Floating value in javascript

Number

Number values represent floating-point numbers like 37 or -9.25 .

The Number constructor contains constants and methods for working with numbers. Values of other types can be converted to numbers using the Number() function.

Description

Numbers are most commonly expressed in literal forms like 255 or 3.14159 . The lexical grammar contains a more detailed reference.

255; // two-hundred and fifty-five 255.0; // same number 255 === 255.0; // true 255 === 0xff; // true (hexadecimal notation) 255 === 0b11111111; // true (binary notation) 255 === 0.255e3; // true (decimal exponential notation) 

A number literal like 37 in JavaScript code is a floating-point value, not an integer. There is no separate integer type in common everyday use. (JavaScript also has a BigInt type, but it’s not designed to replace Number for everyday uses. 37 is still a number, not a BigInt.)

When used as a function, Number(value) converts a string or other value to the Number type. If the value can’t be converted, it returns NaN .

Number("123"); // returns the number 123 Number("123") === 123; // true Number("unicorn"); // NaN Number(undefined); // NaN 

Number encoding

The JavaScript Number type is a double-precision 64-bit binary format IEEE 754 value, like double in Java or C#. This means it can represent fractional values, but there are some limits to the stored number’s magnitude and precision. Very briefly, an IEEE 754 double-precision number uses 64 bits to represent 3 parts:

• 1 bit for the sign (positive or negative)
• 11 bits for the exponent (-1022 to 1023)
• 52 bits for the mantissa (representing a number between 0 and 1)

The mantissa (also called significand) is the part of the number representing the actual value (significant digits). The exponent is the power of 2 that the mantissa should be multiplied by. Thinking about it as scientific notation:

Number = ( − 1 ) sign ⋅ ( 1 + mantissa ) ⋅ 2 exponent \text = ()^> \cdot (1 + \text) \cdot 2^>

The mantissa is stored with 52 bits, interpreted as digits after 1.… in a binary fractional number. Therefore, the mantissa’s precision is 2 -52 (obtainable via Number.EPSILON ), or about 15 to 17 decimal places; arithmetic above that level of precision is subject to rounding.

The largest value a number can hold is 2 1024 — 1 (with the exponent being 1023 and the mantissa being 0.1111… in base 2), which is obtainable via Number.MAX_VALUE . Values higher than that are replaced with the special number constant Infinity .

Integers can only be represented without loss of precision in the range -2 53 + 1 to 2 53 — 1, inclusive (obtainable via Number.MIN_SAFE_INTEGER and Number.MAX_SAFE_INTEGER ), because the mantissa can only hold 53 bits (including the leading 1).

More details on this are described in the ECMAScript standard.

Number coercion

Many built-in operations that expect numbers first coerce their arguments to numbers (which is largely why Number objects behave similarly to number primitives). The operation can be summarized as follows:

• Numbers are returned as-is.
• undefined turns into NaN .
• null turns into 0 .
• true turns into 1 ; false turns into 0 .
• Strings are converted by parsing them as if they contain a number literal. Parsing failure results in NaN . There are some minor differences compared to an actual number literal:
  • Leading and trailing whitespace/line terminators are ignored.
  • A leading 0 digit does not cause the number to become an octal literal (or get rejected in strict mode).
  • + and — are allowed at the start of the string to indicate its sign. (In actual code, they «look like» part of the literal, but are actually separate unary operators.) However, the sign can only appear once, and must not be followed by whitespace.
  • Infinity and -Infinity are recognized as literals. In actual code, they are global variables.
  • Empty or whitespace-only strings are converted to 0 .
  • Numeric separators are not allowed.

  There are two ways to achieve nearly the same effect in JavaScript.

  • Unary plus: +x does exactly the number coercion steps explained above to convert x .
  • The Number() function: Number(x) uses the same algorithm to convert x , except that BigInts don’t throw a TypeError , but return their number value, with possible loss of precision.

  Number.parseFloat() and Number.parseInt() are similar to Number() but only convert strings, and have slightly different parsing rules. For example, parseInt() doesn’t recognize the decimal point, and parseFloat() doesn’t recognize the 0x prefix.

  Integer conversion

  Some operations expect integers, most notably those that work with array/string indices, date/time components, and number radixes. After performing the number coercion steps above, the result is truncated to an integer (by discarding the fractional part). If the number is ±Infinity, it’s returned as-is. If the number is NaN or -0 , it’s returned as 0 . The result is therefore always an integer (which is not -0 ) or ±Infinity.

  Notably, when converted to integers, both undefined and null become 0 , because undefined is converted to NaN , which also becomes 0 .

  Fixed-width number conversion

  JavaScript has some lower-level functions that deal with the binary encoding of integer numbers, most notably bitwise operators and TypedArray objects. Bitwise operators always convert the operands to 32-bit integers. In these cases, after converting the value to a number, the number is then normalized to the given width by first truncating the fractional part and then taking the lowest bits in the integer’s two’s complement encoding.

  new Int32Array([1.1, 1.9, -1.1, -1.9]); // Int32Array(4) [ 1, 1, -1, -1 ] new Int8Array([257, -257]); // Int8Array(2) [ 1, -1 ] // 257 = 0001 0000 0001 // = 0000 0001 (mod 2^8) // = 1 // -257 = 1110 1111 1111 // = 1111 1111 (mod 2^8) // = -1 (as signed integer) new Uint8Array([257, -257]); // Uint8Array(2) [ 1, 255 ] // -257 = 1110 1111 1111 // = 1111 1111 (mod 2^8) // = 255 (as unsigned integer) 

  Constructor

  Creates a new Number value.

  When Number is called as a constructor (with new ), it creates a Number object, which is not a primitive. For example, typeof new Number(42) === «object» , and new Number(42) !== 42 (although new Number(42) == 42 ).

  Warning: You should rarely find yourself using Number as a constructor.

  Static properties

  The smallest interval between two representable numbers.

  The maximum safe integer in JavaScript (2 53 — 1).

  The largest positive representable number.

  The minimum safe integer in JavaScript (-(2 53 — 1)).

  The smallest positive representable number—that is, the positive number closest to zero (without actually being zero).

  Special «Not a Number» value.

  Special value representing negative infinity. Returned on overflow.

  Special value representing infinity. Returned on overflow.

  Static methods

  Determine whether the passed value is a finite number.

  Determine whether the passed value is an integer.

  Determine whether the passed value is NaN .

  Determine whether the passed value is a safe integer (number between -(2 53 — 1) and 2 53 — 1).

  This is the same as the global parseFloat() function.

  This is the same as the global parseInt() function.

  Instance properties

  These properties are defined on Number.prototype and shared by all Number instances.

  The constructor function that created the instance object. For Number instances, the initial value is the Number constructor.

  Instance methods

  Returns a string representing the number in exponential notation.

  Returns a string representing the number in fixed-point notation.

  Returns a string with a language sensitive representation of this number. Overrides the Object.prototype.toLocaleString() method.

  Returns a string representing the number to a specified precision in fixed-point or exponential notation.

  Returns a string representing the specified object in the specified radix («base»). Overrides the Object.prototype.toString() method.

  Returns the primitive value of the specified object. Overrides the Object.prototype.valueOf() method.

  Examples

  Using the Number object to assign values to numeric variables

  The following example uses the Number object’s properties to assign values to several numeric variables:

  const biggestNum = Number.MAX_VALUE; const smallestNum = Number.MIN_VALUE; const infiniteNum = Number.POSITIVE_INFINITY; const negInfiniteNum = Number.NEGATIVE_INFINITY; const notANum = Number.NaN; 

  Integer range for Number

  The following example shows the minimum and maximum integer values that can be represented as Number object.

  const biggestInt = Number.MAX_SAFE_INTEGER; // (2**53 - 1) => 9007199254740991 const smallestInt = Number.MIN_SAFE_INTEGER; // -(2**53 - 1) => -9007199254740991 

  When parsing data that has been serialized to JSON, integer values falling outside of this range can be expected to become corrupted when JSON parser coerces them to Number type.

  A possible workaround is to use String instead.

  Larger numbers can be represented using the BigInt type.

  Using Number() to convert a Date object

  The following example converts the Date object to a numerical value using Number as a function:

  const d = new Date("1995-12-17T03:24:00"); console.log(Number(d)); 

  Convert numeric strings and null to numbers

  Number("123"); // 123 Number("123") === 123; // true Number("12.3"); // 12.3 Number("12.00"); // 12 Number("123e-1"); // 12.3 Number(""); // 0 Number(null); // 0 Number("0x11"); // 17 Number("0b11"); // 3 Number("0o11"); // 9 Number("foo"); // NaN Number("100a"); // NaN Number("-Infinity"); // -Infinity 

  Specifications

  Browser compatibility

  BCD tables only load in the browser

  See also

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  This page was last modified on Jun 20, 2023 by MDN contributors.

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  JavaScript Numbers

  JavaScript has only one type of number. Numbers can be written with or without decimals.

  Example

  Extra large or extra small numbers can be written with scientific (exponent) notation:

  Example

  JavaScript Numbers are Always 64-bit Floating Point

  Unlike many other programming languages, JavaScript does not define different types of numbers, like integers, short, long, floating-point etc.

  JavaScript numbers are always stored as double precision floating point numbers, following the international IEEE 754 standard.

  This format stores numbers in 64 bits, where the number (the fraction) is stored in bits 0 to 51, the exponent in bits 52 to 62, and the sign in bit 63:

  Value (aka Fraction/Mantissa)	Exponent	Sign
  52 bits (0 — 51)	11 bits (52 — 62)	1 bit (63)

  Integer Precision

  Integers (numbers without a period or exponent notation) are accurate up to 15 digits.

  Example

  let x = 999999999999999; // x will be 999999999999999
  let y = 9999999999999999; // y will be 10000000000000000

  The maximum number of decimals is 17.

  Floating Precision

  Floating point arithmetic is not always 100% accurate:

  To solve the problem above, it helps to multiply and divide:

  Adding Numbers and Strings

  JavaScript uses the + operator for both addition and concatenation.

  Numbers are added. Strings are concatenated.

  If you add two numbers, the result will be a number:

  Example

  If you add two strings, the result will be a string concatenation:

  Example

  If you add a number and a string, the result will be a string concatenation:

  Example

  If you add a string and a number, the result will be a string concatenation:

  Example

  A common mistake is to expect this result to be 30:

  Example

  A common mistake is to expect this result to be 102030:

  Example

  The JavaScript interpreter works from left to right.

  First 10 + 20 is added because x and y are both numbers.

  Then 30 + «30» is concatenated because z is a string.

  Numeric Strings

  JavaScript strings can have numeric content:

  let x = 100; // x is a number

  let y = «100»; // y is a string

  JavaScript will try to convert strings to numbers in all numeric operations:

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