bignumber.js

A JavaScript library for arbitrary-precision arithmetic.

Hosted on GitHub.

The library is incorporated into this page, so it should be available in the console now.

API

See the README on GitHub for a quick-start introduction.

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 (if ERRORS is true) 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 valid, as are string values with the octal and binary prefixs '0o' and '0b'. String values in octal literal form without the prefix 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 ALPHABET 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 configuration.

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

x = new BigNumber(9)                       // '9'
y = new BigNumber(x)                       // '9'

// 'new' is optional if ERRORS is false
BigNumber(435.345)                         // '435.345'

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(-0b10110100.1)               // '-180.5'
new BigNumber('123412421.234324', 5)       // '607236.557696'
new BigNumber('ff.8', 16)                  // '255.5'
new BigNumber('0xff.8')                    // '255.5'

The following throws 'not a base 2 number' if ERRORS is true, otherwise it returns a BigNumber with value NaN.

new BigNumber(9, 2)

The following throws 'number type has more than 15 significant digits' if ERRORS is true, otherwise it returns a BigNumber with value 96517860459076820.

new BigNumber(96517860459076817.4395)

The following throws 'not a number' if ERRORS is true, otherwise it returns a BigNumber with value NaN.

new BigNumber('blurgh')

A value is only rounded by the constructor if a base is specified.

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

Methods

The static methods of a BigNumber constructor.

another.another([obj]) ⇒ BigNumber constructor

obj: object

Returns a new independent BigNumber constructor with configuration as described by obj (see config), or with the default configuration if obj is null or undefined.

BigNumber.config({ DECIMAL_PLACES: 5 })
BN = BigNumber.another({ DECIMAL_PLACES: 9 })

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

x.div(3)                        // 0.33333
y.div(3)                        // 0.333333333

// BN = BigNumber.another({ DECIMAL_PLACES: 9 }) is equivalent to:
BN = BigNumber.another()
BN.config({ DECIMAL_PLACES: 9 })
configset([obj]) ⇒ object

obj: object: an object that contains some or all of the following properties.

Configures the settings for this particular BigNumber constructor.

Note: the configuration can also be supplied as an argument list, see below.

DECIMAL_PLACES
number: integer, 0 to 1e+9 inclusive
Default value: 20
The maximum number of decimal places of the results of operations involving division, i.e. division, square root and base conversion operations, and power operations with negative exponents.
BigNumber.config({ DECIMAL_PLACES: 5 })
BigNumber.set({ DECIMAL_PLACES: 5 })    // equivalent
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 the default rounding mode of 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, 0 or 1.
Default value: true
The value that determines whether BigNumber Errors are thrown.
If ERRORS is false, no errors will be thrown.
See Errors.
BigNumber.config({ ERRORS: false })
CRYPTO
boolean|number: true, false, 0 or 1.
Default value: false
The value that determines whether cryptographically-secure pseudo-random number generation is used.
If CRYPTO is set to true then the random method will generate random digits using crypto.getRandomValues in browsers that support it, or crypto.randomBytes if using a version of Node.js that supports it.
If neither function is supported by the host environment then attempting to set CRYPTO to true will fail, and if ERRORS is true an exception will be thrown.
If CRYPTO is false then the source of randomness used will be Math.random (which is assumed to generate at least 30 bits of randomness).
See random.
BigNumber.config({ CRYPTO: true })
BigNumber.config().CRYPTO       // true
BigNumber.random()              // 0.54340758610486147524
MODULO_MODE
number: integer, 0 to 9 inclusive
Default value: 1 (ROUND_DOWN)
The modulo mode used when calculating the modulus: a mod n.
The quotient, q = a / n, is calculated according to the ROUNDING_MODE that corresponds to the chosen MODULO_MODE.
The remainder, r, is calculated as: r = a - n * q.
The modes that are most commonly used for the modulus/remainder operation are shown in the following table. Although the other rounding modes can be used, they may not give useful results.
PropertyValueDescription
ROUND_UP0 The remainder is positive if the dividend is negative, otherwise it is negative.
ROUND_DOWN1 The remainder has the same sign as the dividend.
This uses 'truncating division' and matches the behaviour of JavaScript's remainder operator %.
ROUND_FLOOR3 The remainder has the same sign as the divisor.
This matches Python's % operator.
ROUND_HALF_EVEN6 The IEEE 754 remainder function.
EUCLID9 The remainder is always positive. Euclidian division:
q = sign(n) * floor(a / abs(n))
The rounding/modulo modes are available as enumerated properties of the BigNumber constructor.
See modulo.
BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
BigNumber.config({ MODULO_MODE: 9 })          // equivalent
POW_PRECISION
number: integer, 0 to 1e+9 inclusive.
Default value: 0
The maximum number of significant digits of the result of the power operation (unless a modulus is specified).
If set to 0, the number of signifcant digits will not be limited.
See toPower.
BigNumber.config({ POW_PRECISION: 100 })
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 the other configuration properties, 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,
    CRYPTO: true,
    MODULO_MODE: BigNumber.ROUND_FLOOR,
    POW_PRECISION: 80,
    FORMAT: {
        groupSize: 3,
        groupSeparator: ' ',
        decimalSeparator: ','
    }
});

// Alternatively but equivalently (excluding FORMAT):
BigNumber.config( 40, 7, [-10, 20], 500, 1, 1, 3, 80 )

obj = BigNumber.config();
obj.ERRORS       // true
obj.RANGE        // [-500, 500]
max.max([arg1 [, arg2, ...]]) ⇒ BigNumber

arg1, arg2, ...: number|string|BigNumber
See BigNumber for further parameter details.

Returns a BigNumber whose value is the maximum of arg1, arg2,... .

The argument to this method can also be an array of values.

The return value is always exact and unrounded.

x = new BigNumber('3257869345.0378653')
BigNumber.max(4e9, x, '123456789.9')          // '4000000000'

arr = [12, '13', new BigNumber(14)]
BigNumber.max(arr)                            // '14'
min.min([arg1 [, arg2, ...]]) ⇒ BigNumber

arg1, arg2, ...: number|string|BigNumber
See BigNumber for further parameter details.

Returns a BigNumber whose value is the minimum of arg1, arg2,... .

The argument to this method can also be an array of values.

The return value is always exact and unrounded.

x = new BigNumber('3257869345.0378653')
BigNumber.min(4e9, x, '123456789.9')          // '123456789.9'

arr = [2, new BigNumber(-14), '-15.9999', -12]
BigNumber.min(arr)                            // '-15.9999'
random.random([dp]) ⇒ BigNumber

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

Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and less than 1.

The return value will have dp decimal places (or less if trailing zeros are produced).
If dp is omitted then the number of decimal places will default to the current DECIMAL_PLACES setting.

Depending on the value of this BigNumber constructor's CRYPTO setting and the support for the crypto object in the host environment, the random digits of the return value are generated by either Math.random (fastest), crypto.getRandomValues (Web Cryptography API in recent browsers) or crypto.randomBytes (Node.js).

If CRYPTO is true, i.e. one of the crypto methods is to be used, the value of a returned BigNumber should be cryptographically-secure and statistically indistinguishable from a random value.

BigNumber.config({ DECIMAL_PLACES: 10 })
BigNumber.random()              // '0.4117936847'
BigNumber.random(20)            // '0.78193327636914089009'

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 the value of this BigNumber.

The return value is always exact and unrounded.

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 positive 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 BigNumber 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 BigNumber 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 configuration.

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 BigNumber for further parameter details.

Return a BigNumber whose value is the integer part 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 BigNumber 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 negative 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 BigNumber 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 BigNumber 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 BigNumber 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 BigNumber 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 BigNumber for further parameter details.

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

The return value is always exact and unrounded.

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 BigNumber 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 value returned, and in particular its sign, is dependent on the value of the MODULO_MODE setting of this BigNumber constructor. If it is 1 (default value), the result will have the same sign as this BigNumber, and it will match that of Javascript's % operator (within the limits of double precision) and BigDecimal's remainder method.

The return value is always exact and unrounded.

See MODULO_MODE for a description of the other modulo modes.

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 BigNumber for further parameter details.

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

The return value is always exact and unrounded.

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'
precision.sd([z]) ⇒ number

z: boolean|number: true, false, 0 or 1

Returns the number of significant digits of the value of this BigNumber.

If z is true or 1 then any trailing zeros of the integer part of a number are counted as significant digits, otherwise they are not.

x = new BigNumber(1.234)
x.precision()                   // 4
y = new BigNumber(987000)
y.sd()                          // 3
y.sd(true)                      // 6
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, ROUNDING_MODE 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'
shift.shift(n) ⇒ BigNumber

n: number: integer, -9007199254740991 to 9007199254740991 inclusive

Returns a BigNumber whose value is the value of this BigNumber shifted n places.

The shift is of the decimal point, i.e. of powers of ten, and is to the left if n is negative or to the right if n is positive.

The return value is always exact and unrounded.

x = new BigNumber(1.23)
x.shift(3)                      // '1230'
x.shift(-3)                     // '0.00123'
squareRoot.sqrt() ⇒ BigNumber

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

The return value will be correctly rounded, i.e. rounded as if the result was first calculated to an infinite number of correct digits before rounding.

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 BigNumber for further parameter details.

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

The return value is always exact and unrounded.

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'
toDigits.toDigits([sd [, rm]]) ⇒ BigNumber

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

Returns a BigNumber whose value is the value of this BigNumber rounded to sd significant digits using rounding mode rm.

If sd is omitted or is null or undefined, the return value will not be rounded.
If rm is omitted or is null or undefined, ROUNDING_MODE will be used.

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

BigNumber.config({ precision: 5, rounding: 4 })
x = new BigNumber(9876.54321)

x.toDigits()                          // '9876.5'
x.toDigits(6)                         // '9876.54'
x.toDigits(6, BigNumber.ROUND_UP)     // '9876.55'
x.toDigits(2)                         // '9900'
x.toDigits(2, 1)                      // '9800'
x                                     // '9876.54321'
toExponential.toExponential([dp [, rm]]) ⇒ string

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

Returns a string representing the value of this BigNumber in exponential notation rounded using rounding mode rm to dp decimal places, i.e with one digit before the decimal point and dp digits after it.

If the value of this BigNumber in exponential notation has fewer than dp fraction digits, 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.
If rm is omitted or is null or undefined, ROUNDING_MODE is used.

See Errors for the treatment of other non-integer or out of range dp or rm 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'
y.toExponential(1, 1)           // '4.5e+1'  (ROUND_DOWN)
x.toExponential(3)              // '4.560e+1'
y.toExponential(3)              // '4.560e+1'
toFixed.toFixed([dp [, rm]]) ⇒ string

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

Returns a string representing the value of this BigNumber in normal (fixed-point) notation rounded to dp decimal places using rounding mode rm.

If the value of this BigNumber in normal notation has fewer than dp fraction digits, 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, the return value will be unrounded and in normal notation. This is also unlike Number.prototype.toFixed, which returns the value to zero decimal places.
It is useful when fixed-point notation is required and the current EXPONENTIAL_AT setting causes toString to return exponential notation.
If rm is omitted or is null or undefined, ROUNDING_MODE is used.

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

x = 3.456
y = new BigNumber(x)
x.toFixed()                     // '3'
y.toFixed()                     // '3.456'
y.toFixed(0)                    // '3'
x.toFixed(2)                    // '3.46'
y.toFixed(2)                    // '3.46'
y.toFixed(2, 1)                 // '3.45'  (ROUND_DOWN)
x.toFixed(5)                    // '3.45600'
y.toFixed(5)                    // '3.45600'
toFormat.toFormat([dp [, rm]]) ⇒ string

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

Returns a string representing the value of this BigNumber in normal (fixed-point) notation rounded to dp decimal places using rounding mode rm, 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.
If rm is omitted or is null or undefined, ROUNDING_MODE is used.

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

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]) ⇒ [string, string]

max: 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.

If a maximum denominator, max, 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 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 valueOf.

x = new BigNumber('177.7e+457')
y = new BigNumber(235.4325)
z = new BigNumber('0.0098074')

// Serialize an array of three BigNumbers
str = JSON.stringify( [x, y, z] )
// "["1.777e+459","235.4325","0.0098074"]"

// Return an array of three BigNumbers
JSON.parse(str, function (key, val) {
    return key === '' ? val : new BigNumber(val)
})
toNumber.toNumber() ⇒ number

Returns the value of this BigNumber as a JavaScript number primitive.

Type coercion with, for example, the unary plus operator will also work, except that a BigNumber with the value minus zero will be converted 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 [, m]) ⇒ BigNumber

n: number: integer, -9007199254740991 to 9007199254740991 inclusive
m: number|string|BigNumber

Returns a BigNumber whose value is the value of this BigNumber raised to the power n, and optionally modulo a modulus m.

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

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 9007199254740991, it is interpreted as Infinity;
else if n is less than -9007199254740991, it is interpreted as -Infinity;
else if n is otherwise a number, it is truncated to an integer;
else it is interpreted as NaN.

As the number of digits of the result of the power operation can grow so large so quickly, e.g. 123.45610000 has over 50000 digits, the number of significant digits calculated is limited to the value of the POW_PRECISION setting (unless a modulus m is specified).

By default POW_PRECISION is set to 0. This means that an unlimited number of significant digits will be calculated, and that the method's performance will decrease dramatically for larger exponents.

Negative exponents will be calculated to the number of decimal places specified by DECIMAL_PLACES (but not to more than POW_PRECISION significant digits).

If m is specified and the value of m, n and this BigNumber are positive integers, then a fast modular exponentiation algorithm is used, otherwise if any of the values is not a positive integer the operation will simply be performed as x.toPower(n).modulo(m) with a POW_PRECISION of 0.

Math.pow(0.7, 2)                // 0.48999999999999994
x = new BigNumber(0.7)
x.toPower(2)                    // '0.49'
BigNumber(3).pow(-2)            // '0.11111111111111111111'
toPrecision.toPrecision([sd [, rm]]) ⇒ string

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

Returns a string representing the value of this BigNumber rounded to sd significant digits using rounding mode rm.

If sd is less than the number of digits necessary to represent the integer part of the value in normal (fixed-point) 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().
If rm is omitted or is null or undefined, ROUNDING_MODE is used.

See Errors for the treatment of other non-integer or out of range sd or rm 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'
y.toPrecision(2, 0)             // '4.6e+1'  (ROUND_UP)
y.toPrecision(2, 1)             // '4.5e+1'  (ROUND_DOWN)
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 or is null or undefined.

For bases above 10, values from 10 to 35 are represented by a-z (as with Number.prototype.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 configuration.

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'
truncated.trunc() ⇒ BigNumber

Returns a BigNumber whose value is the value of this BigNumber truncated to a whole number.

x = new BigNumber(123.456)
x.truncated()                   // '123'
y = new BigNumber(-12.3)
y.trunc()                       // '-12'
valueOf.valueOf() ⇒ string

As toString, but does not accept a base argument and includes the minus sign for negative zero.

x = new BigNumber('-0')
x.toString()                    // '0'
x.valueOf()                     // '-0'
y = new BigNumber('1.777e+457')
y.valueOf()                     // '1.777e+457'

Properties

The properties of a BigNumber instance:

Property Description Type Value
c coefficient* number[] Array of base 1e14 numbers
e exponent number Integer, -1000000000 to 1000000000 inclusive
s sign number -1 or 1
isBigNumber type identifier boolean true

*significand

The value of any of the c, e and s properties may also be null.

From v2.0.0 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 v1.x.x

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 necessarily 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

Checking if a value is a BigNumber instance:

x = new BigNumber(3)
x instanceof BigNumber     // true
x.isBigNumber              // true

BN = BigNumber.another();

y = new BN(3)
y instanceof BigNumber     // false
y.isBigNumber              // true

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
modulo
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.
another not an object Ignore.
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 an integer
or not [integer, integer]
Truncate to integer(s).
Ignore if not number(s).
RANGE cannot be zero Ignore.
RANGE out of range
or not [negative, positive]
Ignore.
ERRORS not a boolean
or binary digit
Ignore.
CRYPTO not a boolean
or binary digit
Ignore.
CRYPTO crypto unavailable Ignore.
MODULO_MODE not an integer Truncate to integer.
Ignore if not a number.
MODULO_MODE out of range Ignore.
POW_PRECISION not an integer Truncate to integer.
Ignore if not a number.
POW_PRECISION out of range Ignore.
FORMAT not an object Ignore.
precision argument not a boolean
or binary digit
Ignore.
round 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.
shift argument not an integer Truncate to integer.
Ignore if not a number.
argument out of range Substitute ±Infinity.
toExponential
toFixed
toFormat
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.
toFraction max denominator not an integer Truncate to integer.
Ignore if not a number.
max denominator out of range Ignore.
toDigits
toPrecision
precision not an integer Truncate to integer.
Ignore if not a number.
precision out of range Ignore.
rounding mode not an integer Truncate to integer.
Ignore if not a number.
rounding mode out of range Ignore.
toPower exponent not an integer Truncate to integer.
Substitute NaN if not a number.
exponent out of range Substitute ±Infinity.
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?

Some 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 have, 0.95 + 1.09995 = 2.04995, and if we add the two highest values we have, 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 may be 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 may be 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.