.
base not an integer Truncate to integer.
Ignore if not a number.
base out of range Ignore.
not a number* Substitute NaN.
config DECIMAL_PLACES not an integer Truncate to integer.
Ignore if not a number.
DECIMAL_PLACES out of range Ignore.
ROUNDING_MODE not an integer Truncate to integer.
Ignore if not a number.
ROUNDING_MODE out of range Ignore.
EXPONENTIAL_AT not an integer
or not [integer, integer] 		Truncate to integer(s).
Ignore if not number(s).
EXPONENTIAL_AT out of range
or not [negative, positive] 		Ignore.
RANGE not a non-zero integer
or not [integer, integer] 		Truncate to integer(s).
Ignore if zero or not number(s).
RANGE out of range
or not [negative, positive] 		Ignore.
ERRORS not a boolean
or binary digit 		Ignore.
FORMAT not an object Ignore.
toPower exponent not an integer Truncate to integer.
Substitute NaN if not a number.
exponent out of range Substitute ±Infinity.
round decimal places not an integer Truncate to integer.
Ignore if not a number.
decimal places out of range Ignore.
mode not an integer Truncate to integer.
Ignore if not a number.
mode out of range Ignore.
toExponential
toFixed
toFormat 		decimal places not an integer Truncate to integer.
Ignore if not a number.
decimal places out of range Ignore.
toFraction max denominator not an integer Truncate to integer.
Ignore if not a number.
max denominator out of range Ignore.
toPrecision precision not an integer Truncate to integer.
Ignore if not a number.
precision out of range Ignore.
toString base not an integer Truncate to integer.
Ignore if not a number.
base out of range Ignore.

*No error is thrown if the value is NaN or 'NaN'

The message of a BigNumber Error will also contain the name of the method from which the error originated.

To determine if an exception is a BigNumber Error: 

try {
    // ...
} catch (e) {
    if ( e instanceof Error && e.name == 'BigNumber Error' ) {
        // ...
    }
}

FAQ

Why are trailing fractional zeros removed from BigNumbers?

Many arbitrary-precision libraries retain trailing fractional zeros as they can indicate the precision of a value. This can be useful but the results of arithmetic operations can be misleading. 

x = new BigDecimal("1.0")
y = new BigDecimal("1.1000")
z = x.add(y)                      // 2.1000

x = new BigDecimal("1.20")
y = new BigDecimal("3.45000")
z = x.multiply(y)                 // 4.1400000

To specify the precision of a value is to specify that the value lies within a certain range.

In the first example, x has a value of 1.0. The trailing zero shows the precision of the value, implying that it is in the range 0.95 to 1.05. Similarly, the precision indicated by the trailing zeros of y indicates that the value is in the range 1.09995 to 1.10005. If we add the two lowest values in the ranges we get 0.95 + 1.09995 = 2.04995 and if we add the two highest values we get 1.05 + 1.10005 = 2.15005, so the range of the result of the addition implied by the precision of its operands is 2.04995 to 2.15005. The result given by BigDecimal of 2.1000 however, indicates that the value is in the range 2.09995 to 2.10005 and therefore the precision implied by its trailing zeros is misleading.

In the second example, the true range is 4.122744 to 4.157256 yet the BigDecimal answer of 4.1400000 indicates a range of 4.13999995 to 4.14000005. Again, the precision implied by the trailing zeros is misleading.

This library, like binary floating point and most calculators, does not retain trailing fractional zeros. Instead, the toExponential, toFixed and toPrecision methods enable trailing zeros to be added if and when required.