JavaScript Numbers

JavaScript Numbers


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


Example

var x = 3.14;    // A number with decimals
var y = 3;       // A number without decimals

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

Example

var x = 123e5;    // 12300000
var y = 123e-5;   // 0.00123

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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)

Precision

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

Example

var x = 999999999999999;   // x will be 999999999999999
var y = 9999999999999999;  // y will be 10000000000000000
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The maximum number of decimals is 17, but floating point arithmetic is not always 100% accurate:

Example

var x = 0.2 + 0.1;         // x will be 0.30000000000000004

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

Example

var x = (0.2 * 10 + 0.1 * 10) / 10;       // x will be 0.3
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Adding Numbers and Strings

WARNING !!

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

var x = 10;
var y = 20;
var z = x + y;           // z will be 30 (a number)
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If you add two strings, the result will be a string concatenation:

Example

var x = "10";
var y = "20";
var z = x + y;           // z will be 1020 (a string)
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If you add a number and a string, the result will be a string concatenation:

Example

var x = 10;
var y = "20";
var z = x + y;           // z will be 1020 (a string)
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If you add a string and a number, the result will be a string concatenation:

Example

var x = "10";
var y = 20;
var z = x + y;           // z will be 1020 (a string)
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A common mistake is to expect this result to be 30:

Example

var x = 10;
var y = 20;
var z = "The result is: " + x + y;
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A common mistake is to expect this result to be 102030:

Example

var x = 10;
var y = 20;
var z = "30";
var result = x + y + z;
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The JavaScript compiler 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:

var x = 100;         // x is a number

var y = "100";       // y is a string

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

This will work:

var x = "100";
var y = "10";
var z = x / y;       // z will be 10

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This will also work:

var x = "100";
var y = "10";
var z = x * y;       // z will be 1000

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And this will work:

var x = "100";
var y = "10";
var z = x - y;       // z will be 90

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But this will not work:

var x = "100";
var y = "10";
var z = x + y;       // z will not be 110 (It will be 10010)

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In the last example JavaScript uses the + operator to concatenate the strings.


NaN - Not a Number

NaN is a JavaScript reserved word indicating that a number is not a legal number.

Trying to do arithmetic with a non-numeric string will result in NaN (Not a Number):

Example

var x = 100 / "Apple";  // x will be NaN (Not a Number)

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However, if the string contains a numeric value , the result will be a number:

Example

var x = 100 / "10";     // x will be 10
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You can use the global JavaScript function isNaN()) to find out if a value is a number:

Example

var x = 100 / "Apple";
isNaN(x);               // returns true because x is Not a Number
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Watch out for NaN. If you use NaN in a mathematical operation, the result will also be NaN:

Example

var x = NaN;
var y = 5;
var z = x + y;         // z will be NaN
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Or the result might be a concatenation:

Example

var x = NaN;
var y = "5";
var z = x + y;         // z will be NaN5
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NaN is a number: typeof NaN returns number:

Example

typeof NaN;            // returns "number"
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Infinity

Infinity (or -Infinity) is the value JavaScript will return if you calculate a number outside the largest possible number.

Example

var myNumber = 2;
while (myNumber != Infinity) {          // Execute until Infinity
  myNumber = myNumber * myNumber;
}
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Division by 0 (zero) also generates Infinity:

Example

var x =  2 / 0;          // x will be Infinity
var y = -2 / 0;          // y will be -Infinity
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Infinity is a number: typeof Infinity returns number.

Example

typeof Infinity;        // returns "number"
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Hexadecimal

JavaScript interprets numeric constants as hexadecimal if they are preceded by 0x.

Example

var x = 0xFF;           // x will be 255
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Never write a number with a leading zero (like 07).
Some JavaScript versions interpret numbers as octal if they are written with a leading zero.

By default, JavaScript displays numbers as base 10 decimals.

But you can use the toString() method to output numbers from base 2 to base 36.

Hexadecimal is base 16. Decimal is base 10. Octal is base 8. Binary is base 2.

Example

var myNumber = 32;
myNumber.toString(10);  // returns 32
myNumber.toString(32);  // returns 10
myNumber.toString(16);  // returns 20
myNumber.toString(8);   // returns 40
myNumber.toString(2);   // returns 100000
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Numbers Can be Objects

Normally JavaScript numbers are primitive values created from literals:

var x = 123;

But numbers can also be defined as objects with the keyword new:

var y = new Number(123);

Example

var x = 123;
var y = new Number(123);

// typeof x returns number
// typeof y returns object
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Do not create Number objects. It slows down execution speed.
The new keyword complicates the code. This can produce some unexpected results:

When using the == operator, equal numbers are equal:

Example

var x = 500;             
var y = new Number(500);

// (x == y) is true because x and y have equal values
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When using the === operator, equal numbers are not equal, because the === operator expects equality in both type and value.

Example

var x = 500;             
var y = new Number(500);

// (x === y) is false because x and y have different types
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Or even worse. Objects cannot be compared:

Example

var x = new Number(500);             
var y = new Number(500);

// (x == y) is false because objects cannot be compared
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Note the difference between (x==y) and (x===y).
Comparing two JavaScript objects will always return false.