 # Math Constants in JavaScript

Math in JavaScript is made easier by the language’s support for a series of mathematical constants. If it’s been a while since you’ve dealt with more than multiplication and division, I’ve also included a brief explanation of each in this article.

These JavaScript constants are all properties of the `Math` object. Note that, as constants, the properties are UPPERCASE, rather than the camelCase of most JavaScript.

## Math.PI

Pi - popularly shortened to 3.14159 - is the circumference - that is, the outside perimeter - of a circle with diameter 1. For circles with a diameter greater or less than 1, we typically use the formula 2 × pi × r (The radius being exactly half the diameter, or the distance between the center of the circle and the perimeter).

Pi is irrational - it goes on forever and ever - and can never be expressed completely as a number, fraction, or decimal. Your browser can’t store an infinite number, so JavaScript shortens PI to 3.141592653589793, which is more than accurate enough for most purposes.

While it’s most common application is finding the circumference and area of circles, pi is also used in probability, statistics, engineering and science: as a universal constant, it shows up everywhere.

## Math.SQRT2

The square root of 2. Like pi, it is an irrational number; it is also the length of a diagonal across a square with sides of length 1. JavaScript approximates it to 1.4142135623730951. (Due to rounding errors, `Math.SQRT2 * Math.SQRT2` is not exactly 2).

## Math.SQRT1_2

The square root of 0.5, equivalent to 1 divided by the square root of 2. Again, an irrational number.

## Math.E

`e` is also known as Euler’s number, and is the base of natural logarithms. Again, it is an irrational number: JavaScript approximates it as `2.718281828459045`

e is the base rate of growth, a constant shared by every continually growing processes; compound interest, population growth, radioactive decay, and more. Examples of these processes are everywhere. Things grow at different rates over time, but they all share a commonality with `e`, which can be used as a “growth factor” in calculations. For example, a cell in a human embryo that divides and doubles continuously. In the console:

``````Math.pow(Math.E,1)
> 2.718281828459045

Math.pow(Math.E,2)
> 7.3890560989306495

Math.pow(Math.E,3)
> 20.085536923187664``````

## Natural Logarithms

The “natural” log is the inverse of `e^x`: rather than providing the amount of growth, the natural log (and its relations) provide the time needed to reach a certain level of growth. `Math.log(x)` provides the base `e` of a given number (`x`), but there are several built-in constants:

### Math.LN2

The natural logarithm of 2. In JavaScript, rounded to 0.6931471805599453

### Math.LN10

The natural logarithm of 10: rounded to 2.302585092994046

### Math.LOG2E

The base-2 logarithm of e. Rounded to 1.4426950408889634

### Math.LOG10E

The base-10 logarithm of e. Rounded to 0.4342944819032518

Photograph by Petra van der Ree, used under a Creative Commons license